In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of c...

This paper provides a comprehensive survey of the most popular constraint-handling techniques currently used with evolutionary algorithms. We review approaches that go from simple variations of a penalty function, to others, more sophisticated, that are biologically inspired on emulations of the immune system, culture or ant colonies. Besides describing briefly each of these approaches (or groups of techniques), we provide some criticism regarding their highlights and drawbacks. A small comparative study is also conducted, in order to assess the performance of several penalty-based approaches with respect to a dominance-based technique proposed by the author, and with respect to some mathematical programming approaches. Finally, we provide some guidelines regarding how to select the most appropriate constraint-handling technique for a certain application, ad we conclude with some of the the most promising paths of future research in this area.

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.

s: Jan. 1992 -- Dec. 1994 ffl CTI: Current Technology Index Jan./Feb. 1993 -- Jan./Feb. 1994 ffl DAI: Dissertation Abstracts International: Vol. 53 No. 1 -- Vol. 55 No. 4 (1994) ffl EEA: Electrical & Electronics Abstracts: Jan. 1991 -- Dec. 1994 ffl P: Index to Scientific & Technical Proceedings: Jan. 1986 -- Feb. 1995 (except Nov. 1994) ffl EI A: The Engineering Index Annual: 1987 -- 1992 ffl EI M: The Engineering Index Monthly: Jan. 1993 -- Dec. 1994 The following GA researchers have already kindly supplied their complete autobibliographies and/or proofread references to their papers: Dan Adler, Patrick Argos, Jarmo T. Alander, James E. Baker, Wolfgang Banzhaf, Ralf Bruns, I. L. Bukatova, Thomas Back, Yuval Davidor, Dipankar Dasgupta, Marco Dorigo, Bogdan Filipic, Terence C. Fogarty, David B. Fogel, Toshio Fukuda, Hugo de Garis, Robert C. Glen, David E. Goldberg, Martina Gorges-Schleuter, Jeffrey Horn, Aristides T. Hatjimihail, Mark J. Jakiela, Richard S. Judson, Akihiko Konaga...

This paper presents a Particle Swarm Optimization (PSO) algorithm for multiobjective optimization problems. PSO is modified by using a dynamic neighborhood strategy, new particle memory updating, and one-dimension optimization to deal with multiple objectives. Several benchmark cases were tested and showed that PSO could efficiently find multiple Pareto optimal solutions.

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.

Abstract: Developments in computational models of evolutionary processes have led to the realisation of powerful, robust and general optimization and adaptive systems collectively called evolutionary algorithms. In this paper we provide an overview of evolutionary algorithms and consider the features and characteristics that are particularly appropriate for control engineering applications. The versatile and robust qualities of these algorithms are considered and a number of application areas described.

Evolutionary computation is emerging as a new engineering computational paradigm, which may significantly change the present structural design practice. For this reason, an extensive study of evolutionary computation in the context of structural design has been conducted in the Information Technology and Engineering School at George Mason University and its results are reported here. First, a general introduction to evolutionary computation is presented and recent developments in this field are briefly described. Next, the field of evolutionary design is introduced and its relevance to structural design is explained. Further, the issue of creativity/novelty is discussed and possible ways of achieving it during a structural design process are suggested. Current research progress in building engineering systems ’ representations, one of the key issues in evolutionary design, is subsequently discussed. Next, recent developments in constraint-handling methods in evolutionary optimization are reported. Further, the rapidly growing field of evolutionary multiobjective optimization is presented and briefly described. An emerging subfield of coevolutionary design is subsequently introduced and its current advancements reported. Next, a comprehensive review of the applications of evolutionary computation in structural design is provided and chronologically classified. Finally, a summary of the current research status and a discussion on the most promising paths of future research are also presented.

The use of evolutionary algorithms (EAs) to solve problems with multiple objectives (known as Multi-objective Optimization Problems (MOPs)) has attracted much attention recently. Being popula-tion based approaches, EAs offer a means to find a group of pareto-optimal solutions in a single run. Differential Evolution (DE) is an EA that was developed to handle optimization problems over continuous domains. The objective of this paper is to introduce a novel Pareto–frontier Differential Evolution (PDE) algorithm to solve MOPs. The solutions provided by the proposed algorithm for two standard test problems, outperform the Strength Pareto Evolutionary Algorithm, one of the state-of-the-art evolutionary algorithm for solving MOPs. 1