Abstract-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 ( ) 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.

Abstract-A common approach to constraint handling in evolutionary optimization is to apply a penalty function to bias the search towards a feasible solution. It has been proposed that the subjective setting of various penalty parameters can be avoided using a multi-objective formulation. This paper analyses and explains in depth why and when the multi-objective approach to constraint handling is expected to work or fail. Furthermore, an improved evolutionary algorithm based on evolution strategies and differential variation is proposed. Extensive experimental studies have been carried out. Our results reveal that the unbiased multi-objective approach to constraint handling may not be as effective as one may have assumed.

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Abstract-This paper compares the use of temporal difference learning (TDL) versus co-evolutionary learning (CEL) for acquiring position evaluation functions for the game of Othello. The paper provides important insights into the strengths and weaknesses of each approach. The main findings are that for Othello, TDL learns much faster than CEL, but that properly tuned CEL can learn better playing strategies. For CEL, it is essential to use parent-child weighted averaging in order to achieve good performance. Using this method a high quality weighted piece counter was evolved, and was shown to significantly outperform a set of standard heuristic weights.

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