Fund Allocation for Civil Infrastructure Security Upgrade

Nikos D. Lagaros, Ph.D., M.ASCE1; Konstantinos Kepaptsoglou, Ph.D., M.ASCE2; and Matthew G. Karlaftis, Ph.D., M.ASCE3

Abstract: Security of transportation infrastructure is of primary importance in recent years as a result of various breaches worldwide. Increased security concerns lead transportation authorities to improve, upgrade, and enhance surveillance, prevention, and response equipment in facilities, frequently under tight budgetary and operational constraints. In this context, a generic selection and resource allocation (S&RA) model is proposed for security upgrades of civil infrastructure, along with a novel technique for efficiently solving the model for real-world instances. An application of the model is offered for the case of the metro system in Athens, Greece, and results are discussed. DOI: 10.1061/(ASCE)ME.1943-5479.0000133. © 2013 American Society of Civil Engineers. CE Database subject headings: Infrastructure; Security; Funding; Optimization. Author keywords: Transportation security; Selection and resource allocation; Budget; Particle swarm optimization.

Introduction as potential targets for terrorist activities (Meyer 2010; Cox et al. 2011). Worldwide, transportation authorities are increasingly Project selection and resource allocation (S&RA) are at the core concerned with security of their facilities and keep upgrading and of management tasks and activities encountered by organizations expanding relevant surveillance, prevention, and response equip- and authorities that deal with transportation networks and infra- ment and tactics, often under operational difficulties and budget structure. Indeed, organizations regularly face the need to allocate limitations. In this context, this paper focuses on S&RA for the their limited funds to different programs/projects, often satisfying upgrade and expansion of security equipment in transportation conflicting objectives and interests (Zanakis et al. 1995). Examples infrastructures and proposes a nonlinear programming model in the transportation sector include optimal programming of main- and a metaheuristics algorithm for solving it. A comprehensive tenance, repair, and rehabilitation (MR&R) activities in pavements application of the model for the Athens, Greece, metro system and bridges and the replacement of transit fleets. The correspond- is also offered. The remainder of the paper is structured as follows: ing S&RA problem can be formally described as follows (Zanakis A subsequent section offers a comprehensive overview of S&RA et al. 1995): “Consider a set of alternative programs/projects, with methods and techniques and their applications in different areas of a quantified benefit assigned to each program/project. The S&RA transportation. Then, the S&RA model for the problem at hand is problem focuses on the decision on which project to fund and in presented along with the proposed solution method. An application what amount. This decision is subject to constraints and dictated of the model for the case of the Athens metro system is provided, by—often conflicting—objectives.” and results are discussed. The paper concludes with model appli- Security in transportation has become a topic of primary cation insights and proposals for future research in the area. importance in recent years primarily because of attacks against transportation systems, such as the cases of the Tokyo, London, ’ and Madrid, Spain, metro systems and Moscow s Domodedovo air- Background port. Indeed, concentration of passengers in confined transportation facilities along with the significant role of transportation in modern Selection and resource allocation are the final steps of the so-called societies and the economy make transportation systems attractive project-evaluation process; previous steps include identification of candidate projects, determination of evaluation criteria, and es- 1Lecturer, School of Civil Engineering, Institute of Structural Analysis timation of benefits and costs per alternative project. As a problem, and Seismic Research, National Technical Univ. of Athens, 9, Iroon S&RA have been extensively investigated in the literature, with Polytechniou St., Zografou Campus, GR-15780 Athens, Greece. E-mail: excellent surveys offered by Zanakis et al. (1995), Heidenberger [email protected] 2 and Stummer (1999), and a reference textbook by Bower (1986).

Downloaded from ascelibrary.org by Heriot-Watt University on 07/30/13. Copyright ASCE. For personal use only; all rights reserved. Postdoctoral Researcher, School of Civil Engineering, Dept. of Transportation Planning and Engineering, National Technical Univ. of In this section, an overview of the methods and techniques used Athens, 5, Iroon Polytechniou St., Zografou Campus, GR-15780 Athens, for S&RA of projects is provided, and relevant work in the field Greece (corresponding author). E-mail: [email protected] of civil infrastructure and transportation is then reviewed. 3Associate Professor, School of Civil Engineering, Dept. of Transporta- tion Planning and Engineering, National Technical Univ. of Athens, 5, Iroon Polytechniou Str., Zografou Campus, GR-15780 Athens, Greece. Selection and Resource Allocation Methods and E-mail: [email protected] Techniques Note. This manuscript was submitted on December 15, 2011; approved Typically, the process of S&RA consists of two tasks: (1) measure- on May 1, 2012; published online on May 3, 2012. Discussion period open until September 1, 2013; separate discussions must be submitted ment of benefits and (2) optimal selection/allocation of resources. for individual papers. This paper is part of the Journal of Management The first task pertains to determining the benefits associated in Engineering, Vol. 29, No. 2, April 1, 2013. © ASCE, ISSN 0742- with each alternative project; these benefits, in turn, refer to 597X/2013/2-172-182/$25.00. establishing and quantifying various decision/evaluation criteria

