On Local Optima Distribution in Buffer Allocation Problem for Production Line with Unreliable Machines

Abstract

In this paper, we consider a buffer allocation problem in manufacturing flow lines with series-parallel network structure where nodes correspond to buffers of finite capacity, and arcs correspond to the machines. The machines are supposed to be unreliable, their time to failure and repair time are assumed to be exponentially distributed. Different machines may have different production rates and the production rates of all machines are assumed to be deterministic. The buffer allocation problem is to determine the capacities of all buffers with respect to a given optimality criterion, which is a function of the average production rate of the line, the buffer acquisition and installation cost and the inventory cost. In search for the optimum, the tentative solutions are evaluated by means of an approximate method based on the Markov models aggregation. We carry out computational experiments with the local search and genetic algorithms. It turns out that the “massif central” or “big valley” structure of the fitness landscape is present but only partially: The fitness of the local optima is negatively correlated with the distance to the best found solution, yet the set of local optima can not be encompassed by a ball of relatively small radius. Moreover, we show that in many problem instances, several clusters of local optima can be identified. The symmetries of the fitness function are discussed and suggested as the possible cause of the local optima clustering. Finally the performance of genetic algorithms is bfiefly discussed with respect to solutions clustering.