DEGREE PROJECT IN MATHEMATICS, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2018

Optimizing the placement of cleanup systems for marine plastic debris: A multi-objective approach

ANISA NORDÉN

STINA KARLSSON

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

Optimizing the placement of cleanup systems for marine plastic debris: A multi-objective approach

ANISA NORDÉN

STINA KARLSSON

Degree Projects in Optimization and Systems Theory (30 ECTS credits) Degree Programme in Industrial Engineering and Management (120 credits) KTH Royal Institute of Technology year 2018 SupervisorS at DHI group Jonas Brandi Mortensen, Teo Zhi En Theophilus Supervisor at KTH: Per Enqvist Examiner at KTH: Per Enqvist

TRITA-SCI-GRU 2018:260 MAT-E 2018:58

Royal Institute of Technology School of Engineering Sciences KTH SCI SE-100 44 Stockholm, Sweden URL: www.kth.se/sci

Abstract

Marine plastic pollution is a pervasive problem and is estimated to only increase over the coming years. The realization of this has made several actors take action, of which one is the Danish Hydraulic Institute. Their simulation software MIKE allows for particle tracking in water environments, making it possible to forecast the movement of marine plastic debris. In addition to this, new advancements in marine plastic cleanup technology arise the following question; where are cleanup systems to be placed in order to remove as much plastic as possible? This study presents a mathematical model which, in combination with simulations of marine plastic debris movement, aims to find the optimal placement of cleanup systems alongside coastal areas. In addition to solely place the systems to maximize the amount of collected plastic particles, minimizing the plastic particles’ impact on sensitive areas is also considered. This is achieved by proposing a multi-objective optimization model. The obtained results present the optimal cleanup system placement in the pilot case of Jakarta Bay, Indonesia.

Optimera placeringen av uppsamlingsenheter f¨ormarint plastskr¨ap- en multi-objektiv approach

Sammanfattning

Marina plastf¨ororeningar¨arett stort problem som enbart uppskattas ¨oka under de kommande ˚aren.Detta har f˚attflera akt¨oreratt vidta ˚atg¨arder, varav en ¨arDanish Hydraulic Institute. Deras mjukvara MIKE till˚ater sp˚arningav partiklar i vattenmilj¨oer,vilket g¨ordet m¨ojligtatt f¨orutse hur marint plastskr¨apkommer r¨orasig. Dessutom har nya teknologiska framsteg inom upprensning av marin plast gett upphov till f¨oljandefr˚agest¨allning;vart ska man placera uppsamlingsenheter f¨oratt ta bort s˚amycket plast som m¨ojligt?Denna studie presenterar en matematisk modell som, i kombination med simuleringar av plastpartiklars r¨orelsei vatten, ¨amnarhitta den optimala placeringen av uppsamlingsenheter l¨angskustn¨atverk. Ut¨over att bara placera systemen f¨oratt maximera m¨angdenuppsamlad plast, ¨arminimeringen av plastens inverkan p˚ak¨ansligaomr˚adenocks˚ai fokus. Detta uppn˚asgenom att skapa en multi-objektiv optimeringsmodell. Resultaten presenterar de optimala placeringarna av uppsamlingsenheter f¨orJakarta Bay, Indonesien.

Acknowledgements

We, Stina Karlsson and Anisa Nord´en,would like to thank our supervisor Per Enqvist, associate professor in the optimization and systems theory group of the department of mathematics, KTH. Throughout the process, Enqvist has provided us with feedback and guidance regarding the construction of the optimization model, as well as the overall thesis work. We would also like to give a special thanks to Jonas Brandi Mortensen and Teo Zhi En Theophilus from The Danish Hydraulic Institute’s Singapore office, who have provided us with insight and support on the simulation of particles in water environments and assisted with the learning of their software MIKE for this purpose.

Contents

1 Introduction 1 1.1 Background ...... 1 1.2 Problem Formulation ...... 2 1.3 Research question ...... 2 1.4 Scope ...... 2

2 Current situation 3 2.1 Plastic pollution along coastal areas ...... 3 2.2 Plastic cleanup ...... 3 2.2.1 Ship-based solutions ...... 4 2.2.2 Drone-based solutions ...... 4 2.2.3 The Seabin ...... 5 2.2.4 The Ocean Cleanup ...... 5 2.3 Placement of cleanup systems ...... 5

3 Mathematical Theory 6 3.1 Optimizing locations ...... 6 3.2 Optimization formulation ...... 7 3.3 Integer Programming ...... 8

4 Method 9 4.1 Cleanup systems ...... 9 4.2 Simulation of plastic movement in waterways ...... 9 4.2.1 Particle tracking ...... 10 4.2.2 Particle characteristics ...... 10 4.2.3 Simulation output ...... 10

5 Mathematical Formulation 11 5.1 Assumptions ...... 12 5.2 Parameters and variables of the model ...... 12 5.3 Mathematical model ...... 13

6 Pilot case - Jakarta Bay, Indonesia 14 6.1 Area Description ...... 14 6.1.1 Bathymetry ...... 15 6.1.2 Hydrodynamic model ...... 15 6.2 Impact areas ...... 15 6.2.1 Coral reef areas ...... 16 6.2.2 Tourism areas ...... 16 6.3 Simulation characteristics ...... 17 6.3.1 Plastic sources and dispersion characteristics ...... 17 6.3.2 Plastic characteristics ...... 18 6.4 Data processing ...... 19 6.5 Cleanup station costs ...... 20 6.5.1 Placement cost ...... 20 6.5.2 Transportation cost ...... 20 6.5.3 Maintenance cost ...... 21 6.5.4 Cost summary ...... 21

7 Results and analysis 22 7.1 Simulation results ...... 22 7.2 Optimal placement of booms ...... 24 7.2.1 Maximizing the amount of collected particles ...... 24 7.2.2 Maximizing reduced impact ...... 26 7.2.3 Multi-objective approach ...... 27 7.3 Cost curve trade-off ...... 29 7.4 Result summary ...... 36

8 Discussion 37 8.1 Optimization model improvements ...... 37 8.2 Multi-objective optimization ...... 37 8.3 Simulation of plastic movement ...... 38 8.3.1 Simulation ...... 38 8.3.2 Time period and time steps ...... 38 8.3.3 Plastic drift characteristics ...... 39

9 Conclusion 40

10 References 41 List of Tables

1 The weights of different plastic size groups and their contribution to the composition of marine plastic debris...... 18 2 Characteristics of used vessel ...... 21 3 The associated cost parameters for the mathematical model . . . . . 21

List of Figures

1 Element mesh for Jakarta Bay ...... 15 2 Coral reef areas in Jakarta Bay ...... 16 3 Tourism areas in Jakarta Bay ...... 17 4 Plastic pollution sources ...... 18 5 Placement sites for the Jakarta Bay area ...... 19 6 Three hour simulation ...... 22 7 Six hour simulation ...... 22 8 Nine hour simulation ...... 22 9 Twelve hour simulation ...... 22 10 Fifteen hour simulation ...... 23 11 Eighteen hour simulation ...... 23 12 Twenty-one hour simulation ...... 23 13 Twenty-four hour simulation ...... 23 14 Plastic particle tracks at the end of the simulation ...... 23 15 w=0: Optimal placement of one boom ...... 24 16 w=0: Optimal placement of three booms ...... 25 17 w=0: Optimal placement of five booms ...... 25 18 w=100: Optimal placement of one boom ...... 26 19 w=100: Optimal placement of three booms ...... 27 20 w=100: Optimal placement of five booms ...... 27 21 w=10: Optimal placement of one boom ...... 28 22 w=10: Optimal placement of three booms ...... 29 23 w=10: Optimal placement of five booms ...... 29 24 Increase in objective value from the placement of an additional boom 30 25 Increase in amount of collected particles from the placement of an additional boom ...... 31 26 Increase in reduced impact from the placement of an additional boom 32 27 Increase in objective value with increased budget ...... 32 28 Increase in amount of collected particles with increased budget . . . . 33 29 Percentage increase in objective value from an additional boom . . . 34 30 Percentage increase in collected particles with an additional boom . . 34 31 Increase in total reduced impact with increased budget ...... 35 32 Percentage increase in total reduced impact with additional boom . . 35

1 INTRODUCTION

1 Introduction

1.1 Background Marine plastic debris is a pervasive problem as it pollutes the world’s oceans and waterways. It is difficult to obtain reliable estimates on how much plastic enters the oceans on a yearly basis. However, scientists and researchers at the University of Santa Barbara have estimated that 4.8-12.7 million metric tons of plastic waste from coastal countries entered the oceans in 2010 (Jambeck et al, 2015). Similarly, there have been attempts to estimate the economic cost of marine plastic debris. For the 21 economies of the Asia-Pacific region, it is estimated that the damage to marine industries by marine plastic pollution amounts to USD 1.26 billion each year (Camp- bell et al, 2011). In addition, the United Nations assessed that marine plastic debris has a financial cost of USD 13 billion each year, as a consequence of its damage on tourism, marine life, businesses and fishing industries (UNEP, 2016).