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J. Manage. Eng. 2013.29:172-182. (Zanakis et al. 1995). The second task refers to optimally selecting thickness for the case of a highway project) as independent projects and allocating funds under budget constraints. variables for cost estimation. For more information on project cost estimation, recent work has been undertaken by Anderson et al. Benefit Measurement (2009), Tan and Mackwasa (2010), El Asmar et al. (2011), and Various approaches have been proposed in the literature for Bokor (2011). measuring project benefits, These approaches may be categorized into four groups (Heidenberger and Stummer 1999): comparative Optimal Selection of Projects and Allocation of Resources approaches, scoring approaches, traditional economic models, and Once project benefits are measured, their ranking becomes readily group-decision techniques. available. However, the question regarding how to select projects Comparative approaches refer to pairwise comparison of proj- under budgetary, time, and other constraints still remains largely ects using either an additive or a ratio scale. Although these meth- unaddressed. Further, the amount of funds to be allocated to each ods often require a large number of project-to-project comparisons project often becomes an additional item to be derived. In this and the need to repeat any measurement when a project is added, context, the prevailing approaches for optimal project selection their advantage is the minimum impact of errors, attributable to the (particularly in the area of transportation) and fund allocation are large number of comparisons involved (Locket and Startford 1987). based on optimization models, and other methods involve decision The most popular among comparative methods is the analytical and game theory, statistical models, and simulation (Heidenberger hierarchy process (AHP), introduced by Saaty (1980). Scoring and Stummer 1999). methods assign an overall benefit measure to each project. Scores Traditional optimization-oriented approaches for S&RA are of alternative projects with respect to each decision criterion are based on mathematical programming models. These models seek determined and then combined to yield the overall project score. to maximize benefits from selected projects under various budget- The simplest among scoring methods is the checklist technique, ary and other constraints. Depending on the nature of the S&RA, in which fulfillment of requirements is examined along with the a variety of linear, integer, and nonlinear specifications may be level of conformation to that requirement. Traditional scoring considered. For instance, linear models assume both linear con- models, on the other hand, use multiple value-assessment scores sumption of resources and benefit contribution of projects as well and weights for each decision criterion. These models are widely as independence of projects (Winston 2003). Conversely, nonlinear applied for measuring project benefits because in most cases they models are used in cases of complex decision problems, implying succeed in offering a consistent ranking of projects (Krawiec 1984). that benefits and constraints are represented by nonlinear objective Utility analysis (often referred to as multiattribute utility analysis) is functions. As for integer programming models, these are intro- an advanced, axiomatically founded scoring method (Heidenberger duced in cases of explicit selection of projects because of their and Stummer 1999). The method is based on aggregating evalu- ability to represent yes/no and discrete decisions (Winston 2003). ation criteria in a single utility function, which expresses a decision Although optimization models may offer a straightforward repre- maker’s preference toward a project. Utility functions are less sentation of S&RA problems, they often require increased compu- preferred by practitioners owing to the complexity involved in tational power for obtaining optimal solutions, particularly when their derivation and their inferior performance (Schoemaker and problem sizes increase. This is particularly true for discrete and Waid 1982). integer programming models, which are usually combinatorial in Economic methods are based on the monetary perspective nature and thus difficult to solve (Winston 2003). For this reason, of projects and exploit capital-budgeting techniques for estimat- a number of heuristic and metaheuristic techniques have been pro- ing the economic performance of alternative projects. Relevant posed by the literature to solve such problems (with Lagrangian methods include the estimation of economic indices, discounted relaxation and genetic algorithms as frequently used examples). cash-flow methods, and the options approach (Heidenberger and Ibaraki and Katoh (1988) present a detailed discussion on complex- Stummer 1999). As for group-decision techniques, they combine ity and methods for solving relevant resource allocation problems. knowledge and experience collected by experts to rate and rank Apart from straightforward mathematical programming models, projects. The Delphi method is probably the most popular group- techniques such as goal, dynamic, and stochastic programming decision technique; it relies on a consensus by a panel of experts have been considered for S&RA. In goal programming, projects who offer their judgment for alternative projects on the basis of are selected so that a set of goals (in terms of project benefits) structured questionnaires (Zanakis et al. 1995). are achieved, whereas dynamic programming models focus on resource allocation problems in which programming of projects in Project Costs a subsequent time period is affected by S&RA decisions made in a A prerequisite for resource allocation is the estimation of costs for previous period. Finally, stochastic models are used in cases in candidate projects. In general, depending upon the type and nature which some inputs are uncertain and subject to variation, whereas of projects, three typical approaches exist for obtaining an estima- fuzzy programming is exploited in cases of broad (fuzzy) ranges of tion of costs (Anderson et al. 2009). The first approach focuses on inputs and similar expectations in the S&RA results. historical data regarding bids for similar, past projects and extracts Downloaded from ascelibrary.org by Heriot-Watt University on 07/30/13. Copyright ASCE. For personal use only; all rights reserved. As an alternative to mathematical programming models, the unit costs for different project types (for example, resurfacing costs literature has proposed decision and game theory methods, simula- per lane mile or purchase costs per bus). The second method is cost- tion, and cognitive emulation approaches (e.g., statistical models, based estimation, which estimates and then aggregates costs for the expert systems) for S&RA; interested readers can refer to particular elements of a project according to production rates, unit Heidenberger and Stummer (1999) for more details and references labor, and material costs per element. For instance, in such a case, on these methods and their application in S&RA. Table 1 summa- ’ estimation of a bridge s replacement cost would include the de- rizes tasks and techniques exploited for S&RA of projects. tailed calculation of individual costs for its deck, superstructure, and substructure by considering labor and material costs for each Selection and Resource Allocation Applications in component. As for the third element, it directly relates a project’s Transportation costs to its main parameters, again on the basis of historical data. Essentially, this implies that a statistical model is built, having ma- Transportation systems are vital lifelines in constant need of main- jor project parameters (e.g., road length and width and resurfacing tenance, improvement, upgrade, and expansion. Given economic,

