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.

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.

In this paper we describe a method for improving genetic-algorithm-based optimization using search control. The idea is to utilize the sequence of points explored during a search to guide further exploration. The proposed method is particularly suitable for continuous spaces with expensive evaluation functions, such as arise in engineering design. Empirical results in several engineering design domains demonstrate that the proposed method can significantly improve the efficiency and reliability of the GA optimizer.

In this paper we describe a method for improving genetic-algorithm-based optimization using reduced models. The main idea is to maintain a large sample of the points encountered in the course of the optimization divided into clusters. Least squares quadratic approximations are periodically formed of the entire sample as well as the big enough clusters. These approximations are used as a reduced model to compute cheap approximations of the fitness function through a two phase approach in which the point is first classified (into potentially feasible, infeasible or unevaluable) and then its fitness is computed accordingly. We then use the reduced models to speedup the GA optimization by making the genetic operators such as mutation and crossover more informed. The proposed approach is particularly suitable for search spaces with expensive evaluation functions, such as arise in engineering design. Empirical results in several engineering design domains demonstrate that the proposed metho...

Abstract—In this paper, an adaptive tradeoff model (ATM) is proposed for constrained evolutionary optimization. In this model, three main issues are considered: 1) the evaluation of infeasible solutions when the population contains only infeasible individuals; 2) balancing feasible and infeasible solutions when the population consists of a combination of feasible and infeasible individuals; and 3) the selection of feasible solutions when the population is composed of feasible individuals only. These issues are addressed in this paper by designing different tradeoff schemes during different stages of a search process to obtain an appropriate tradeoff between objective function and constraint violations. In addition, a simple evolutionary strategy (ES) is used as the search engine. By integrating ATM with ES, a generic constrained optimization evolutionary algorithm (ATMES) is derived. The new method is tested on 13 well-known benchmark test functions, and the empirical results suggest that it outperforms or performs similarly to other state-of-the-art techniques referred to in this paper in terms of the quality of the resulting solutions. Index Terms—Constrained optimization, evolutionary strategy (ES), multiobjective optimization, tradeoff model. I.

Abstract: Constrained optimization problems (COPs) are mathematical programming problems frequently encountered in the disciplines of science and engineering application. Solving COPs has become an important research area of evolutionary computation in recent years. In this paper, the state-of-the-art of constrained optimization evolutionary algorithms (COEAs) is surveyed from two basic aspects of COEAs (i.e., constraint-handling techniques and evolutionary algorithms). In addition, this paper discusses some important issues of COEAs. More specifically, several typical algorithms are analyzed in detail. Based on the analyses, it concluded that to obtain competitive results, a proper constraint-handling technique needs to be considered in conjunction with an appropriate search algorithm. Finally, the open research issues in this field are also pointed out. Key words: evolutionary algorithm; constraint-handling technique; constrained optimization; multi-objective

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Intheir originalversions, nature-inspiredsearch algorithmslackamechanism to deal with the constraints of a numerical optimization problem. Nowadays, however, there exists a considerable amount of research devoted to design techniques for handling constraints within a nature-inspired algorithm. This paper presents ananalysis ofthe most relevant types of thosetechniques. For each one of them, the most popular approaches are analyzed in more detail and some representative instantiations are further discussed. In the last part of the paper, some of the future trends in the area are briefly presented and then the conclusions of this paper are shown.