Genetic Algorithm for Constrained Optimization with Stepwise Approach in Search Interval Selection of Variables

Abstract

Genetic algorithms are evolutionary algorithms that are well suited in searching global solution to varied nature of optimization problems. The inspirations in developing GA are derived from working principle of natural genetics. The operators such as reproduction, crossover & mutation are employed similar to natural genetics. These steps involved elements of probability that make search for optimal solution random making GA stochastic & nondeterministic. There are several initiatives made by researcher in improving the search direction & making it more definitive. Present work aims at suggesting a novel stepwise approach in search interval selection of variables using Genetic algorithm. Three nonlinear optimization problems are selected for numerical experimentation with comparative studies of respective solution using conventional methods and GA techniques with & without stepwise approach. Test run are conducted with constant GA parameters and the best function values for five consecutive run are tabulated. Corresponding values of variables decide the search interval selection criteria for step 1. Five elite-GA run are conducted for step 1 for newly defined search interval of variables. The corresponding values of the variables obtained as in step 1 decide the search interval selection for step 2. Number of steps continues till no further improvement in the function values is obtained. Based on the result of the present work it can be concluded that the optimal values obtained for all the three test problems evaluated using the stepwise approach are better than those obtained using GA without stepwise approach & conventional techniques. The present work is demonstrative & it is felt necessary to substantiate the claim by extending this stepwise search interval approach of GA in selection of variables to other problems of optimization.