SOLUTION OF MIXED/DISCRETE/INTEGER OPTIMIZATION PROBLEMS WITH GENETIC ALGORITHS

Abstract

Mathematical non-linear programming algorithms have emerged as the method of choice for applications in engineering optimization problems. They provide a general approach for obtaining solutions to both single and multiobjective design problems with a mix of equality and inequality constraints. The disadvantage of the traditional methods is that they find optimum closest to the initial guess, with no guarantee of locating the global optimum; they also fail to obtain optimum for non-convex design space or discontinuous space, where the derivatives cease to exist and become singular across the boundary of discontinuity. GAs are search algorithms based on the mechanics of natural selection (natural genetics). They combine survival of fittest among the string structures by performing randomized information exchange to form the search with a innovative flair of human search. In every generation , a new set of artificial creatures or strings is created using bits and pieces of the fittest amongst the old; an occasional new part is being tried for good measure. GAs efficiently exploit historical information to speculate on new search points with expected improved performance. Though exhaustive search and random search methods are stochastic in nature, they need large number of function evaluations to achieve feasible optimum values. GAs belonging to a category of stochastic search techniques have the potential to successfully fill this gap. In GAs, only the most promising regions of the design space are enumerated to locate the optimal design.. Analogous to the natural process where a population of designs is created and is then allowed to adapt to the design requirements. Designs that do not adapt in a favourable manner to the requirements are eliminated from consideration. The mechanism of adaptation borrows extensively from the principles of biological evolution, in that basic characteristics of designs in one population are transferred to a population in another generation through gene transfers. The objective here is to solve the design problems which have a mix of continuous, discrete and integer design variables. In traditional methods , these problems are approached by treating all variables as continuous and then rounding specific variables either up or down to V the nearest integer or discrete variable. This simple rounding procedure often fails completely , resulting in either a sub-optimal design or even generating an infeasible design. Algorithms for solving mixed integer problems have been proposed, however the original optimization problem is undesirably expanded to a large number of sub-optimization problems. The mechanics of genetic search, though simple to implement, encompass features that render the approach highly applicable to the problem with mixed type of variables. These desirable characteristics are largely attributed to the fact that genetic search moves from a population of designs to another population of designs; this is in contrast to the point to point search available in traditional mathematical programming methods and therefore offers a better possibility of locating a global optimum. Furthermore, genetic algorithms work on a coding of the design variables rather than the variables themselves. This allows for an efficient treatment of integer and discrete variables. Nevertheless, certain crucial issues are to be considered , for better performance of GAs, The main issue being the premature convergence which is due to getting trapped to a local optima. Precautions have been taken to alleviate the inherent difficulties , by using appropriate genetic operators and performance enhancement techniques. The program developed has been tested on various design problems and has performed satisfactorily. The techniques adapted for treating the integer, discrete variables have been incorporated. The performance criteria for the sample solved problems have been depicted with the respective response curves.