Marine plastic debris enters the oceans and waterways through human activities. The United Nations Joint Group of Experts on the Scientific Aspects of Marine Pollution found that approximately 80 percent of marine plastic debris originates from land- based activities (GESAMP, 1991). Nets, food wrappers, bottles and other types of plastic litter are carried into the ocean along with rainwater. In addition, waste and contents spilled by ships at sea contribute to an increased volume of plastic litter. Plastics are durable, buoyant and have a degradation time of hundreds or thousand years. These characteristics cause them to accumulate in oceans and travel long dis- tances via currents (Sheavly, Register, 2007).

Implications of marine plastic debris range from human health and safety, economic impacts, wildlife entanglement, ingestion to habitat destruction (Derraik, 2002). The ingestion of plastic by marine life can cause internal or external injuries as well as alterations to inner biochemical processes. Entanglement of larger marine animals in nets and lines can limit animal mobility and potentially cause mortality. Entangle- ment and injuries from marine plastic debris also proposes a threat to beach visitors, snorkelers and divers. Plastic debris moved by currents and tides can break and destroy aquatic habitats, and also damage shorelines and living coral reefs. Further- more, the pollution of marine plastic debris has a financial damage as it affects marine transportation, tourism and recreational activities (Sheavly, Register, 2007).

In order to solve the problem with marine plastic debris, society first has to change its attitude towards the use of plastic and the way in which it is disposed. This requires a collective effort in form of educational awareness, implemented policies and the synthesis of substitutional and biodegradable materials which carry the same function. Although there are advancements within these areas, the process of change

1 of 44 1.2 Problem Formulation 1 INTRODUCTION will take several years. As current marine plastic debris keeps accumulating, there is a great need in finding solutions to remove existing plastic from the oceans. One of these solutions is the use of cleanup systems. Cleanup systems is a new and ongoing developing technology for the capture of marine plastic debris. In comparison to conventional methods, such as using active entrapment with vessels and nets, cleanup systems are passively stationed. This is a relatively new area of study. However, due to their positive implications, several actors have started to investigate how cleanup systems would help clean the oceans and where they should be employed.

1.2 Problem Formulation Previous identification of optimal cleanup system locations have primarily been done through visual inspection, which does not necessarily ensure optimality. This pro- poses the possibility of further investigation of a more systematic and analytical way of finding the placement of cleanup systems which can minimize the amount and im- pact of marine plastic debris. The existing research that has been done have also been focusing on identifying the optimal locations out in the ocean. By instead capturing plastic closer to its pollution source, there is a greater opportunity of preventing the spread of marine plastic debris before it does more harm (Sherman and Sebille, 2016).

When there are several plastic pollution dispersion sources, it can however be of difficulty to determine where to place cleanup systems for optimal effect. Due to scarcity of resources and typically limited budgets associated with cleanup efforts, the ability to find the optimal placement is of high relevance. It might simply not be economically feasible to place the systems directly at pollution sources. Thus, this study aims to continue the initiated research by creating a mathematical model to determine the optimal placement of cleanup systems at coastal areas. Its results could lay a basis for decision making processes regarding plastic cleanup efforts and the implementation of cleanup systems for best effect.

1.3 Research question Where is the optimal placement of cleanup systems given the objective to minimize marine plastic debris and its impact given certain constraints?

1.4 Scope The aim of the study is to determine the optimal placement of cleanup systems along- side coastal areas. Hence, the study does not investigate the effect of using active plastic entrapment, such as the use of vessels, but instead that of passive plastic en- trapment. Passive cleanup methods are methods, or systems, that require less human interference and can thus save both operational expenses and time (TOC Feasibility

2 of 44 2 CURRENT SITUATION

Study, 2016). This follows the assumption that it will be possible to employ cleanup systems closer to the coastline. It can be of importance to bare in mind that this cleanup system attribute will not affect the mathematical model per say, but rather the implementability of cleanup systems closer to coasts.

In addition, the mathematical model will use the results from a plastic tracking simulation as input. The current plastic simulation model is of simple kind and does not account for several plastic drift characteristics such as buoyancy and densities. Since the focus of the study lays on creating a mathematical model to determine the optimal placement of cleanup systems, the development of the plastic tracking simulation does not lay within the study’s main focus area.

2 Current situation

The following section describes the current situation of marine plastic pollution along coastal areas and the existing cleanup methods, as well as the developing technology. Current research regarding the determination of the placement of cleanup systems is presented.

2.1 Plastic pollution along coastal areas The majority of the world’s coastal areas have been reported to be damaged from some sort of pollution, plastic being one of them. Plastics are disposed in huge volumes into a variety of waterways such as rivers, lakes and canals. With this high volume of dumped waste comes damage to both marine ecosystems and commercial activities (Islam and Tanaka, 2004). A study conducted by the United Nations estimated that more than 65% of large cities are located along a coastal area. This means that more than 60% of the global population live within 100 km of a coastal area (UNEP, 1991). Two thirds of the global plastic pollution comes from the 20 most polluting rivers, the Yangtze River in China and the Ganges river in India being the major ones. Indonesia is also identified as a major contributor to the plastic pollution from the Asian continent with an estimated 200 000 tonnes of plastic entering the ocean from Indonesian rivers and streams every year. This constitutes to approximately 14.2% of the total global plastic pollution (Lebreton et al, 2017). Since the largest majority of marine plastic pollution comes from coastal areas, the importance of a better management system and cleanup for these areas is being stressed by various actors.

2.2 Plastic cleanup The concept of using passive cleanup systems, which uses natural ocean forces to remove marine plastic debris, is somewhat new and limited research has been done

3 of 44 2.2 Plastic cleanup 2 CURRENT SITUATION in this area. However, due to an increasing awareness of marine plastic debris pol- lution and its impact on both marine life and human health, the concept of passive cleanup systems is starting to draw more attention. Some of the cleanup solutions are presented below.

2.2.1 Ship-based solutions The most conservative approach to collect marine plastic debris is by the use of ship vessels (TOC Feasibility Study, 2014). Ship-based solutions tend to use already exist- ing technology, where either industrial or sailing vessels are modified to be equipped with collecting nets or alternative extraction equipments. An example of this is the for non-profit organization Ocean Voyages Institute. With their cleanup initiative Project Kasei, they investigate which collecting methods to be use for collecting var- ious types of plastics (Project Kasei, 2017). In general, the ship-based solutions involves sailing through heavily dense plastic areas and attach fine mesh nets to the ships. An advantage of this type of cleanup is that the majority of the technology and equipment is already developed and available. However, due to the problem of scale, this cleanup solution requires a vast amount of vessels and thousands of years in order to remove all marine plastic debris from the ocean (TOC Feasibility Study, 2014). In addition to this, underwater noise from ships is recognized as a major pollutant to marine ecosystems as it for instance exposes ocean mammals to anthropogenic sonar (Williams et al, 2015).

2.2.2 Drone-based solutions With advancements in technology, companies have started to investigate alterna- tive collecting methods to the traditional ship-based solutions. Projects such as the Oceanic Cleaning System by Erik Borg, Project Floating Horizon by Robert Schnei- der and Project Protei by Ceasar Harda (TOC, 2014), investigate the concept of using automated drones in the collection of marine plastic debris. The idea behind the drone-based solution is to use a large number of small floating buoyant vehicles to collect plastic and when full, these are emptied by a maintenance vessel.

