A Niched-Penalty Approach for Constraint Handling in Genetic Algorithms
Most applications of genetic algorithms (GAs) in handling constraints use a straightforward penalty function method. Such techniques involve penalty parameters which must be set right in order for GAs to work. Although many researchers use adaptive variat
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Abstract Most applications of genetic algorithms (GAs) in handling constraints use a straightforward penalty function method. Such techniques involve penalty parameters which must be set right in order for GAs to work. Although many researchers use adaptive variation of penalty parameters and penalty functions. the general conclusion is that these variations are specific to a problem and cannot be generalized. In this paper, we propose a niched-penalty approach which does not require any penalty parameter. The penalty function creates a selective pressure towards the feasible region and a niching maintains diversity among feasible solutions for the genetic recombination operator to find new feasible solutions. The approach is only applicable to population-based approaches, thereby giving GAs (or other evolutionary algorithms) a niche in exploiting this penalty-paramcter-Iess penalty approach. Simulation results on a number of constrained optimization problems suggest the efficacy of the proposed method.
1 Introduction Real-world search and optimization problems are written a'i nonlinear programming (NLP) problem of the following kind [2. 16]: Minimize J(x) Subject to 9j(X) ~ 0, hk(x) = 0, x~ :S Xi :S xi,
j = I, ... , J, k=I, ... ,f{, i=l, ... ,n.
(1)
In the above NLP problem. there are n variables (that is, x is a vector of size n), J greater-than-equal-to type inequality constraints, and J{ equality constraints. The function J(x) is the objective function, 9j(X) is the jth inequality constraints, and hdx) is the k-th equality constraints. The i-th variable varies in the range [xL xil. A solution x that satisfies all the above equality and inequality constraints and above variable bounds is called afeasible solution. Other solutions are called infeasible solutions. Most cla
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