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J. Manage. Eng. 2013.29:172-182. Table 1. Selection and Resource Allocation Methods and Techniques Focus is given to improving the quality and performance of infra- (Data from Heidenberger and Stummer 1999) structures and to minimizing their life-cycle costs. Project selection Type of method Examples and resource allocation are obviously critical tasks in infrastructure management because they set optimal courses of action for main- Measurement of benefits taining and/or improving transportation infrastructures and deter- Comparative methods Analytical hierarchy process Scoring methods Checklist, scoring models, utility analysis mine required funding for those purposes. Economic methods Economic indices, discounted cash-flow The literature exhibits a variety of models proposed and incor- methods, options approach porated for S&RA actions in pavement and bridge management, Group-decision techniques Delphi and during the last decade the concept of highway asset management (including bridge, pavement, and roadside elements) in Optimal project selection and resource allocation Mathematical programming Linear models, nonlinear models, integer S&RA has gained attention (Tiewater and Zimmerman 2010). models, goal programming, dynamic In the area of pavement management, S&RA examples include programming, stochastic programming, linear models (Hajek and Phang 1988; Seyedshohadaie et al. 2010), fuzzy programming dynamic programming (Feighan et al. 1988; Ouyang 2007), goal Decision and game theory Decision trees, game theory programming (Sharaf and Youssef 2001), multiobjective models Simulation Monte Carlo simulation (Chan et al. 2003), robust programming (Gao and Zhang 2008), Cognitive emulation Statistical models, expert systems, fuzzy programming (Mellano et al. 2009), and stochastic multiob- heuristic approaches jective models (Wu and Flintsch 2009). Bridge management has exhibited a variety of S&RA optimization models, including linear specifications by Guigner and Madanat (2000), integer program- social, organizational, and other constraints along with the size, ming (Al-Subhi et al. 1990), dynamic programming (Jiang and cost, and impact of transportation projects, optimal S&RA appli- Sinha 1989; Razaqpur et al. 1996), incremental benefit–cost ap- cation in transportation systems has attracted considerable interest proach (Farid et al. 1994a, b; Robert et al. 2009), and multiobjective in both academia and practice. Indeed, the literature includes a models (Hammad et al. 1996; Itoh et al. 1997; Liu and Frangopol vast number of S&RA cases and applications in the transportation 2005a, b; Neves et al. 2006; Thompson et al. 2008). sector. In this section, different S&RA areas of application in trans- Asset management S&RA models in transportation have be- portation and indicative references are provided. come popular in recent years; a notable earlier work was the integer programming model proposed by Ahmed (1983) for S&RA in Transportation Fund Allocation at the Network Level highway maintenance management. Recently, Li and Puyan (2006) Fund distribution at the network level is a common problem for and Li et al. (2010) proposed stochastic binary programming governments and upper-level decision makers; the scope is to models for supporting highway asset investment decisions under allocate funds so that network performance is maintained at desir- budget uncertainty. able levels. As such, Haghani and Wei (1993) proposed a binary nonlinear programming model for capacity expansion of a network Transit Fleet Replacement and used a linear transformation to solve it. Another study (Tao Frequently operating under strict budgetary constraints, decreased and Schonfeld 2005) considered a nonlinear model specification ridership, and low fares, transit agencies constantly face the need in which network impacts were evaluated using a user equilibrium for replacing their aging fleets (Karlaftis and McCarthy 1997, model for fund allocation in a network. Gorloo et al. (2009) pro- 1998); this comes as part of an effort to offer adequate levels of posed an integer programming model for S&RA that maximized service to passengers and maintaining market shares (Karlaftis et al. network reliability. Ferguson et al. (2010) developed a bilevel, non- 1999; Kepaptsoglou and Karlaftis 2009). In this context, optimal linear optimization model for determining capacity-improvement transit fleet–replacement funding has been examined by some re- projects in a transportation network; this model considered environ- searchers: Khasnabis et al. (2002) developed a linear programming mental impacts (emissions) as benefits with the use of appropriate model for determining purchase and rebuild of buses in a transit utility functions. fleet. Mathew et al. (2010) and Mishra et al. (2010) introduced nonlinear programming models for allocating funds to transit agencies Optimal Programming of New Highway Project on the basis of the fleet’s average remaining life and used both Construction branch-and-bound and genetic algorithm techniques for solving Programming of highway projects is among those strategic trans- the model. portation issues that directly fit the context of the S&RA problem. For example, Leu et al. (1999) used fuzzy optimization for sched- Traffic Safety Improvements uling highway project construction under resource constraints and Safety improvement in highways involves the selection of appro- uncertainty duration. Among recent studies, a multiobjective inte- priate countermeasures and allocation of resources in an effort to reduce the impacts of traffic accident. Early work on this topic was