An advantage of using drone solutions is their mobility. Due to the drones’ deploy- ment flexibility they can be moved to marine plastic concentrated areas. Their mobil- ity possibilities make them advantageous in regard to traditional collection methods. However, the drones have to travel at high speed to withstand strong currents, requir- ing a high amount of energy, and thus costs. Marine plastic debris tend to concentrate in large areas. This, in combination with the drones’ limited capacity, means that they would have to be emptied frequently and, similarly to vessel-based concepts, drones are thus subjected to the problem of scale (TOC Feasibility Study, 2016).

4 of 44 2.3 Placement of cleanup systems 2 CURRENT SITUATION

2.2.3 The Seabin The Seabin is a floating device that catches floating marine debris. It is designed for the purpose of being deployed in calm water environments such as those of marinas and ports. It has a daily catching possibility of 1.5kg. Due to its design features the Seabin is not suitable to be placed at coastal areas, mainly because of its capture amount but also due to the rougher weather conditions (The Seabin Project, 2018).

2.2.4 The Ocean Cleanup The Ocean Cleanup (TOC) is a non-profit organization that, with the help of a pas- sive drifting boom technology, aim to clean up half of the Great Garbage Patch in five years time. The Great Pacific Garbage Patch is often recalled as a ”trash vortex” zone where, due to large offshore current systems also called gyres, marine plastic accumulates (The Ocean Cleanup, 2018). The passive floating structure consists of two passive booms made from high density polyethylene, making the booms flexible and able to follow waves and currents whilst also maintaining its shape. The booms range from 1-2 km in length and together they take on an u-shaped form to collect and concentrate plastic. The boom is weighted down by an anchor. Once the boom is full, the plastic is extracted and loaded into a support vessel for transportation back to shore (The Ocean Cleanup, 2017).

The technology’s size allows the system to clean up a large amount of accumulated plastic. However, it is argued that removing plastic closer to polluting sources at coastal networks would minimize the plastics’ harmful impact and also be more cost effective due to shorter transportation distances (Stokstad, 2017). Although TOC’s technology is not yet suited or designed for coastal areas, they are considering to in the future introduce spin-off systems for coastal areas. Thus these systems would remove marine plastic debris before it reaches the ocean (TOC Frequently asked questions, 2017).

2.3 Placement of cleanup systems No existing studies are found which present an optimization model to determine the optimal placement of these. Further research has to be done as to guarantee this. In their study, Sherman and Sebille (2016) used a model of ocean plastics movement based on satellite-tracked observations to analyze the optimal marine micro plastic removal locations. However, the result was obtained by brute-force searching, going through possible removal locations, thus implying a time-consuming and computa- tionally expensive method. Creating a mathematical model to assess the optimal locations would mean a more effective approach towards solving the problem, as well as the possibility of including economical and capability constraints. Whilst the method mentioned might give a good indication of the optimal placements they do

5 of 44 3 MATHEMATICAL THEORY not guarantee optimality. In addition, this technique does not take different con- straints into account and thus it might not be in accordance with, and represent, real life placement possibilities. Although little research have been done on the optimal placement of cleanup systems, its concept can be compared to that of optimizing the allocation of equipment in response to oil spills, where oil spill particles can be comparable to those of plastics. This area has been widely studied and its existing literature will be explained further in the following section.

3 Mathematical Theory

As there is limited research on optimizing the placement of cleanup systems for the collection of plastic particles, the mathematical theory presented in this section is drawn from similar optimization problems. In addition, general optimization theory is presented.

3.1 Optimizing locations There are several studies that look at the optimization of locations. Authors Dai et al (1996) constructed a mathematical model and algorithm for finding the optimal distribution substation locations and sizes. Similarly, authors Iltuarte-Villarreal and Espiritu (2011) present an model and a viral based algorithm to optimize the place- ment of wind turbines.

The placement of cleanup systems can be comparable to oil spill problems, which also use simulations as input to optimization models. In their paper, authors Grubesic, Weib and Nelson (2017) look at how to optimize oil spill cleanup efforts, by developing a mathematical model to optimize the allocation of response crews and equipment for cleaning up an offshore spill. Similarly, authors Zhong and You (2011) create an optimization model to plan the allocation of oil spill responses with the objective to minimize response time and total costs. A mixed-integer linear program was used, solved by an epsilon constraint method.

One difference is that Grubesic et al. (2017) manually remove oil from the simu- lation every day, based on the optimization results. Similarily, authors Zhong and You (2011) use a multiperiod formulation implying that the decision of which optimal sites to send vessels and cleanup equipment to is decided on a hourly basis. Since the cleanup systems in this study are of passive character, and are meant to be deployed over a longer period of time, the location of these will be fixed. Hence, an iterative process to determine their locations is not to be used.

Another major difference is that existing literature on oil spill cleanup optimization do not track, or account for, individual oil spill droplets impact on marine ecosystems

6 of 44 3.2 Optimization formulation 3 MATHEMATICAL THEORY in the objective function. In the study presented by Sherman and Sebille (2016), the authors determine the placement of cleanup systems whilst aiming to minimize the overlap of ocean surface micro plastics and phytoplankton growth, stressing how plas- tic can affect marine life. The authors’ consideration for sensitive areas, in this case phytoplankton growth, served as inspiration for the construction of the mathematical model in this study, namely minimizing the plastics’ impact, and hence overlap, with sensitive areas. However, the major difference between this study and the one of Sherman and Sebille (2016), is that the authors could not determine how much the plastic-phytoplankton overlap changed after plastic was removed. This meant that they simply placed the cleanup systems at areas with maximum overlap, as they could not measure, and thus not account for, the change in overlap due to cleanup system placement. As this thesis aims to use a particle tracking simulation, this gives the possibility to track each individual plastic particle’s impact on sensitive areas, which in turn can be used to directly assess the effect of cleanup systems placement. The construction and choice of sensitive areas will be described and explained further in the report.

Although the differences between oil spill and plastic cleanup, similarities exist re- garding the characteristics of the cleanup methods and the equipment used, serving as foundation for the construction of our mathematical model. This study takes in- spiration from oil spill optimization models whilst determining the optimal placement of cleanup systems with different objectives in mind.

3.2 Optimization formulation Optimization is a branch of the area of applied mathematics. Mathematical methods and models are used in order to find an optimal solution to different decision making processes and objectives, including minimizing costs and waste or maximizing rev- enues. Due to its broad application possibility, an optimization model is seen as a practical tool for decision making. (Griva, Nash and Sofer, 2009).

A prerequisite for using optimization models is that the objective and constraints can be expressed in a quantitative form of mathematical functions and relations. The problem formulation includes decision variables. To optimize is to decide which val- ues of the decision variables contributes to the best result of the desired target. The target is specified as an objective function which depends on the variables. It can be expressed as a minimizing or maximizing function depending on the target. An optimization model also includes constraints which put limits on the variables. A general formulation of an optimization problem is given as the following: ( minimize f(x) (P ) s.t. x ∈ X

7 of 44 3.3 Integer Programming 3 MATHEMATICAL THEORY

T where f(x) is the objective function depending on the variables x = (x1, ..., xn) . The set X defines the allowed solutions to the problem. X is usually included in the constraints and (P) is then expressed in the following alternative form: ( minimize f(x) (P ) s.t. gi(x) ≤ bi, i = 1, ..., m.

where gi(x) are functions depending on x, bi are given coefficients. The above problem (P) is expressed as a minimization problem but could also be of a maximization type, depending on the specified targets of the optimization problem. The construction of f(x) and gi(x) and the given assumptions regarding variables x create different problem classes. Optimization theory can be divided into the following five sub areas (Lundgren, R¨onnkvist & V¨arbrand, 2003):

1. Linear programming

2. Nonlinear programming

3. Integer programming

4. Dynamic programming

5. Combinatorial programming

Integer linear programming is used for the optimization problem to determine the op- timal placement of cleanup systems. The theory of integer programming is introduced in the following section.

