SPEA2: Improving the strength Pareto evolutionary algorithms (2002)

by E Zitzler, M Laumanns, L Thiele
Venue:EUROGEN 2001. Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems
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Evolutionary Algorithms for Multiobjective Optimization

by Eckart Zitzler , 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 ..."
Abstract - Cited by 450 (13 self) - Add to MetaCart
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

by Eckart Zitzler, Simon Künzli - 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 ..."
Abstract - Cited by 172 (12 self) - Add to MetaCart
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
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Scalable Test Problems for Evolutionary Multi-Objective Optimization

by Kalyanmoy Deb, Lothar Thiele, Marco Laumanns, Eckart Zitzler - Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH , 2001
"... After adequately demonstrating the ability to solve di#erent two-objective optimization problems, multi-objective evolutionary algorithms (MOEAs) must now show their e#cacy in handling problems having more than two objectives. In this paper, we have suggested three di#erent approaches for systema ..."
Abstract - Cited by 148 (21 self) - Add to MetaCart
After adequately demonstrating the ability to solve di#erent two-objective optimization problems, multi-objective evolutionary algorithms (MOEAs) must now show their e#cacy in handling problems having more than two objectives. In this paper, we have suggested three di#erent approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of exact shape and location of the resulting Pareto-optimal front, and introduction of controlled di#culties in both converging to the true Pareto-optimal front and maintaining a widely distributed set of solutions are the main features of the suggested test problems. Because of the above features, they should be found useful in various research activities on MOEAs, such as testing the performance of a new MOEA, comparing di#erent MOEAs, and better understanding of the working principles of MOEAs.
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PISA - A Platform and Programming Language Independent Interface for Search Algorithms

by Stefan Bleuler, Marco Laumanns, Lothar Thiele, Eckart Zitzler , 2003
"... This paper int roduces at ext based int rface (PISA)t hat allows t separat ty algorit hm-specific part of an op t mizer fromt he applicat ionspecific part . These part s are implement ed as independent programs forming freelycombinable modules. ..."
Abstract - Cited by 107 (11 self) - Add to MetaCart
This paper int roduces at ext based int rface (PISA)t hat allows t separat ty algorit hm-specific part of an op t mizer fromt he applicat ionspecific part . These part s are implement ed as independent programs forming freelycombinable modules.
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A systematic approach to exploring embedded system architectures at multiple abstraction levels,”

by A D Pimentel, C Erbas, S Polstra - IEEE Transaction Computers, , 2006
"... ..."
Abstract - Cited by 97 (37 self) - Add to MetaCart
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A Tutorial on Evolutionary Multiobjective Optimization

by Eckart Zitzler, Marco Laumanns, Stefan Bleuler - 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. ..."
Abstract - Cited by 78 (0 self) - Add to MetaCart
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
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Multiobjective optimization problems with complicated pareto sets

by Hui Li, Qingfu Zhang, Senior Member - MOEA/D and NSGA-II,” Trans. Evolutionary Computation , 2009
"... Abstract—Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper in-troduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shap ..."
Abstract - Cited by 66 (11 self) - Add to MetaCart
Abstract—Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper in-troduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of multiobjective evolutionary algorithms for dealing with complicated PS shapes. It also pro-poses a new version of MOEA/D based on differential evolution (DE), i.e., MOEA/D-DE, and compares the proposed algorithm with NSGA-II with the same reproduction operators on the test instances introduced in this paper. The experimental results indicate that MOEA/D could significantly outperform NSGA-II on these test instances. It suggests that decomposition based mul-tiobjective evolutionary algorithms are very promising in dealing with complicated PS shapes. Index Terms—Aggregation, decomposition, differential evolu-tion, evolutionary algorithms, multiobjective optimization, Pareto optimality, test problems. I.
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A New Multiobjective Evolutionary Algorithm For Environmental Economic Power Dispatch

by M. A. Abido , 2001
"... In this paper, a new multiobjective evolutionary algorithm for Environmental/Economic power Dispatch (EED) optimization problem is presented. The EED problem is formulated as a nonlInear constrained multiobjective optimization problem with both equality and inequality constraints. A new Nondominated ..."
Abstract - Cited by 60 (1 self) - Add to MetaCart
In this paper, a new multiobjective evolutionary algorithm for Environmental/Economic power Dispatch (EED) optimization problem is presented. The EED problem is formulated as a nonlInear constrained multiobjective optimization problem with both equality and inequality constraints. A new Nondominated Sorting Genetic Algorithm (NSGA) based approach is proposed to handle the problem as a true multiobjective optimization problem with competing and non-commensurable objectives. The proposed approach employs a diversity-preserving technique to overcome the premature convergence and search bias problems and produce a well-distributed Pareto-optimal set of nondominated solutions. A hierarchical clustering technique is also imposed to provide the decision maker with a representative and manageable Pareto- optimal set. Several optimization runs of the proposed approach are carded out on a standard IEEE test system. The results demonstrate the capabilities of the proposed NSGA based approach to generate the true Pareto-optimal set of nondominated solutions of the multiobjective EED problem in one single run. Simulation results with the proposed approach have been compared to those reported in the literature. The comparison shows the superiority of the proposed NSGA based approach and confirms its potential to solve the multiobjective EED problem.
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Performance Scaling of Multi-Objective Evolutionary Algorithms

by Vineet Khare , 2002
"... In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. If none of the objectives have preference over the othe ..."
Abstract - Cited by 57 (5 self) - Add to MetaCart
In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. If none of the objectives have preference over the other, none of these trade-off solutions can be said to be better than any other solution in the set. Multi-objective Evolutionary Algorithms (MOEAs) can find these optimal trade-offs in order to get a set of solutions that are optimal in an overall sense.

DEMO: Differential Evolution for multiobjective optimization

by Tea Robič, Bogdan Filipič - In Proceedings of the 3rd International Conference on Evolutionary MultiCriterion Optimization (EMO 2005 , 2005
"... Abstract. Differential Evolution (DE) is a simple but powerful evolutionary optimization algorithm with many successful applications. In this paper we propose Differential Evolution for Multiobjective Optimization (DEMO) – a new approach to multiobjective optimization based on DE. DEMO combines the ..."
Abstract - Cited by 53 (2 self) - Add to MetaCart
Abstract. Differential Evolution (DE) is a simple but powerful evolutionary optimization algorithm with many successful applications. In this paper we propose Differential Evolution for Multiobjective Optimization (DEMO) – a new approach to multiobjective optimization based on DE. DEMO combines the advantages of DE with the mechanisms of Paretobased ranking and crowding distance sorting, used by state-of-the-art evolutionary algorithms for multiobjective optimization. DEMO is implemented in three variants that achieve competitive results on five ZDT test problems. 1