Heuristic Algorithm with Oscillation Strategy for a New Class of Assignment Problem

Abstract

A new class of assignment problem which roots in the optimization management of slabs in steel industry is considered in this article. Compared with the generalized assignment problem, flow constraints should be considered in this problem besides the capacity constraints when assigning items to knapsacks. This problem could be reduced to the generalized assignment problem, and so is NP-hard. A heuristic with oscillation strategy and long-term memory list is proposed to solve it. The oscillation strategy makes it possible that the local search oscillates between the feasible and infeasible solution spaces to find better feasible solutions. A long-term memory list is embedded to encourage the diverse moves of items, which improves the diversity of the algorithm. In order to testify the efficiency of the heuristic, 23 instances have been randomly generated for the computational experiments. The results show that for small-size instances, the maximum deviation of the heuristic from the optimal solution is 0.55% and for larger-size instances, the heuristic could find good solutions in a very short time.