3.3 Integer Programming Integer Programming is a mathematical technique aiming to find the best solution for an optimization problem with limited resources. An application of integer pro- gramming involves answering questions to a number of yes-or-no decisions, where yes or no is the only possible choices. Here, the decision variables represent decisions and are restricted by solely taking on two integer values such as 0 for the choice no, and 1 for the choice yes. A yes-or-no decision can be presented by, for instance, xj where ( 1 if yes xj = 0 if no

The variable xj is often referred to as a binary variable (Lieberman and Heiller, 2015). The application of integer programming in the construction of the optimization model is further presented under the mathematical formulation of the problem.

8 of 44 4 METHOD

4 Method

In order to investigate the optimal placement of cleanup systems, a simulation of the movement of marine plastic debris combined with a mathematical optimization model is used. The optimization model is of a multi-objective type with the aim to both maximize the number of collected plastic particles, as well as minimizing their impact on surrounding sensitive areas. The optimization model is constructed to be of generalizable type and can be applied to any coastal area, with different simulation results and constraint characteristics. The ability to include impact in the optimization formulation arises from the possibility of individual plastic particle tracking. Hence, it is possible to keep track of each individual’s total impact.

For test and validation reasons, the model is applied to the river and coastal net- work Jakarta Bay, Indonesia. The data obtained from the simulation is saved as an xml file which consists of all the desired outputs specified beforehand. Matlab is used for variable and set creation of the input data, and the optimization model is then solved by Matlab’s intlinprog solver using branch-and-bound as default algorithm.

4.1 Cleanup systems The cleanup systems used in the mathematical optimization model will be based on the same boom technology as that presented by The Ocean Cleanup (TOC). The choice of using TOC’s booms for the mathematical model is due to the booms being of passive character and that they have a larger capture capacity than the previ- ously mentioned Seabin. In addition to this, cleanup by drones is a not as developed technology and will thus be of greater complexity to use in the mathematical model. However, as TOC’s booms are designed and manufactured to be placed out at the Great Garbage Patch, its current capacity and functionality is designed for that spe- cific purpose. As the objective of this study is to determine where along coastal areas it is most optimal to place cleanup systems, assumptions and modifications are made regarding TOC’s cleanup systems. The parameters for these are further presented under the mathematical model.

4.2 Simulation of plastic movement in waterways The Danish Hydraulic Institute (DHI) is one actor aiming to solve the world’s most pressing issues related to water environments, including that of marine plastic debris pollution. With the help of their software MIKE, DHI works with simulations in water environments, providing research and consultancy services in areas such as Coast and Marine, Urban Water and Climate Change. The software uses agent-based modeling coupled with hydrodynamic models to simulate the drift characteristics of marine plastic debris. Agent-based modeling simulates how individual organisms and

9 of 44 4.2 Simulation of plastic movement in waterways 4 METHOD particles interact and move in relation to their surrounding environment. An example of the MIKE software technology is MIKE ZERO, which is a modeling tool for coastal and sea environments. For the purpose of the thesis, MIKE ZERO is used to simulate the movement of plastic particles in waterways and the software’s output serves as an input to the mathematical model.

4.2.1 Particle tracking MIKE ZERO includes a particle tracking model, which enables the transportation and fate of particles discharged from lakes, estuaries, coastal areas or seas. The particle tracking module is a Lagrangian solver of dispersion equations, and is complemented with DHI’s Eco Lab module - a numerical simulation software customized for aquatic ecosystem models. The Eco Lab module allows the definition of different plastic characteristic and functions as a module in the MIKE simulation software and is coupled to DHI’s hydrodynamic flow models. Hydrodynamic modeling is used to represent the motion of fluid in sea and river dynamics and to investigate the fates and locations of plastic particles (DHI, 2017).

4.2.2 Particle characteristics As for now, DHI doesn’t have an extensive model for marine plastic, but simply a general debris model that is based on the passive tracking of objects. The current model is thus not accounting for the particular drift characteristics of different types of plastic, neither is characteristics such as degradation or leaking of toxic compounds included. As the focus of the study lays on creating an optimization model which can be applied to different locations with various input values, creating an extensive plastic particle tracking simulation model that better capture the real movement of plastic debris, is however not a priority. This since a more precise simulation wouldn’t directly affect the reliability of the mathematical model formulation, but only it’s op- timization results.

For the purpose of this thesis and the optimization model, the plastic particles vary in size and depth. This since the plastic particles have to fulfill certain criteria in order to be collected by a cleanup system. As the considered cleanup system is inspired by The Oceans Cleanup’s boom technology, its functionalities are to be accounted for in the model. However, as the model aims to be of a generalizable type, changes in these characteristics should be easily accounted for.

4.2.3 Simulation output The simulation output comes in the form of a dsfu file and xml file. The dfsu file is a visual map representation of the simulation results from MIKE, either in 2D or 3D. For the purpose of this thesis, a 2D representation is used. Besides the visual

10 of 44 5 MATHEMATICAL FORMULATION representation, the software also provides a xml file consisting of data from the sim- ulated particles and the particle tracks. The user can in the MIKE software program specify what characteristics of the particles are to be outputted. This can for ex- ample be particle numbers and longitudinal and latitudinal coordinates. Hence, the xml output consists of plastic particle characteristics in different grids or areas, at certain times. For this study, the used simulation has been constructed to output the following information:

• Particle number

• Longitude and latitude coordinates

• Depth

• Size

• Impact number

Each particle number, which represents a plastic particle, has for each time step an associated coordinate pair, depth and impact number. For the purpose of the thesis, an impact count is created where its number represents the amount of damage that the plastic particle has exerted on their surroundings so far. As the particles move across an impact area, its impact number will increase by the value which is assigned to the area. The particles will thus ”read” when they come in contact with, or travel over, high sensitive areas which makes it possible to track each particle’s potential harmful impact.

5 Mathematical Formulation

The mathematical model will be formulated as a multi-objective integer linear pro- gramming problem, with the aim to maximize the amount of collected plastic particles and minimize their potential impact. To fulfill the purpose of the study, the model is created as to be generalizable, thus applicable for different capture constraints, locations and plastic characteristics.

As described in the method section, the MIKE output consists of a series of plastic particles which all have an unique identifier throughout the simulation. The identifier makes it possible to assign each of the particles a binary variable reflecting if it has been collected by a boom or not, which can then be used in the optimization for- mulation to decide which particles are to be collected. The model will consider each particle’s characteristics at every time step, and decide where to place the booms most optimally.

11 of 44 5.1 Assumptions 5 MATHEMATICAL FORMULATION

The booms will be represented by a set of sites, symbolizing possible locations for the booms to be placed. The sites will all have their respective coverage area and are constructed by considering the current geographical area. This means that unde- sirable placement locations, for instance where ships passes, won’t be considered as possible placement sites in order to increase the applicability of the model.

5.1 Assumptions To begin with, it is assumed that all plastic particles of a certain size and depth that pass through a site with a placed boom is collected, and that it cannot escape once captured. Since TOC’s boom is in the shape of a u, plastic particles have to travel in an angle allowing their capture. The current model does not take boom angle and particle direction into account, why it’s assumed that the boom is placed perpendicular to the particles direction path.

5.2 Parameters and variables of the model The table with all sets, parameters and variables used in the optimization model is shown below.

Sets Jp set of all sites j that particle p passes through P set of all particles p

Parameters Ip impact of particle p if not collected ijp impact of particle p when at site j Imax maximum impact among all particles djp depth of particle p when at site j D boom depth sp size of particle p S minimum size of a particle for it to be collected kj cost of placing a boom at site j q capital budget w impact weight

Decision variables ujp binary variable describing if particle p is collected at site j cj binary variable describing if a boom is placed at site j

12 of 44 5.3 Mathematical model 5 MATHEMATICAL FORMULATION

5.3 Mathematical model The objective function and constraints may now be defined. Firstly, the objective is to maximize the number of collected plastic particles, as well as their reduced impact: X X ujp(1 + (Ip − ijp) × w/Imax) (5.1)

p∈P j∈Jp The reduced impact is expressed by taking the difference between the impact of par- ticle p if it is not collected, Ip, and the impact of particle p if it is collected at site j, ijp. Hence, Ip − ijp corresponds to the reduced impact of a particle, given if it gets collected by a boom or not. The reduced impact is normalized by a factor Imax, the maximum impact of all particles, to get a comparable order of magnitude between collected particles and their impact count. The normalized impact is then multiplied by a factor w to be able to decide the relative weight of the impact, compared to the collection count.

