Computers & Operations Research 35 (2008) 2925 – 2936 www.elsevier.com/locate/cor Design of an adaptive mutation operator in an electrical load management case study A. Gomes a, b, ∗ , C. Henggeler Antunes a, b , A. Gomes Martins a, b a Department of Electrical Engineering and Computers, Polo II, 3030-290 Coimbra, Portugal b INESC Coimbra, R. Antero de Quental 199, 3000-033 Coimbra, Portugal Available online 9 February 2007 Abstract An adequately designed and parameterized set of operators is crucial for an efficient behaviour of Genetic Algorithms (GAs). Several strategies have been adopted in order to better adapt parameters to the problem under resolution and to increase the algorithm’s performance. One of these approaches consists in using operators presenting a dynamic behaviour, that is displaying a different qualitative behaviour in different stages of the evolutionary process. In this work a comparative analysis of the effects of using an adaptive mutation operator is presented in the operational framework of a multi-objective GA for the design and selection of electrical load management strategies. It is shown that the use of a time/space varying mutation operator depending on the values achieved for each objective function increases the performance of the algorithm.  2007 Elsevier Ltd. All rights reserved. Keywords: Adaptive control; Genetic algorithms; Multiobjective optimization 1. Introduction It is well known that the performance of multi-objective GAs strongly depends on the parameter setting of the operators [1–4], thus making the identification and the selection of a suitable value or range of values for every parameter an essential step. The choice of an adequately designed and parameterized set of operators is a crucial task for an efficient performance of GAs, namely in multi-objective problems, by making GAs better adapted to the current search space and allowing them to evolve according to the objectives being evaluated. This issue is even more relevant in the context of real-world case studies, in which the Pareto frontier is seldom known and the search space is generally non-smooth. Usually, two different approaches are used in the identification process of the parameter values. One consists in tuning the parameters through experimentation based on the analyst’s expertise. Several runs are executed until the parameters are calibrated, and the process ends when the results produced are good enough according to the analyst’s opinion and/or the decision maker’s (DM) preferences. This approach relies on the expertise of the actors involved (the DM and the analyst who mediates the communication of the DM with the computer tools). The second approach for parameter setting is through adaptive control. Instead of being constant over each simulation, like in the tuning process, the values of different parameters may vary with time [3,5,6]. This variation may appear in two forms. ∗ Corresponding author. Department of Electrical Engineering and Computers, Polo II, 3030-290 Coimbra, Portugal. Tel.: +351 239 796280; fax: +351 239 796247. E-mail addresses: agomes@deec.uc.pt (A. Gomes), ch@deec.uc.pt (C.H. Antunes), amartins@deec.uc.pt (A.G. Martins). 0305-0548/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2007.01.003