A genetic algorithm for the optimal sequential partitioning problem

The optimal sequential problem is defined as the problem of finding the minimum cost partition of the nodes of a directed acyclic graph into subsets of a given size, subject to the constraint that the precedence relationships among the elements are satisfied. A heuristic algorithm based on tabu search has been proposed for this problem [2]. However, there is a tendency for the solutions obtained by tabu search to become trapped in bad local optima in parallel graphs with random edge costs. In this paper we present a genetic algorithm for the optimal sequential partitioning problem. We develop an effective two-point partial order crossover satisfying sequential conditions, which preserve better blocks that have a larger sum of edge costs. In this crossover we introduce the roulette selection method to escape local optima. We also assess the effectiveness of the algorithm. The results show that this proposed algorithm outperforms any other algorithm using tabu search in terms of solution quality. (C) 2001 Scripta Technica.