The boom can only capture plastic particles with certain characteristics. This is achieved with the following constraints:

ujp(djp − D) ≤ 0, j ∈ Jp, p ∈ P (5.2) which makes sure that the plastic particles are not deeper down under the surface than the boom screen and:

ujp(S − sp) ≤ 0, j ∈ Jp, p ∈ P (5.3) which specifies that only plastic particles of a certain size can be collected by the booms.

Moreover, a plastic particle can only be collected at site j if there is a boom placed there. This is achieved with the constraint:

ujp ≤ cj, j ∈ Jp, p ∈ P (5.4) A plastic particle can also only be collected by a boom once: X ujp ≤ 1, p ∈ P (5.5)

j∈Jp Finally, a cost constraint is needed to limit the amount of placed booms. This is achieved by constraint: X cjkj ≤ q (5.6) j∈J

where q is the capital budget and kj is the cost of placing a boom at site j.

13 of 44 6 PILOT CASE - JAKARTA BAY, INDONESIA

Finally, the integer linear program can be defined as X X maximize ujp(1 + (Ip − ijp) × w/Imax)

p∈P j∈Jp

subject to ujp(djp − D) ≤ 0, j ∈ Jp, p ∈ P (1)

ujp(S − sp) ≤ 0, j ∈ Jp, p ∈ P (2)

ujp ≤ cj, j ∈ Jp, p ∈ P (3) X ujp ≤ 1, p ∈ P (4)

j∈Jp X cjkj ≤ q (5) j∈J

ujp ∈ {0, 1}, cj ∈ {0, 1}

It is important to note that, even if the model is formulated for the purpose of optimizing the placement of booms, its general features makes it easily adjusted as to be applicable to other cleanup systems that are of passive character. Although the optimization program uses a multi-objective function, it can easily be formulated to suit a single-objective function, whether it being the objective to only maximize the amount of collected particles or minimizing its impact, by choosing a suitable value of w. This depends on the intention and purpose of the user.

6 Pilot case - Jakarta Bay, Indonesia

The optimization model is applied to Jakarta Bay, Indonesia, for validation and test purposes. Jakarta Bay is situated along the north coast of the Indonesian is- land Java and is connected to a river system of 13 rivers (Damar, 2003), namely the Angke, Bekasi, Cakung, Cidurian, Ciliwung, Cikarang, Cimancuri, Ciranjang, Cisadane, Citarum, Karawang Krukut and Sunter river (Arifin, 2004). Plastics from both domestic and industrial use in the city of Jakarta are directly disposed into Jakarta Bay, causing a growing concern for the effects of marine litter (Willoughby, 1986).

6.1 Area Description The area description of Jakarta Bay is presented in meter units. The map was created by the MIKE Mesh generator and provided by the DHI Singapore office. The MIKE mesh generator provides a triangular mesh over the considered area, where the mesh resolution, i.e. triangular sizes, adjust accordingly to its adjacent areas (Mike Zero Mesh Generator training guide, 2012).

14 of 44 6.2 Impact areas 6 PILOT CASE - JAKARTA BAY, INDONESIA

6.1.1 Bathymetry Bathymetry data is often used in simulation and model inputs. The National Ocean Service explains bathymetry as the description of physical forms, such as depths and shapes, of surfaces below water (National Ocean Service, 2015). The bathymetry will affect the hydrodynamic forces below surface and is thus combined with the land area mesh and boundaries. The figure below shows the triangular mesh and how sea level depth varies over the considered study area.

Figure 1: Element mesh for Jakarta Bay

6.1.2 Hydrodynamic model The hydrodynamic model over Jakarta Bay is based on an existing model by DHI, where water level measurements and data were collected. DHI’s MIKE 21 Spectral wave model was also used to create a wind-wave model which simulates various char- acteristics of wind-generated waves including their growth, decay and transformation (Appendix-final-HD Calibration, 2017). The model further accounts for currents and river dispersions into Jakarta Bay.

6.2 Impact areas An impact number is generated for each plastic particle during the simulation. For the pilot case Jakarta Bay, a plastic particle gets an impact value of 1 added to its impact count when passing through an impact area. The impact areas may vary, but

15 of 44 6.2 Impact areas 6 PILOT CASE - JAKARTA BAY, INDONESIA

for the Jakarta Bay pilot case study two different types of impact area are considered, namely, coral reef and tourism areas. In order to account for these areas, maps for each of them were created and combined with the map file. The two impact counts are equally weighted and prioritized. However, due to the generalizability of the impact count, it is possible to weight and prioritize impact areas differently if desirable.

6.2.1 Coral reef areas In their paper Plastic waste associated with disease on coral reefs, authors Lamb et al. (2018) describe that the likelihood of disease on corals increases from 4% to 89% when in contact with plastic. With this research in mind, and the current global threat to coral reefs, they are considered as an impact area. Global visual data from ReefBase was used to determine the occurrence and locations of coral reefs in the Jakarta Bay area (ReefBase, 2018). In the below map, the red and green concentrations represent the presence of coral reef areas.

Figure 2: Coral reef areas in Jakarta Bay

6.2.2 Tourism areas Marine plastic pollution also impacts recreational areas such as tourism sites and can minimize tourism attraction. Thus, tourism areas are also considered as an impact area (UNEP, 2016). The below figure shows a tourism map over Jakarta Bay. Since the availability of exact data over tourism sites was limited, Google Maps was used to localize hotel locations and thus give an indicator of the presence of tourism areas.

16 of 44 6.3 Simulation characteristics 6 PILOT CASE - JAKARTA BAY, INDONESIA

Figure 3: Tourism areas in Jakarta Bay

6.3 Simulation characteristics The movement of plastic particles along Jakarta Bay is simulated in order to get input data for the optimization model. The following section explains the simulation characteristics for the pilot case, as well as defined characteristics of released particles.

6.3.1 Plastic sources and dispersion characteristics In total, seven sources were placed outside discharge rivers in Jakarta Bay. The lo- cations of these were chosen to get a spread of the released particles in the bay and the sources were placed outside river discharge sources from the hydrodynamic model. Each source was placed at surface level and released a plastic particle once every hour. The hourly release rate of plastic particles is flexible and can be adjusted according to the situation. Since there was no variation in the release rate of particles depend- ing on the time of the day, the rate remained constant throughout the simulation. The simulation was run for one week between the dates 2011-02-01 and 2011-02-07 and there were no already existing plastic particles present at the beginning of the simulation. The figure below shows the distribution of plastic sources, indicated in white, along Jakarta Bay.

17 of 44 6.3 Simulation characteristics 6 PILOT CASE - JAKARTA BAY, INDONESIA

Figure 4: Plastic pollution sources

6.3.2 Plastic characteristics TOC’s booms are used as cleanup systems in this study. As they can only capture plastic particles of specific characteristics these are specified as output for each par- ticle.

Particle size

Firstly, the boom cannot collect plastic particles smaller than a certain size. In the Feasibility Study by TOC (2014) plastic particles is categorized into four differ- ent size groups: micro, small, medium and large. The boom is not able to collect micro plastics of sizes < 20 mm. The sizes of the plastics dispersed from the river discharges into Jakarta Bay are represented in the below table. The sizes are released with different probabilities, as given by a study over plastic composition made by TOC. This was obtained by using a discrete distribution in MIKE.

Plastic sizes Average length (mm) Plastic composition (%) Micro <20 15.1 Small 20-99 33.2 Medium 100-300 22.4 Large >300 29.3

Table 1: The weights of different plastic size groups and their contribution to the composition of marine plastic debris.

18 of 44 6.4 Data processing 6 PILOT CASE - JAKARTA BAY, INDONESIA

Particle depth

Secondly, the boom can collect plastic particles up to a depth of 4 m. As all of the sources are placed at the surface level, with surface elevation of zero meters, all particles start with a depth of 0 meters.

