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SPEA2: Improving the Strength Pareto Evolutionary Algorithm
, 2001
"... The Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler and Thiele 1999) is a relatively recent technique for finding or approximating the Pareto-optimal set for multiobjective optimization problems. In different studies (Zitzler and Thiele 1999; Zitzler, Deb, and Thiele 2000) SPEA has shown very ..."
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Cited by 708 (19 self)
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The Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler and Thiele 1999) is a relatively recent technique for finding or approximating the Pareto-optimal set for multiobjective optimization problems. In different studies (Zitzler and Thiele 1999; Zitzler, Deb, and Thiele 2000) SPEA has shown very good performance in comparison to other multiobjective evolutionary algorithms, and therefore it has been a point of reference in various recent investigations, e.g., (Corne, Knowles, and Oates 2000). Furthermore, it has been used in different applications, e.g., (Lahanas, Milickovic, Baltas, and Zamboglou 2001). In this paper, an improved version, namely SPEA2, is proposed, which incorporates in contrast to its predecessor a fine-grained fitness assignment strategy, a density estimation technique, and an enhanced archive truncation method. The comparison of SPEA2 with SPEA and two other modern elitist methods, PESA and NSGA-II, on different test problems yields promising results.
Evolutionary Algorithms for Multiobjective Optimization
, 2002
"... Multiple, often conflicting objectives arise naturally in most real-world optimization scenarios. As evolutionary algorithms possess several characteristics due to which they are well suited to this type of problem, evolution-based methods have been used for multiobjective optimization for more than ..."
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Cited by 450 (13 self)
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Multiple, often conflicting objectives arise naturally in most real-world optimization scenarios. As evolutionary algorithms possess several characteristics due to which they are well suited to this type of problem, evolution-based methods have been used for multiobjective optimization for more than a decade. Meanwhile evolutionary multiobjective optimization has become established as a separate subdiscipline combining the fields of evolutionary computation and classical multiple criteria decision making. In this paper, the basic principles of evolutionary multiobjective optimization are discussed from an algorithm design perspective. The focus is on the major issues such as fitness assignment, diversity preservation, and elitism in general rather than on particular algorithms. Different techniques to implement these strongly related concepts will be discussed, and further important aspects such as constraint handling and preference articulation are treated as well. Finally, two applications will presented and some recent trends in the field will be outlined.
Indicator-based selection in multiobjective search
- in Proc. 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII
, 2004
"... Abstract. This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection ..."
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Cited by 172 (12 self)
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Abstract. This paper discusses how preference information of the decision maker can in general be integrated into multiobjective search. The main idea is to first define the optimization goal in terms of a binary performance measure (indicator) and then to directly use this measure in the selection process. To this end, we propose a general indicator-based evolutionary algorithm (IBEA) that can be combined with arbitrary indicators. In contrast to existing algorithms, IBEA can be adapted to the preferences of the user and moreover does not require any additional diversity preservation mechanism such as fitness sharing to be used. It is shown on several continuous and discrete benchmark problems that IBEA can substantially improve on the results generated by two popular algorithms, namely NSGA-II and SPEA2, with respect to different performance measures. 1
Combining convergence and diversity in evolutionary multi-objective optimization
- Evolutionary Computation
, 2002
"... Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms c ..."
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Cited by 159 (15 self)
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Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to �nd a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Paretooptimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modi�cations to the baseline algorithm are also suggested. The concept of-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.
Multi-Objective Optimization Using Genetic Algorithms: A Tutorial
"... abstract – Multi-objective formulations are a realistic models for many complex engineering optimization problems. Customized genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In many real-life problems, objectives under consid ..."
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Cited by 114 (0 self)
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abstract – Multi-objective formulations are a realistic models for many complex engineering optimization problems. Customized genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to these problems. In many real-life problems, objectives under consideration conflict with each other, and optimizing a particular solution with respect to a single objective can result in unacceptable results with respect to the other objectives. A reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. In this paper, an overview and tutorial is presented describing genetic algorithms developed specifically for these problems with multiple objectives. They differ from traditional genetic algorithms by using specialized fitness functions, introducing methods to promote solution diversity, and other approaches. 1.
Balance between Genetic Search and Local Search in Memetic Algorithms for Multiobjective Permutation Flowshop Scheduling
- IEEE Trans. on Evolutionary Computation
, 2002
"... This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by the hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Paretofront. On the other hand, the main negative ..."
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Cited by 100 (14 self)
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This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by the hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Paretofront. On the other hand, the main negative effect is the increase in the computation time per generation. Thus the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: SPEA and NSGA-II. Finally, we demonstrate that local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.
The Pareto Envelope-based Selection Algorithm for Multiobjective Optimization
- Proceedings of the Parallel Problem Solving from Nature VI Conference
, 2000
"... . We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelope-based Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hyper-grid based scheme. PESA's selection method is relatively unusual in comparison with current ..."
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Cited by 96 (2 self)
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. We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelope-based Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hyper-grid based scheme. PESA's selection method is relatively unusual in comparison with current well known multiobjective evolutionary algorithms, which tend to use counts based on the degree to which solutions dominate others in the population. The diversity maintenance method is similar to that used by certain other methods. The main attraction of PESA is the integration of selection and diversity maintenance, whereby essentially the same technique is used for both tasks. The resulting algorithm is simple to describe, with full pseudocode provided here and real code available from the authors. We compare PESA with two recent strongperforming MOEAs on some multiobjective test problems recently proposed by Deb. We find that PESA emerges as the best method overall on these problems...
The Self-Adaptive Pareto Differential Evolution
- In Congress on Evolutionary Computation (CEC’2002
, 2002
"... The Pareto Differential Evolution (PDE) algorithm was introduced last year and showed competitive results. The behavior of PDE, as in many other evolutionary multiobjective optimization (EMO) methods, varies according to the crossover and mutation rates. In this paper, we present a new version of PD ..."
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Cited by 79 (4 self)
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The Pareto Differential Evolution (PDE) algorithm was introduced last year and showed competitive results. The behavior of PDE, as in many other evolutionary multiobjective optimization (EMO) methods, varies according to the crossover and mutation rates. In this paper, we present a new version of PDE with self-adaptive crossover and mutation. We call the new version Self-adaptive Pareto Differential Evolution (SPDE). The emphasis of this paper is to analyze the dynamics and behavior of SPDE. The experiments will also show that the algorithm is very competitive to other EMO algorithms.
A Tutorial on Evolutionary Multiobjective Optimization
- In Metaheuristics for Multiobjective Optimisation
, 2003
"... Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. ..."
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Cited by 78 (0 self)
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Mu l ip often conflicting objectives arise naturalj in most real worl optimization scenarios. As evol tionaryalAxjO hms possess several characteristics that are desirabl e for this type of probl em, this clOv of search strategies has been used for mul tiobjective optimization for more than a decade. Meanwhil e evol utionary mul tiobjective optimization has become establ ished as a separate subdiscipl ine combining the fiel ds of evol utionary computation and cl assical mul tipl e criteria decision ma ing. This paper gives an overview of evol tionary mu l iobjective optimization with the focus on methods and theory. On the one hand, basic principl es of mu l iobjective optimization and evol tionary alA#xv hms are presented, and various al gorithmic concepts such as fitness assignment, diversity preservation, and el itism are discussed. On the other hand, the tutorial incl udes some recent theoretical resul ts on the performance of mu l iobjective evol tionaryalvDfifl hms and addresses the question of how to simpl ify the exchange of methods and appl ications by means of a standardized interface. 1
