An Approach Integrating Simulated Annealing and Variable Neighborhood Search for the Bidirectional Loop Layout Problem

In the bidirectional loop layout problem (BLLP), we are given a set of machines, a set of locations arranged in a loop configuration, and a flow cost matrix. The problem asks to assign machines to locations so as to minimize the sum of the products of the flow costs and distances between machines. The distance between two locations is calculated either in the clockwise or in the counterclockwise direction, whichever path is shorter. We propose a hybrid approach for the BLLP which combines the simulated annealing (SA) technique with the variable neighborhood search (VNS) method. The VNS algorithm uses an innovative local search technique which is based on a fast insertion neighborhood exploration procedure. The computational complexity of this procedure is commensurate with the size of the neighborhood, that is, it performs O(1) operations per move. Computational results are reported for BLLP instances with up to 300 machines. They show that the SA and VNS hybrid algorithm is superior to both SA and VNS used stand-alone. Additionally, we tested our algorithm on two sets of benchmark tool indexing problem instances. The results demonstrate that our hybrid technique outperforms the harmony search (HS) heuristic which is the state-of-the-art algorithm for this problem. In particular, for the 4 Anjos instances and 4 sko instances, new best solutions were found. The proposed algorithm provided better average solutions than HS for all 24 Anjos and sko instances. It has shown robust performance on these benchmarks. For 20 instances, the best known solution was obtained in more than 50% of the runs. The average time per run was below 10 s. The source code implementing our algorithm is made publicly available as a benchmark for future comparisons.