Multistart search for the Cyclic Cutwidth Minimization Problem

• Published in: Computers & operations research Vol. 126; pp. 105116 - 18
• Main Authors: Cavero, