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.