Downloaded from ascelibrary.org by Heriot-Watt University on 07/30/13. Copyright ASCE. For personal use only; all rights reserved. ger programming model was proposed by Iniestra and Gutierrez (2009) for evaluating interdependent problems, and Teng et al. undertaken by Sinha et al. (1981), who proposed a multiyear (2010) applied an extension of the analytical hierarchy process optimization framework and a stochastic model and attempted to technique (fuzzy AHP) for ranking and allocating funds for new minimize the number of accidents in a highway network. Brown highway projects in Taiwan. Following a different, decision theory– et al. (1990) developed integer and dynamic programming tech- oriented approach, Owens et al. (2011) used complexity maps and niques for allocating highway-safety grants and for achieving panels of experts for resource allocation among projects. maximum benefits in terms of life and injury savings. Chowdhury and Garber (1996) and Chowdhury et al. (2000) used multiobjec- Infrastructure Management tive analysis for optimally selecting safety countermeasures, and Infrastructure (asset) management in transportation refers to the in- Melachrinoudis and Kozanidis (2002) formulated a mixed-integer tegrated process for effectively operating, maintaining, upgrading, model that considered both regular and custom-made safety inter- and expanding transportation infrastructures (assets) such as pave- ventions in highways. Harwood et al. (2003) developed a resource ments, bridges, rails, and roadside elements (Sinha and Labi 2007). allocation model [the Resurfacing Safety Resource Allocation

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J. Manage. Eng. 2013.29:172-182. Program (RSRAP)] and software for optimizing systemwide safety by Orabi et al. (2009, 2010) focused on optimal resource allocation with a given number of resurfacing projects under budget con- for reconstruction of infrastructures; for this purpose, they proposed straints. Finally, Kar and Datta (2004) formulated a linear model multiobjective resource allocation models for project programming for allocating resources to safety projects for the state of Michigan and allocation of resources. A framework for minimizing the cost on the basis of a safety-performance index. of hazard preparedness and appropriate allocation of resources was developed by El-Adaway and El-Anwar (2010). Finally, a recent Emergency Response and Security report by Bier et al. (2009) derives analytical functions for allocat- Following a disaster, recovery efforts are required to reduce impacts to local societies and to restore normal life activities (Lagaros and ing resources with the objective of transportation infrastructure Karlaftis 2011). Transportation networks are vital lifelines and are protection. Table 2 summarizes examples of S&RA applications therefore of primary importance in the overall recovery process and in transportation. allocation of funds. In this context, Karlaftis et al. (2007) developed Overall, the literature on S&RA models and applications in a three-stage integer programming model for allocating funds to transportation infrastructure expansion and management is rich. transportation infrastructure–recovery projects following a cata- Most papers exploit mathematical programming models, whereas strophic event and solved it by using a genetic algorithm; Lagaros the stochastic nature of relevant problems is also considered in and Karlaftis (2011) extended this research using a variety of evolu- some cases. In this context, the objective of this paper is to con- tionary optimization approaches, such as particle swarm and har- tribute to existing knowledge by offering a generic model targeted mony search, and compared algorithmic performance. Two papers toward transportation security upgrades.

