A Genetic Algorithm for Minimax Optimization Problems

Robust discrete optimization is a technique for structuring uncertainty in the decision-making process. The objective is to find a robust solution that has the best worst-case performance over a set of possible scenarios. However, this is a difficult optimization problem. This paper proposes a two-space genetic algorithm as a general technique to solve minimax optimization problems. This algorithm maintains two populations. The first population represents solutions. The second population represents scenarios. An individual in one population is evaluated with respect to the individuals in the other population. The populations evolve simultaneously, and they converge to a robust solution and its worst-case scenario. Since minimax optimization problems occur in many areas, the algorithm will have a wide variety of applications. To illustrate its potential, we use the two-space genetic algorithm to solve a parallel machine scheduling problem with uncertain processing times. Experimental results show that the two-space genetic algorithm can find robust solutions.