6.4 Data processing The simulation resulted in an xml file which was read into Matlab for analysis and model creation. The data was constructed as a table with rows representing particles at each time step and columns including the particles’ different characteristics. For the purpose of the analysis, the original data was reduced as to only include rows de- scribing particles at a site. The sites are represented as circular areas with a distance of 1 km between one site’s center point to another, and radius equal half the boom length, in this case 150 m. If a particle had remained at a site for several time steps, only its first occurrence was considered.

Since Jakarta Bay has a busy port, the overlap of shipping tracks and sites was analyzed. The shipping tracks were created in Matlab after a visual inspection of Google Maps, and sites with any shipping track passing through them were removed as possible boom placement sites. The below figure shows how the placement sites are distributed in the Jakarta Bay area together with shipping tracks, indicated by a darker blue.

Figure 5: Placement sites for the Jakarta Bay area

19 of 44 6.5 Cleanup station costs 6 PILOT CASE - JAKARTA BAY, INDONESIA

6.5 Cleanup station costs The considered costs in the mathematical model is the placement cost of one boom, as well as the maintenance- and transportation costs associated with traveling to and from the boom to empty it. Cost kj can then be summarized as kj = p + tj + mj where p is the placement cost of a boom, tj is the transporting and emptying cost for a boom placed at site j, and mj is the boom maintenance cost. The cost calculations are made by using data provided by TOC’s Feasibility Study. However, as the booms used for the purpose of this thesis is of much smaller length and scale, the costs have been scaled down to better reflect reality. The so called ”fictional” booms have a length of 300 m compared to those presented in TOC’s Feasibility Study.

6.5.1 Placement cost The placement cost of one boom given a boom length of 1-2 km is 5 000 000e (TOC Communication Team, 2018). This is scaled down to represent the size of the fictional boom used for the purpose of this thesis. Since its length will be between 0-1 km in length, the placement cost of 5 000 000e is divided by two to represent this respective spread of length, giving a cost p of placing the fictional boom of 2 500 000e . This is further scaled down to suit the economics of the pilot case country, Indonesia. Hence the total placement cost is 1 250 000e .

6.5.2 Transportation cost It is assumed that the booms have to be emptied once every second month. With this comes an additional transportation cost to transport vessels to the booms, empty them, and bring back the collected plastic debris to land and landfills. The consumed fuel for the boom emptying time of three days is accounted for in the cost. As the running period of each placed boom is assumed to be 10 years, the transportation cost is multiplied by 120 to get the total transportation cost for the total running period.

The data used for calculating the cost of traveling to a boom with a certain ves- sel is taken from TOC’s Feasibility Study. The rent of a vessel is 6000e per day. Given that it takes three days to empty a full boom the total vessel cost will be 18 000e per emptying and transporting operation. Furthermore, assuming a crew of six people, the crew cost is 500e per day. Hence, the total crew cost for one emptying and transportation round is 1500e .

Vessel characteristics, such as the speed and fuel consumption, are used when cal- culating the transportation cost tj to a boom located at site j. The below table summarizes the characteristics of the vessel used in the calculation of tj. Its fuel con- sumption is based on a speed of 10 knots, or similarly, 18.5 km/h. The summarized

20 of 44 6.5 Cleanup station costs 6 PILOT CASE - JAKARTA BAY, INDONESIA data is calculated from information presented in TOC’s Feasibility Study (2016).

Type Speed, km/h Fuel consumption, kg/h Fuel cost per kg, e Used vessel 18.5 290 0.132

Table 2: Characteristics of used vessel

The data presented in the table is used in the following equation to calculate the fuel cost of traveling to a boom at site j: fj = distance(km)/speed(km/h) × fuel consumption (kg/h) × fuel cost per kg (e).

6.5.3 Maintenance cost

An associated maintenance cost mj comes with a placement of booms. Maintenance includes operations such as the recoupling and replacement of boom sections after storms and the removal of unwanted life growing attached to the boom surface (TOC, 2016). Maintenance operations are carried out every sixth month and takes one day to complete. The rent of a maintenance vessel is 6 000e each day and renting a crew comes with a cost of 500e each day. There will also be an additional fuel cost for transporting the maintenance vessel to and from the boom site. This transportation cost will depend on the distance to the boom in a similar way as for the emptying of booms. The maintenance cost, excluding fuel cost, is then 39 000e for a 10 year period.

6.5.4 Cost summary

As to be recalled, total cost kj is a summation of placement, maintenance and trans- portation cost of each placed boom. These are summarized in the table below.

Cost Parameter Euros Placement p 1 250 000 Transportation tj depends on the traveling distance to boom Maintenance mj depends on the traveling distance to boom Table 3: The associated cost parameters for the mathematical model

Whilst the placement cost for any boom is fixed, its transportation and maintenance cost will depend on the traveling distance to the boom.

21 of 44 7 RESULTS AND ANALYSIS

7 Results and analysis

This section presents the simulation and optimization results for Jakarta Bay. The optimal placements are shown for different amounts of placed booms and objectives, and a cost trade-off analysis is applied to investigate the effects of an increased capital budget. To account for uncertainty in the simulation output, a total number of 10 simulations were run when producing the results. Despite including randomness to the simulation run, the outputs however showed minor differences between them, thus not affecting the optimization results.

7.1 Simulation results The below figures show snapshots from the first day of simulation to get a sense of how the plastic particles, shown as white circles, moved. As recalled, seven dispersion sources were used, each with a plastic particle release rate of one per hour. In total a number of 1003 particles were released during the simulation period.

Figure 6: Three hour simulation Figure 7: Six hour simulation

Figure 8: Nine hour simulation Figure 9: Twelve hour simulation

22 of 44 7.1 Simulation results 7 RESULTS AND ANALYSIS

Figure 10: Fifteen hour simulation Figure 11: Eighteen hour simulation

Figure 12: Twenty-one hour simulation Figure 13: Twenty-four hour simulation

The below figure shows the movement tracks of all released plastic particles, at the end of the one week simulation.

Figure 14: Plastic particle tracks at the end of the simulation

23 of 44 7.2 Optimal placement of booms 7 RESULTS AND ANALYSIS

7.2 Optimal placement of booms Although the optimization model uses a multi-objective function, its flexibility allows an option for the objective to only maximize the amount of collected plastic particles, only minimize the plastic’s impact on sensitive areas, and a multi-objective approach which considers both of these cases. The following section presents the visual results of the optimal placement of one, three respective five booms for each scenario. As Matlab’s solver returned the optimal value to be found, with an exitflag describing the algorithm stopping condition to be convergence to solution x, this ensures optimality of the solutions. As the relativegap and absolutegap were further 0 for all runs, this is another indication that the results is reliable. The running time of the algorithm ranged between 0.35 and 2.80 seconds depending on the amount of booms to be placed.

7.2.1 Maximizing the amount of collected particles For this case the impact weight w in the objective function was set to 0. The place- ment of one boom is presented in figure 15, and may seem non intuitive at first glance; it is far away from any dispersion sources and there seem to be more apparent areas with higher density of particles. The boom is however placed at a site where many particles eventually end up.

Figure 15: w=0: Optimal placement of one boom

When increasing the budget for a placement of three booms, the following placements are decided as optimal. The additional two booms are now placed closer to the eastern coastline of Jakarta Bay. As can be seen by the movement tracks, particles from most sources travel past the east side of the bay, resulting in a high density of plastic particles in this area.

24 of 44 7.2 Optimal placement of booms 7 RESULTS AND ANALYSIS

Figure 16: w=0: Optimal placement of three booms

Increasing the amount of booms from three to five gives a similar logic. The additional two booms are placed in areas with a high concentration of plastic. As can be seen from the figure, two booms are placed next to each other. One may think that a greater placement distribution of booms would be more effective. Also, a placement near the coast may not seem like a desirable result. However, it is of value to recall that these type of placements have at least a 1 km distance between them, both for neighboring placement sites and placement sites directly outside a coast. An area with high plastic concentration could thus make it optimal to place two booms adjacent to one another.

Figure 17: w=0: Optimal placement of five booms

25 of 44 7.2 Optimal placement of booms 7 RESULTS AND ANALYSIS

7.2.2 Maximizing reduced impact The objective to solely maximize the reduced impact was achieved by assigning w a sufficiently large number, in this case 100. The optimal placement of one boom is shown below. Many of the particles released by a dispersion source in this area of the bay pass through sensitive tourism and coral reef locations, hence, the result seems reasonable.

