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...

Though it has been claimed that elitism could improve evolutionary multi-objective search significantly, a thorough and extensive evaluation of its effects is still missing. Guidelines on how elitism could successfully be incorporated have not yet been developed. This paper presents a unified model of multi-objective evolutionary algorithms, in which arbitrary variation and selection operators can be combined as building blocks, including archiving and re-insertion strategies. The presented model enables most specific multi-objective (evolutionary) algorithm to be formulated as an instance of it, which will be demonstrated by simple examples. We will further show how elitism can be quantified by the model's parameters and how this allows an easy evaluation of the effect of elitism on different algorithms. 1 Introduction The aim of this study is to provide a systematic approach to elitism in multi-objective evolutionary algorithms (MOEA). Multi-objective optimization can be seen as a ...

Th practical use of multiobjective optimization tools in industry is still an open issue. A strategy for reduction of objective function calls is often essential, at a fixed degree of Pareto Optimal Front (POF) approximation accuracy . Toth aim an extension of single-objective NN-based GRS meth ods to Pareto Optimal Front (POF) approximation is proposed.

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Abstract. When tackling the multicriteria optimization of a device in electrical engineering, the exhaustive sampling of Pareto optimal front implies the use of complex and timeconsuming algorithms that are unpractical from the industrial viewpoint. In several cases, however, the accurate identification of a few non-dominated solutions is often sufficient for the design purposes. An evolutionary methodology of lowest order, dealing with a small number of individuals, is proposed to obtain a cost-effective approximation of non-dominated solutions. In particular, the algorithm assigning the fitness enables the designer to pursue either shape or performance diversity of the device. The optimal shape design of a shielded reactor, based on the optimization of both cost and performance of the device, is presented as a real-life case study. 1

In this thesis the problem of conceptual engineering design and the possible use of adaptive search techniques and other machine based methods therein are explored. For the multi–objective optimisation (MOO) within conceptual design problem, genetic algorithms (GA) adapted to MOO are used and various techniques explored: weighted sums, lexicographic order, Pareto method with and without ranking, VEGA–like approaches etc. Large number of runs are performed for finding the optimal configuration and setting of the GA parameters. A novel method, weighted Pareto method is introduced and applied to a real–world optimisation problem. Decision support methods within conceptual engineering design framework are discussed and a new preference method developed. The preference method for translating vague qualitative categories (such as “more important”, “much less important ” etc.) into quantitative values (numbers) is based on fuzzy preferences and graph theory methods. Several applications of preferences are presented and discussed: ¯in weighted sum based optimisation methods; ¯in weighted Pareto method;

Though optimization problems in industrial electromagnetic design are often truly multiobjective, solving them by evolutionary Pareto Optimal Front approximation is often unpractical, due to the high computational cost of objective evaluations. In order to overcome this drawback, an extension of classical single-objective Generalized Response Surface (GRS) methods to Pareto-optimal front approximation is proposed. Such an extension implies essential modifications, due to the increased complexity of multiobjective optimization problems.