Constrained optimization based on a multiobjective evolutionary algorithm

Abstract

-A criticism of Evolutionary Algorithms (EAs) might be the lack of efficient and robust generic methods to handle constraints. The most widespread approach for constrained search problems is to use penalty methods. EAs have received increased interest during the last decade due to the ease of handling multiple objectives., A constrained Optimization problem or a n unconstrained multiobjective problem may in principle be two different ways to pose the same underlying I problem. In this paper an alternative approach for the constrained optimization problem is presented. The method is a variant of a multiobjective real coded Genetic Algorithm (CA) inspired by the penalty approach. It is evaluated on six different constrained single objective problems found in the literature. The results show that the proposed method performs well in terms of efficiency, and that it is rohust for a majority of the test problems.

Simple addition of ranking method for constrained optimization in evolutionary algorithms

“…From this study, the suitable range for B values was found to be from 0.01 (1%) to 0.2 (20%). It has to be noted that some of the best solutions found were even better than the optimal values, which is due to the approximation of the equality constraints into inequality constraints using (1).…”

“…The ranking methodology used here is fast and direct as the information from the constraint violation are represented by the sum of squares value and the number of constraints violated. This is in contrast to the time consuming pareto ranking which needs to take into account the values of each constraint function separately (e.g., in [1] and [8]). The biggest contribution from this work is the idea of using ranking to convert the information from the objective function and constraint violation into values which are in the same order of magnitude, such that direct summation of the ranking terms can then be used to integrate all of the information into one term.…”

“…Although the idea of individuals ranking based on objective function and constraint violation is not new, e.g., the works of Angantyr et al [1], Ray et al [8], and Runarsson and Yao [10], the proposed method offers a much simpler way of ranking and aggregation strategies when compared to the existing methodologies. For the optimization problems with equality constraints, a simple reinitialization scheme of the whole population is incorporated to maintain diversity within the population.…”

“…To find a suitable value for δ1j , we use the information from (1). By ignoring the δ value in (1), we have the maximum value of the function as max (|hj ( x)|).…”

“…A recent review by Coello Coello [4] has discussed on various techniques available for the handling of constraints in EAs. Other than that, recently published new techniques included the use of an improved diversity mechanism [7], the use of multiobjective optimization concept with a new ranking scheme [1] or a mechanism to reduce the constrained search space [5]. Despite the varieties available, the main issues when dealing with constraint handling in EAs are concerned with the scaling and aggregation of objective function and constraint violation, and also on the maintenance of diversity within a population such that the global minimum can be found.…”