Table 2. Selection and Resource Allocation Example Applications in Transportation Area Article S&RA method Transportation fund allocation at network level Haghani and Wei (1993) Nonlinear model with linear transformation Tao and Schonfeld (2005) Nonlinear model combined with user equilibrium Gorloo et al. (2009) Integer model Ferguson et al. (2010) Bilevel nonlinear model Optimal programming of new projects Leu et al. (1999) Fuzzy programming Iniestra and Gutierrez (2009) Multiobjective integer model Teng et al. (2010) Fuzzy AHP Owens et al. (2011) Complexity maps–expert panel Pavement management Hajek and Phang (1988) Linear model Seyedshohadaie et al. (2010) Linear model Feighan et al. (1988) Dynamic programming Ouyang (2007) Dynamic programming Sharaf and Youssef (2001) Goal programming Chan et al. (2003) Multiobjective model Gao and Zhang (2008) Robust programming Mellano et al. (2009) Fuzzy programming Wu and Flintsch (2009) Stochastic multiobjective model Bridge management Guigner and Madanat (2000) Linear model Al-Subhi et al. (1990) Integer model Jiang and Sinha (1989) Dynamic programming Razaqpur et al. (1996) Dynamic programming Hammad et al. (1996) Multiobjective model Itoh et al. (1997) Multiobjective model Liu and Frangopol (2005a, b) Multiobjective model Neves et al. (2006) Multiobjective model Thompson et al. (2008) Multiobjective model Farid et al. (1994a, b) Incremental benefit–cost analysis Robert et al. (2009) Incremental benefit–cost analysis Asset management Ahmed (1983) Integer model Li and Puyan (2006) Stochastic binary model Li et al. (2010) Stochastic binary model Transit fleet replacement Khasnabis et al. (2002) Linear model Downloaded from ascelibrary.org by Heriot-Watt University on 07/30/13. Copyright ASCE. For personal use only; all rights reserved. Mathew et al. (2010) Nonlinear model Mishra et al. (2010) Nonlinear model Traffic safety improvement Sinha et al. (1981) Multiyear optimization Brown et al. (1990) Integer model and dynamic programming Chowdhury and Garber (1996) Multiobjective model Chowdhury et al. (2000) Multiobjective model Melachrinoudis and Kozanidis (2002) Mixed-integer model Harwood et al. (2003) Integer model Kar and Datta (2004) Linear model Emergency response and security Karlaftis et al. (2007) Integer model Orabi et al. (2009) Multiobjective model Orabi et al. (2010) Multiobjective model Bier et al. (2009) Analytical model

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J. Manage. Eng. 2013.29:172-182. Problem Overview and Methodology sjðt þ 1Þ¼sjðtÞþvjðt þ 1Þð5Þ Problem Overview i x j Consider a transportation facility being at a level i;initial with where v ðtÞ = velocity vector of particle j at time t; sjðtÞ = position respect to the capacity and condition of its security infrastructure. vector of particle j at time t; vector sPb;j = personal best-ever This facility is assumed to have importance ratings with respect position of jth particle; and vector sGb = global best location found σ σ to its ridership ( trans;i) and its location ( strategic;i). The system/ by entire swarm. The acceleration coefficients c1 and c2 indicate facility operator wishes to upgrade the security of the transportation the degree of confidence in the best solution found by the individ- facility to the maximum possible level given existing equipment ual particle (c1, cognitive parameter) and by the whole swarm conditions, capacities, and station importance, under the constraint (c2, social parameter), respectively, and r1 and r2 are two random of available funds; the main interest is to optimally allocate funds to vectors uniformly distributed in the interval [0,1]. The symbol ∘ in stations for best overall security upgrades. Eq. (4) indicates the Hadamard product, i.e., the elementwise vector or matrix multiplication. Methodology Fig. 1 shows the flowchart of the PSO algorithm, and Fig. 2 depicts a particle’s movement in a two-dimensional design space. ’ sjðtÞ t Model Formulation The particle s current position at time is represented by the dotted circle at the lower left quadrant of the drawing, whereas the Optimal fund allocation in the context discussed is defined as a sjðt þ 1Þ t þ 1 nonlinear programming problem, formulated as follows: new position at time is represented by the dotted bold circle at the upper right of the drawing. Fig. 2 depicts how the XN particle’s movement is affected by (1) its velocity, vjðtÞ; (2) the σ • σ • ðx − x Þð1Þ Pb;j max trans;i strategic;i upgrade;i initial;i personal best-ever position of the particle, s ; and (3) the global i¼1 best location found by the entire swarm, sGb. subject to XN Kð ; ; x ; x Þ ≤ B ð2Þ Sizei Agei upgrade;i initial;i Target i¼1

