Introduction Genetic programming is a domain-independent problem-solving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring genetic operations such as crossover (sexual recombination) and mutation. John Holland's pioneering Adaptation in Natural and Artificial Systems (1975) described how an analog of the evolutionary process can be applied to solving mathematical problems and engineering optimization problems using what is now called the genetic algorithm (GA). The genetic algorithm attempts to find a good (or best) solution to the problem by genetically breeding a population of individuals over a series of generations. In the genetic algorithm, each individual in the population represents a candidate solut

. This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described mentioning its advantages and disadvantages, their degree of applicability and some of their known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed. Keywords: multiobjective optimization, multicriteria optimization, vector optimization, genetic algorithms, evolutionary algorithms, artificial intelligence. 1 Introduction Since the pioneer work of Rosenberg in the late 60s regarding the possibility of using genetic-based search to deal with multiple objectives, this new area of research (now called evolutionary multiobjective optimization) has grown 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.

Penalty functions are often used in constrained optimization. However, it is very difficult to strike the right balance between objective and penalty functions. This paper introduces a novel approach to balance objective and penalty functions stochastically, i.e., stochastic ranking, and presents a new view on penalty function methods in terms of the dominance of penalty and objective functions. Some of the pitfalls of naive penalty methods are discussed in these terms. The new ranking method is tested using a (µ, ) evolution strategy on 13 benchmark problems. Our results show that suitable ranking alone (i.e., selection), without the introduction of complicated and specialized variation operators, is capable of improving the search performance significantly.

This paper presents a new approach to handle constraints using evolutionary algorithms. The new technique treats constraints as objectives, and uses a multiobjective optimization approach to solve the re-stated single-objective optimization problem. The new approach is compared against other numerical and evolutionary optimization techniques in several engineering optimization problems with different kinds of constraints. The results obtained show that the new approach can consistently outperform the other techniques using relatively small sub-populations, and without a significant sacrifice in terms of performance.

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Despite the extended applicability of evolutionary algorithms to a wide range of domains, the fact that these algorithms are unconstrained optimization techniques leaves open the issue regarding how to incorporate constraints of any kind (linear, non-linear, equality and inequality) into the fitness function as to search efficiently. The main goal of this paper is to provide a detailed and comprehensive survey of the many constraint handling approaches that have been proposed for evolutionary algorithms, analyzing in each case their advantages and disadvantages, and concluding with some of the most promising paths of research.

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.

This paper introduces the notion of using co-evolution to adapt the penalty factors of a fitness function incorporated in a genetic algorithm for numerical optimization. The proposed approach produces solutions even better than those previously reported in the literature for other (GA-based and mathematical programming) techniques that have been particularly fine-tuned using a normally lengthy trial and error process to solve a certain problem or set of problems. The present technique is also easy to implement and suitable for parallelization, which is a necessary further step to improve its current performance. Key words: genetic algorithms, constraint handling, co-evolution, penalty functions, self-adaptation, evolutionary optimization, numerical optimization. 1 Introduction The importance of genetic algorithms (GAs) as a powerful tool for engineering optimization has been widely shown in the last few years through a vast amount of applications ([1,2]). However, even when GAs hav...

In this paper we explore established methods for optimising multi-objective functions whilst addressing the problem of preliminary design. Methods from the literature are investigated and new ones introduced. All methods are evaluated within a collaborative project with British Aerospace for whole system airframe design and the basic problems and difficulties of preliminary design methodology are discussed. Our Genetic Algorithm is expanded to integrate different methods for optimising multi--objective functions. First, methods based on scalarisation and the utilisation of weights are addressed. Methods based on Pareto order are then analysed and two different sorting techniques (dominated/non--dominated and Pareto rank) investigated. Finally, several variants of sub--population based algorithms are presented. All presented methods are also analysed in the context of whole system design, discussing their advantages and disadvantages. 1 Introduction When dealing with industrial design ...