Neighborhood Search for Collecting Weighted Items in Directed Bipartite Graphs

Abstract

Given a directed bipartite graph with a finite set of items and a finite set of players, the problem discussed in this study asks to find an arc reversing strategy of the players which collects items under a budget constraint so that the total profit of the collected items is maximized. The weighted item collecting problem is viewed as a generalization of an integrated circuit design problem, and it is also a variant of 0-1 knapsack problems in graphs. A heuristic algorithm based on the simulated annealing is designed for the weighted item collecting problem, and numerical experiments are conducted to demonstrate the heuristic performance.