Figure 18: w=100: Optimal placement of one boom

The placement of three and five booms follows the same logic. As the sensitive areas are at this location, the optimization program is solved to minimize the particles’ impact, placing booms at locations to facilitate this aim. As argued before, it might seem reasonable to place the booms at locations with greater distances between them. However, as the majority of particles with an impact count are released from this source, it is optimal to place the booms adjacently.

26 of 44 7.2 Optimal placement of booms 7 RESULTS AND ANALYSIS

Figure 19: w=100: Optimal placement of three booms

Figure 20: w=100: Optimal placement of five booms

7.2.3 Multi-objective approach The multi-objective approach aims to both maximize the amount of collected plas- tic particles and minimize their impact. Finding a value w that balances these two objectives is therefore required, and not necessarily straightforward. In this case, the value of w was chosen to be 10. It was decided not desirable to prioritize particles with a very low impact over the collected amount of particles, e.g. more desirable to collect two particles with no impact over one particle with low impact. As a particle that gets collected get a value of 1, w was set so that only particles with a relatively large impact number got an impact value exceeding 1 in the objective function. If

27 of 44 7.2 Optimal placement of booms 7 RESULTS AND ANALYSIS the normalized impact should have been equally distributed between 0 and 1 for all particles, a w of value 2 could have been argued as suitable. This because particles with a normalized impact number higher than 0.5 would then get a impact value higher than 1, and thus be prioritized over collecting several particles with no im- pact. However, the mean impact of the particles were 4.40 for the run simulation, and maximal impact 87. The normalized values hence becomes generally low, with mean 0.05, why the value of w was chosen to be 10 to make a greater amount of particles pass the limit of 1.

Different values of w was tested in order to see how these affected the objective func- tion and to validate the choice of w=10. As argued before, since the normalized impact for each particle tends to be close to zero, a low value of w, less than 10, gave the same optimal placement of booms as when using an objective function which only seek to maximize the amount of collected particles. As more booms are placed, the investigation showed that a greater value of w was required to make the booms change placement from only considering collected particles to only consider impact minimization. With more booms, the results also became more sensitive to changes in w in terms of boom placement. With one boom, there was only one breaking point of w which made the boom switch from only mass to only impact, but with five booms, smaller and more frequent changes in w were needed in order to make individual booms switch places to fulfill the new impact weight according to w. The choice of w=10 was in accordance with this analysis and shown to make a good bal- ance between the two objectives.

Below follow the optimization results for the multi-objective function. The place- ment of one boom is the same as the case when only the minimization of impact is considered in the objective function.

Figure 21: w=10: Optimal placement of one boom

28 of 44 7.3 Cost curve trade-off 7 RESULTS AND ANALYSIS

The placement of three and five booms however resulted in locations with high plastic concentrations. This can be explained by the fact that there are not many particles with high impact numbers, quickly making it more rewarding to instead place the booms so that many particles are collected.

Figure 22: w=10: Optimal placement of three booms

Figure 23: w=10: Optimal placement of five booms

7.3 Cost curve trade-off A cost trade-off analysis is made in order to investigate how increases in capital budget affects the amount and placement of booms. Hence, the analysis shows the relationship between additional spent capital and its respective results in for instance

29 of 44 7.3 Cost curve trade-off 7 RESULTS AND ANALYSIS objective value and number of collected particles. After analyzing the costs associ- ated with boom placement, it was deduced that the total transportation fuel cost is substantially low in comparison to the fixed costs, such as the placement and main- tenance costs. Given this, the budgeted capital intervals were decided to be the total cost for the placement of an additional boom, regardless of how far it is placed from the initial starting port. If the transportation cost would have been of the same order of magnitude as the fixed cost, the budget could otherwise be affected by distance and this would be accounted for in optimal placement of booms.

The presented results show how the total objective value, total reduced impact and the number of collected particles change with an increased budget, and hence, addi- tional placed booms. The following graphs presents the results from considering the three different cases of the objective function, presented earlier. It should be noted that, while the different cases and resulting boom placements depend on the value of w, the values presented in the graphs is the objective values without w, or similarly, with a w equal to 1. This to be able to compare the different cases directly.

The below graph shows how the total objective value increases with the budget, where each marked dot represents the placement of an additional boom.

Figure 24: Increase in objective value from the placement of an additional boom

A value of w=10 considers the multi-objective function, w=0 represents the objec- tive to only maximize the amount of collected particles without considering their impact and w=100 corresponds to the objective which only aims to minimize the impact and not maximize the amount of collected particles. As can be seen from

30 of 44 7.3 Cost curve trade-off 7 RESULTS AND ANALYSIS the graph, the placement of one boom resulted in the same objective value for both w=100 and w=10. Only having the objective of maximizing particles, w=0, resulted in the highest objective value whilst only considering impact, w=100, gave the low- est objective value with increased boom placement. This can be explained by the fact that the normalized impact counts are of low value and hence not accumulating to as high numbers as the collection count of 1, why it can also be motivated to be of higher relevance to analyze the amount of collected particles and impact separately.

Intuitively, an objective which only aims to maximize the amount of collected parti- cles collects more particles in comparison to the on-its-own impact objective. This resulted to be true, however, the multi-objective function almost captures the same amount of particles. Further, as can be seen from the below figure, the graph over collected particles is very similar to the graph over objective value. This supports the suggestion that collection count values dominates over the normalized impact values.

Figure 25: Increase in amount of collected particles from the placement of an addi- tional boom

The figure below shows how the total reduced impact changes with an increased budget. As expected, an objective function which only aims to minimize reduced impact has the greatest increase in total impact reduction, whilst the objective to only maximize collected particles resulted in the lowest. It is generally hard to grasp the magnitude of the impact values, as this is a self-created value unlike the number of collected particles. However, since the normalization procedure results in impact values of small magnitude, the difference between the total reduced impact for w=0 and w=100, can be considered to be a notable difference.

31 of 44 7.3 Cost curve trade-off 7 RESULTS AND ANALYSIS

Figure 26: Increase in reduced impact from the placement of an additional boom

The following figures present the independent results from the multi-objective case, with w=10. Similarly as before, the below graph shows how the objective value and collected amount of particles increase with the budget. The numbers alongside the graphs show how the results relate (in %) to the total objective value and the total amount of particles.

Figure 27: Increase in objective value with increased budget

32 of 44 7.3 Cost curve trade-off 7 RESULTS AND ANALYSIS

Figure 28: Increase in amount of collected particles with increased budget

The percentages of collected particles ranges from 0.6% (one boom) to 7.0 % (ten booms) of the total amount of released particles, which can be seen as a relatively large difference. As can be seen, the relationship between the objective value/amount of collected particles and additionally placed booms is of somewhat linear relation, where the irregularity stems from also aiming to consider impact.

The below figures show the marginal percentage increase in results by placing ad- ditional booms. As noted before, they both follow a similar pattern and as expected, the decrease in marginal percentage increases with a larger budget. This is due to the first placed boom collecting the most desirable particles, the second boom collecting the next best particles and so on. The placement of a second boom gives approxi- mately a 60% better optimal value and collected particles compared to the placement of one boom.

33 of 44 7.3 Cost curve trade-off 7 RESULTS AND ANALYSIS

Figure 29: Percentage increase in objective value from an additional boom

Figure 30: Percentage increase in collected particles with an additional boom

The next figures shows how the total reduced impact and the marginal reduced impact changes with budget.

34 of 44 7.3 Cost curve trade-off 7 RESULTS AND ANALYSIS

Figure 31: Increase in total reduced impact with increased budget

Figure 32: Percentage increase in total reduced impact with additional boom

Figure 31 shows an increasing trend in total reduced impact with increased budget and additional placed booms. However, the graph doesn’t show an as smooth in- crease as the result for collected particles and total objective value. The placement of boom 8 and 9 for instance both show an reduced impact of 2.4. This stagnation can be explained by the fact that collecting additional particles is prioritized before

35 of 44 7.4 Result summary 7 RESULTS AND ANALYSIS an additional reduced impact. In the simulation results, less particles travel through sensitive areas and do not get any impact count. Hence, between boom 8 and 9, it is more optimal to collect additional particles to maximize the objective. The same can be discussed regarding figure 32 which shows the percentage increase by placing an additional boom, compared to the previous one.