xupgrade;i ∈ Z ð3Þ where I = set of N transportation facilities; i = transportation i ∈ I σ i facility ; trans;i = transportation importance of facility ; σ i x strategic;i = strategic importance of facility ; upgrade;i = anticipated i x (postupgrade) security level of facility ; initial;i = current security level of facility i; Sizei = size of facility i; Agei = age of facility i; K = cost for upgrading facility i from level xinitial;i to level xupgrade;i; and BTarget = available budget. The objective function [Eq. (1)] maximizes security-upgrade levels for facilities; a premium is given to those facilities with increased importance ratings. The budget constraint in Eq. (2) implies that cost K per facility is a function of its characteristics (age, size) and its current and anticipated security level. The aforementioned model is a variant of the well-known knapsack problem (Winston Fig. 1. Flowchart of particle swarm optimization algorithm 2003) with nonlinear constraints and a size of N integer decision variables.

Optimization Method In particle swarm optimization (PSO), multiple candidate solutions coexist and collaborate simultaneously. Each solution is called a particle, having a position and a velocity in the multidimensional design space, whereas a population of particles is called a swarm. A particle flies in the problem search space looking for the optimal Downloaded from ascelibrary.org by Heriot-Watt University on 07/30/13. Copyright ASCE. For personal use only; all rights reserved. position. As time passes through its quest, a particle adjusts its velocity and position according to its own experience and the experience of other (neighboring) particles. A particle’s experience is built by tracking and memorizing the best position encountered. A PSO system combines local search (through self-experience) with global search (through neighboring experience), attempting to balance exploration and exploitation. Each particle maintains in the multidimensional search space its two basic characteristics, velocity and position, which are updated as follows:

j j Pb;j j Gb j v ðt þ 1Þ¼wv ðtÞþc1r1 ∘ ðs − s ðtÞÞ þ c2r2 ∘ ðs − s ðtÞÞ Fig. 2. Visualization of particle’s movement in two-dimensional design ð4Þ space

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J. Manage. Eng. 2013.29:172-182. Fig. 3. Athens metro system

Model Application of the same size and type as the same metro station constructed today) (Table 4). Further, to consider the requirements for upgrad- – σ General Information ing metro stations of different type size parameter, size is used (Table 5). Table 6 lists the 52 metro stations and their age levels, The model is applied for the case of the Athens metro system size–types, strategic importance factors (related to the location of (Fig. 3), particularly in its 52 metro stations, each with a different the metro station), transportation importance (related to station size and age. Five different test cases are examined with varying demand), and initial security levels. target budgets: 5.0-, 10.0-, 20.0-, 40.0-, and 80.0-million monetary units (MUs) (using the data in Tables 3–6, readers can replicate the results of this application; MUs are used instead of actual currency Table 4. Age Levels of Metro Stations values for security purposes). The budget requirements for upgrad- σ ing the ith metro station from its existing security level to different Station construction period age (higher) levels are given in Table 3. To consider the additional 2001–2011 1.0 cost requirements imposed because of station age for the ith metro 1981–2000 1.5 σ 1951–1980 2.5 station, parameter age is used (the parameter is the ratio of the Downloaded from ascelibrary.org by Heriot-Watt University on 07/30/13. Copyright ASCE. For personal use only; all rights reserved. 1900–1950 4.0 budget for upgrading to a predefined security level a metro station

Table 3. Budget Upgrading in Monetary Units Table 5. Size of Metro Stations Security level Budget requirement (MUs) Station size σ 1 1,000 size 2 5,000 Multilevel 3.0 3 10,000 Large 2.0 4 100,000 Medium 1.3 5 500,000 Small 1.0

