A Genetic Algorithm for Finding Good Balanced Sequences in a Customer Assignment Problem with no State Information

Abstract

In this paper, we study the control problem of optimal assignment of tasks to servers in a multi-server queue with inhomogeneous servers. In order to improve the performance of the system, we use a periodic deterministic sequence of job assignments to servers called a billiard sequence. We then use a genetic algorithm (GA) for computing a near-optimal billiard sequence. By means of a recent result obtained in the area of ordinal optimization, we show that the solution found by the GA belongs to the top 1% of possible choices for such a billiard sequence. As illustrated by numerical examples, not only is the performance under a billiard sequence better than that of the corresponding randomized policy, the optimal billiard sequence even outperforms the billiard implementation of the optimal randomized policy. The framework we introduce in this paper is suitable for general optimization problems over (periodic) deterministic decision sequences. Given the significant performance improvement that a switch from randomized policies to billiard sequences yields, this framework is of importance in practical applications. Finally, we show that constrained or multi-objective optimization can be dealt with in our framework as well.