7.4 Result summary Analysis have been made alongside the presentation of results, where different cases of the objective function were tested in order to investigate how this would affect the placement of booms. The optimal placement of booms vary significantly when the objective is to only maximize the amount of collected particles, only minimize the impact and when considering both aims in the same objective function. The great differences in placement is most likely dependent on our specific simulation results, resulting from the fact that the majority of particles don’t pass through impact sites. A hypothetical impact map, in which the impact areas are located at areas where a high amount of particles pass through, would most likely result in the outcomes from the three scenarios being more aligned with one another.

Since the 10 year transportation fuel cost associated with the placement of booms is low in relation to fixed costs such as those of placement and maintenance, the opti- mization model barely takes the distance to the boom into account when determining the optimal placements of these. Thus, the budget increase is instead associated with the fixed costs of additional booms. As shown by the results for the multi-objective function, the relation between additional placed booms and collected plastic is of lin- ear relation. Although the relationship between reduced impact and amount of placed booms was not as evident, the reduced impact increases with an increased budget.

Many of the results can be explained by the certain characteristics of the simula- tion. There are few particles fulfilling the size and depth constraints for capture, thus resulting in few particles being collected. In addition, the considered area of Jakarta Bay is large and the distances between the dispersion sources are reflected in this percentage. As the possible placement sites are located with a distance of 1 km, many particles do not pass through a site area. Moreover, the time step for the simulation, and thus input to the optimization formulation, is one hour. It is possible that particles move pass a site between these time steps and are thus not considered as possible particles to collect. A conclusion is that the model seem to work well in finding the optimal placement but is highly affected by, and requires, a good simulation. By decreasing the time step and site distances, as well as expanding the model to include real particle drift characteristics, would very likely increase the percentage of collected particles, which would in turn make the optimization results more robust.

36 of 44 8 DISCUSSION

8 Discussion

The pilot study presented reasonable results, which emphasizes the accuracy of the optimization model. Due to often limited budgets, the optimization model places the cleanup systems at sites where many particles pass through rather than directly outside dispersion sources which might seem intuitive at first. The following section discusses the current optimization model and simulation, as well as possible improve- ments.

8.1 Optimization model improvements Extensions can be made regarding the mathematical optimization formulation and its constraints. As for now, a plastic particle can be captured if it is in a site area and fulfills the size and depth constraints. Hence, it is assumed that a cleanup system has a 100% boom efficiency, and angle or shape of the used cleanup system is not taken into account. In reality, as the booms used in the pilot case have an u-shaped form, plastic particles have to come in contact with the boom with a certain angle of incidence in order to become collected. The incorporation of the boom angle in the optimization formulation would require the consideration of an additional plastic particle characteristic, namely its direction angle relative to the boom. Alternatively, a boom capture efficiency parameter could be introduced which would, instead of considering plastic particle direction, account for a capture probability for the plastic particles entering a placement site.

Another possible extension could be to prioritize the collection of particles differ- ently, depending on size. It’s likely that some types of particles are considered more important to collect, given their specific characteristics and potential environmental impact.

8.2 Multi-objective optimization A drawback with multi-objective optimization is that it can be of difficulty to find a good balance between two objectives, especially if they are of different unit and magnitude. The two objectives used in the optimization model; to maximize the amount of collected plastic particles and to minimize their impact, do not have to be in conflict. However, there is a possibility for this. As the sensitive impact areas in the pilot case, Jakarta Bay, Indonesia, are not in overlap with many particle tracks, the two objectives can pull in different directions. Thus, the value for impact weight w can have big impact and be difficult to determine in order to obtain a good trade-off between the two.

37 of 44 8.3 Simulation of plastic movement 8 DISCUSSION

8.3 Simulation of plastic movement As the optimization results rely on the simulation output, the model is sensitive to the simulation accuracy of plastic dispersion movement. The MIKE software is a com- prehensive and extensive simulation tool allowing the user to define mathematical expressions of a particle’s response to, and interaction with, surrounding environ- ments. The following section discusses the advantages and disadvantages of the used simulation as well as proposes possible extensions for increased simulation accuracy.

8.3.1 Simulation Numerical models are used in order to track particle movement and get a good ap- proximation of particle dispersion in different environments, such as coastal areas and river networks. The used numerical and hydrodynamic simulation model, com- bined with data packages, accounts for the movement of plastic particles in relation to surrounding dominant physical processes. Using a simulation as input for the math- ematical model brings several advantages. As there is difficulty in finding existing data of plastic particle movement in such a detailed manner, a simulation presents the closest estimate. The used simulation allows for individual plastic particle track- ing, enabling the possibility to incorporate an impact count for each particle and thus the construction of minimized impact in the objective function. However, as the mathematical model depends on the simulation output, the quality of the simulation affects the optimization results. The current simulation is only constructed to present a fairly accurate movement of particles in water environments, accounting for basic drift characteristics. Making the particle tracking more advanced by incorporating more particle characteristics, is a necessary step in making the optimization model fully applicable. It should be noted that, whilst the constructed simulation used as input to the study’s mathematical model is of simple type, research regarding the movement of marine plastic debris is fairly extensive and there exist simulations of advanced manner.

8.3.2 Time period and time steps The simulation was run for a period of one week, using hydrodynamics during the monsoon period in Indonesia. As the simulation was run for a relatively short period of time during one of Indonesia’s most rainy seasons, it does not account for the variation in plastic movements over a longer time frame, and hence not the seasonal variations that arise during the 10 year lifetime of a boom. This affects the accuracy of the simulation and thus the input to the mathematical model.

The plastic particles were released with an hourly rate from the dispersion sources, and the resulting xml file with particle data was outputted with hourly time steps. The particles’ output information can thus come to change with a noticeable amount

38 of 44 8.3 Simulation of plastic movement 8 DISCUSSION for each time step, not presenting any information on the changes between one hour to another. For instance, there is a possibility that a particle fulfilling all capture constraints could have moved pass a site between two time steps and not become captured. This could be one of the reasons for few particles being collected. In the MIKE setup for the simulation the time frequency is of decidable choice and can be adjusted to include fewer or more time steps.

The aim of the pilot case was to demonstrate that the optimization model can find the optimal placement of cleanup systems given the inputted data. To get a realistic placement of cleanup systems, a longer and more detailed simulation would however be required. Given this, the simulation would result in more data which could come to affect the running time of the optimization solver.

8.3.3 Plastic drift characteristics The only plastic characteristics accounted for in the simulation is particle size. Hence, the plastic drift characteristics do not differentiate between different plastic types, such as nets and bottles. Plastics have a wide range of different characteristics, such as surface area and density, and all of these affect the plastic’s buoyancy, and thereby depth, in its surrounding water environment. As only differences in size is considered, the plastic drift characteristics and dispersion used for the purpose of the study are of basic character. The excluded characteristics would effect the speed, direction and depth of the plastic particles.

39 of 44 9 CONCLUSION

9 Conclusion

To conclude, the mathematical model fulfills the multi-objective aim to both maximize the amount of collected plastic particles and minimize their impact on sensitive areas. The characteristics of the cleanup system can in the mathematical model be chosen to suit the purpose and interest of the user. However, for the purpose of the thesis, booms inspired by the cleanup technology developed by The Ocean Cleanup were used. A pilot case was performed on Jakarta Bay, with sensitive coral and tourism areas, to simulate a one week movement of released particles in the area. Three cases to the objective function were considered; the objective to maximize the amount of collected particles, the objective to minimize the plastic particles’ impact and an intertwined objective with the aim to fulfill both simultaneously. A comparison was made to show how the optimal placement of booms varied between these cases and the results showed that these were sensitive to the choice of w. A cost trade-off was further performed to investigate how the placement of cleanup systems varied with increased capital budget. As the optimization model if of general type, improvements and extensions can be made to it in order to advance its real life application. The results from the optimization model are highly dependent on the results of the simulation of particle tracking movement. However, the development of a detailed and accurate simulation was not included in the scope of the thesis, and does not directly effect the reliability of the model.

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