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J. Manage. Eng. 2013.29:172-182. Table 6. Station Characteristics σ σ x Station ID Station name Age (years) Size trans strategic initial 1 Kifisia 30–60 Medium 3 3 1 2KAT10–30 Small 5 2 1 3 Marousi 30–60 Small 3 4 2 4 Neratziotissa Under 10 Small 3 4 3 5 Irini 10–30 Medium 3 3 4 6 Irakleio 30–60 Small 3 4 1 7 Nea Ionia 30–60 Small 4 4 2 8 Pefkakia 30–60 Small 4 4 3 9 Perissos 30–60 Small 4 4 4 10 Ano Patisia 30–60 Small 3 4 3 11 Agios Eleftherios 30–60 Small 3 4 4 12 Patisia 30–60 Small 4 4 1 – 13 Agios Nikolao 30 60 Small 4 4 1 Fig. 4. Latin hypercube sampling in two-dimensional space 14 Attikin (old) 30–60 Medium 2 2 4 15 Attiki (new) Under 10 Large 2 2 3 16 Viktoria 30–60 Small 3 4 3 17 Omonia Under 10 Multilevel 1 1 2 18 Monastiraki (old) Over 60 Large 1 1 2 Table 7. Sensitivity Analysis of PSO Algorithm with Reference to 19 Monastiraki (new) Under 10 Multilevel 1 1 2 Objective Function Value 20 Thisio Over 60 Small 3 4 3 Parameters Standard 21 Petralona Over 60 Small 3 4 1 combination Mean deviation Best Worst 22 Tavros 10–30 Medium 3 4 2 23 Kallithea 30–60 Small 3 4 4 1 3.89E þ 02 1.49E þ 02 5.52E þ 02 1.78E þ 02 24 Moschato 30–60 Small 4 4 4 2 4.30E þ 02 9.87E þ 01 5.52E þ 02 1.78E þ 02 25 Faliro 10–30 Large 3 2 4 3 4.12E þ 02 1.03E þ 02 5.67E þ 02 1.78E þ 02 26 Piraeus Over 60 Multilevel 1 1 4 4 3.98E þ 02 1.01E þ 02 5.67E þ 02 1.78E þ 02 27 Agios Antonios Under 10 Large 2 3 1 5 3.89E þ 02 1.11E þ 02 5.67E þ 02 1.78E þ 02 28 Sepolia 10–30 Medium 4 2 4 6 4.29E þ 02 1.39E þ 02 5.67E þ 02 1.78E þ 02 29 Larisa 10–30 Medium 2 2 3 7 4.26E þ 02 1.07E þ 02 5.67E þ 02 1.78E þ 02 30 Metaxourgio 10–30 Large 3 4 4 8 4.67E þ 02 3.17E þ 01 5.67E þ 02 1.78E þ 02 31 Panepistimio 10–30 Large 2 2 2 9 3.89E þ 02 8.10E þ 01 5.67E þ 02 1.78E þ 02 32 Syntagma 10–30 Multilevel 1 1 1 10 3.88E þ 02 1.73E þ 02 5.67E þ 02 1.75E þ 02 33 Akropoli 10–30 Medium 3 1 4 11 4.52E þ 02 9.17E þ 01 5.67E þ 02 1.60E þ 02 34 Fix 10–30 Medium 3 3 4 12 4.02E þ 02 9.30E þ 01 5.67E þ 02 1.60E þ 02 35 Neos Kosmos 10–30 Medium 3 3 1 13 4.43E þ 02 1.06E þ 02 5.67E þ 02 1.60E þ 02 36 Agios Ioannis 10–30 Medium 3 3 2 14 4.59E þ 02 3.75E þ 01 5.67E þ 02 1.60E þ 02 37 Dafni 10–30 Medium 3 3 1 15 4.53E þ 02 1.21E þ 02 5.67E þ 02 1.60E þ 02 38 Agios Dimitrios Under 10 Large 2 3 4 16 4.72E þ 02 9.88E þ 01 5.67E þ 02 1.60E þ 02 39 Aigaleo Under 10 Large 2 3 2 17 4.70E þ 02 3.08E þ 01 5.67E þ 02 1.60E þ 02 40 Elaionas Under 10 Medium 5 5 1 18 4.55E þ 02 9.72E þ 01 5.67E þ 02 1.60E þ 02 41 Keramikos Under 10 Large 2 3 4 19 3.98E þ 02 1.35E þ 02 5.67E þ 02 1.60E þ 02 42 Evagelismos Under 10 Medium 3 2 4 20 3.73E þ 02 1.55E þ 02 5.67E þ 02 1.60E þ 02 43 Megaro Mousikis Under 10 Medium 3 2 4 44 Ampelokipi Under 10 Medium 2 3 4 45 Panormou Under 10 Large 2 3 4 46 Katechaki Under 10 Medium 3 3 4 The resulting optimization runs for dealing with the fund 47 Ethniki Amyna Under 10 Large 2 1 2 20 × 48 Holargos Under 10 Medium 3 3 1 allocation problem were equal to parameter combinations 49 Nomismatokopeio Under 10 Medium 3 3 2 100 random optimization runs ¼ 2; 000 optimization runs for 50 Agia Paraskevi Under 10 Large 3 3 4 BTarget ¼ 5.0-million MUs. The mean and standard deviation 51 Halandri Under 10 Large 3 3 2 values of the objective function value and the number of function 52 Doukissis Plakentias Under 10 Multilevel 2 3 2 evaluations are given in Tables 7 and 8, respectively. As shown in Table 7, the coefficient of variation of the mean values of the 20 parameter combinations is only 7.5%, whereas Downloaded from ascelibrary.org by Heriot-Watt University on 07/30/13. Copyright ASCE. For personal use only; all rights reserved. with reference to the function evaluations given in Table 8 the corresponding coefficient of variation is only 0.06%. From this, Particle Swarm Optimization Parameters it can be concluded that the PSO algorithm is not sensitive to To examine the influence of the parameters of the PSO algorithm, parameter values in the case of this fund allocation problem. a parametric study was performed to find the best parameters to be On the basis of the maximum mean value of the objective used for the PSO metaheuristic algorithm. For this, a sample of 20 function (Table 7), the 16th combination of parameters is used combinations of the following parameters was considered: number for the PSO metaheuristic algorithm. These values are as follows: of particles NP (defined in the space [50,200]); inertia weight w number of particles NP ¼ 190, inertia weight w ¼ 0.0314, cogni- (defined in the space [0.01,0.7]); cognitive parameter c1 (defined tive parameter c1 ¼ 0.02, and social parameter c2 ¼ 0.0151.For in the space [0.0,1.0]); and social parameter c2 (defined in the space comparative purposes, the termination criterion is the same for [0.0,1.0]). Parameter combinations were generated by means of all optimization runs; each procedure is terminated after 102 circles Latin hypercube sampling (see Fig. 4)(Washington et al. 2010). with no improvement.

