IEEE COMMUNICATIONS SURVEYS AND TUTORIALS, VOL. X, NO. X, 2016 1 A Survey on Modeling and Optimizing Multi-Objective Systems Jin-Hee Cho, Senior Member, IEEE, Yating Wang, Ing-Ray Chen, Member, IEEE, Kevin S. Chan, Member, IEEE, and Ananthram Swami, Fellow, IEEE Abstract—Many systems or applications have been developed no trusted centralized entity). Further, our interest is in how to for distributed environments with the goal of attaining multiple optimize the performance of a system with multiple objectives. objectives in the face of environmental challenges such as high Example applications include coalition formation (or team dynamics/hostility, or severe resource constraints (e.g., energy or communications bandwidth). Often the multiple objectives are composition), cluster formation, task assignment, task schedul- conflicting with each other, requiring optimal tradeoff analyses ing, or resource allocation in various network environments between the objectives. This work is mainly concerned with how including wireless sensor networks, mobile ad hoc networks, to model multiple objectives of a system and how to optimize cloud computing, multi-agent systems, web-based social net- their performance. We first conduct a comprehensive survey of works, supply chain environments, P2P networks, and so the state-of-the-art modeling and solution techniques to solve multi-objective optimization problems. In addition, we discuss forth. Many MOO techniques have been explored, such as pros and cons of each modeling and optimization technique for evolutionary algorithms, game theoretic approaches, and other in-depth understanding. Further, we classify existing approaches metaheuristic algorithms. We aim to summarize the general based on the types of objectives and investigate main problem trends on how modeling and solution techniques to solve MOO domains, critical tradeoffs, and key techniques used in each class. problems evolve as the main concerns of system platforms We discuss the overall trends of the existing techniques in terms of application domains, objectives, and techniques. Further, we change. discuss challenging issues based on the inherent nature of MOO For those who want to take a first step to initiate their problems. Finally, we suggest future work directions in terms of research in the area of modeling and optimizing systems with what critical design factors should be considered to design and multiple objectives, we are hopeful that this paper can provide analyze a system with multiple objectives. useful background and guidelines. Index Terms—Multi-objective optimization, genetic algorithms, evolutionary algorithms, game theory, auction theory, trust, distributed systems. A. Existing Survey Papers on Multi-Objective Optimization Researchers have explored MOO problems since the 1970’s in various domains for system control, decision making, circuit I. INTRODUCTION design, operations research, networking and telecommunica- EAL-world situations, such as those arising in economics tions protocol design, and so forth. Several comprehensive R or engineering environments, are complex and multi- survey papers on MOO solutions have appeared since the dimensional in nature. Oftentimes, the scenarios are charac- 1990’s. terized by actors within these environments who are operating Shin and Ravindran [185] survey interactive methods to with a varied set of motivations and/or objectives [132]. solve continuous MOO problems and corresponding appli- Multiple objectives are often present, typically as a utility (or cations. The authors discuss characteristics of preference payoff) function. In many situations, however, maximizing all assessments, assumptions to ensure the functionality of a of the payoff functions is an over-constrained problem, as the method, and relationships between different methods. Ulungu objectives may be in conflict with each other. One can con- and Teghem [202] review existing work on multi-objective sider Pareto optimal situations where tradeoffs between these combinatorial optimization (MOCO) problems because multi- conflicting payoff functions are studied on a region, called objective linear programming (MOLP) methods had failed to the Pareto frontier. Navigation on the Pareto frontier enables solve MOO problems with discrete variables in many real- one to optimize the design of such systems, performing multi- world applications. objective optimization (MOO) [46]. With significantly increased attention on MOO problems In this survey paper, we are particularly interested in how and solution methods, many survey papers have been pub- to model multiple objectives of a system, interwoven with lished from 2000 until now. In particular, several MOO survey complex system constraints (e.g., resource constraints, high papers discuss evolutionary algorithms [46, 48, 47, 56, 117, adversarial conditions or dynamics, or distributed nature with 198, 205] or bio-inspired algorithms [62, 170]. Okahe et al. [156] conduct a survey on how to measure quality of MOO J-H. Cho, K.S. Chan and A. Swami are with US Army Research algorithms and propose various types of performance indices. Laboratory Adelphi, MD email: fjin-hee.cho.civ, kevin.s.chan.civ, anan- Also very recently Meng et al. [135] published a survey paper [email protected] Y. Wang and I-R. Chen are with the Computer Science Department, Virginia on MOO design methods using game theory. As seen in [135], Tech, Falls Church, VA email: fyatingw, [email protected] a change of MOO modeling technique may be necessitated due IEEE COMMUNICATIONS SURVEYS AND TUTORIALS, VOL. X, NO. X, 2016 2 to diverse needs of distributed systems with distinct multiple C. Structure of this Survey Paper objectives as opposed to centralized systems with only system The rest of this paper is structured as follows. level objectives. Compared to the existing survey papers, our survey paper is • Section II: We survey common applications to which unique in providing a comprehensive survey on both solution MOO modeling and solution techniques are applicable. In techniques (e.g., scalarization-based, metaheuristics, hybrid addition, we discuss conflicting multiple objectives that metaheuristics, and trust-based approaches) and modeling are considered in example applications. techniques (e.g., cooperative game theory or auction theory). • Section III: We provide basic background knowledge We use our prior classification method developed in [43] about MOO problem definition and formulation. We also with an in-depth survey to classify existing MOO modeling explain Pareto optimum and frontier for achieving MOO. and solution techniques based on the types of objectives. • Section VI: We survey solution techniques that solve Then we discuss the overall trends to analyze the tradeoff various MOO problems, including scalarization-based between solution optimality and solution search efficiency methods, metaheuristics, hybrid metaheuristics, and trust- (i.e., complexity) of the surveyed MOO solution techniques. based solutions. We discuss the pros and cons of each We summarize the overall trends of existing works to solve solution technique. MOO problems, provide discussions of key challenging issues • Section V: We survey modeling techniques for appli- in MOO problems, and point to potential research directions cations/systems with MOO goals, including cooperative based on the overall trends observed from the survey results. game theory and auction theory. We discuss the pros and cons of each modeling technique. • Section VI: We classify existing modeling and solution B. Key Contributions techniques to solve various MOO problems into three A preliminary version of this work was published in [43]. classes according to the types of objectives. We substantially extend the conference paper [43] with the • Section VII: We discuss the challenging issues derived following contributions: from the nature of MOO problems, including uncer- 1) This work provides a comprehensive survey of not tainty, Pareto optimality conditions, duality, solvability, only key modeling techniques for modeling applica- and stability, and the tradeoff between optimality and tions/systems with MOO requirements, but also solution complexity. techniques. We discuss each technique with its pros and • Section VIII: We suggest future research directions based cons that could lead to an insightful decision on the on the overall trends observed from the survey results. choice of techniques based on the distinct needs of each • Section IX: We summarize the key ideas from this survey. application; 2) This work uses the classification method, developed in II. SYSTEMS WITH MULTIPLE OBJECTIVES our prior work [43], to categorize existing studies on various MOO problems in terms of the characteristics MOO problems are commonly encountered in many ap- of objectives. This work substantially extends [43] with plications. In this section, we survey the major application more detailed descriptions of techniques and trends domains that have explored techniques or algorithms to solve observed based on the in-depth literature review asso- MOO problems. ciated with the three classes. Based on the classification Business Settings: Multiple criteria decision making sit- method in [43], we classify existing works into three uations are commonly observed where coalitions or alliances classes based on the nature of objectives, either system are established between buyers and sellers [99], customers and objectives or individual objectives in which an individual vendors [30],