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J. Manage. Eng. 2013.29:172-182. Table 8. Sensitivity Analysis of PSO Algorithm with Reference to Number Results of Function Evaluations The resulting optimization runs for the fund allocation problem with Parameters Standard five test cases were equal to 5 test cases × 100 optimization runs ¼ combination Mean deviation Best Worst 500 optimization runs. Figs. 5–9 depict the solutions obtained for 1 1,000,224 9.91E − 05 1,000,224 1,000,224 the optimal fund allocation problem when the PSO algorithm is 2 1,002,144 5.37E − 05 1,000,224 1,002,144 implemented for the five target budgets used. As shown in these 3 1,001,572 6.06E − 05 1,000,224 1,002,144 figures, for the cases of 5.0- to 40.0-million MUs all the available 6 38 − 05 4 1,001,280 . E 1,000,224 1,002,144 budget is used, satisfying constraint 3, whereas implementation of 7 38 − 05 5 1,000,188 . E 1,000,188 1,002,144 the algorithm for the case of B ¼ 80.0-million MUs results in 6 1,000,440 7.59E − 05 1,000,188 1,002,144 Target 7 1,000,080 5.93E − 05 1,000,080 1,002,144 46.7-million MUs used without achieving the upper security level 8 1,000,110 1.46E − 05 1,000,080 1,002,144 for all metro stations (this is denoted as Step1 in Fig. 9). For this 9 1,001,000 5.37E − 05 1,000,080 1,002,144 reason, a second implementation of the algorithm was examined 10 1,000,640 1.16E − 04 1,000,080 1,002,144 for the remaining 80.0 − 46.7 ¼ 33.3-million MUs, considering 11 1,000,512 4.52E − 05 1,000,080 1,002,144 that security levels at metro stations were below maximum (denoted 12 1,000,890 5.77E − 05 1,000,080 1,002,144 as Step2 in Fig. 9). 13 1,000,552 5.42E − 05 1,000,080 1,002,144 14 1,000,350 1.79E − 05 1,000,080 1,002,144 15 1,000,960 5.96E − 05 1,000,080 1,002,144 Conclusions 16 1,000,350 4.46E − 05 1,000,080 1,002,144 17 1,001,300 1.40E − 05 1,000,080 1,002,144 This paper focuses on developing a generic fund allocation 18 1,001,880 4.72E − 05 1,000,080 1,002,144 model and solution method for security upgrades of transportation 19 1,000,286 8.58E − 05 1,000,080 1,002,144 1 12 − 04 infrastructures. The model is a variant of the knapsack problem 20 1,000,400 . E 1,000,080 1,002,144 with a nonlinear budget constraint and is solved with the use of

Fig. 6. Target budget: 10-million MUs

J. Manage. Eng. 2013.29:172-182. Fig. 7. Target budget: 20-million MUs

Fig. 9. Target budget: 80-million MUs

a metaheuristics method (particle swarm optimization). The model fund allocations for different budget scenarios. The proposed was successfully applied to a real-world case (the security upgrade approach can successfully lead to optimal fund allocation for any of the 52 stations of the Athens metro system) and yielded feasible network of civil and transportation infrastructure.

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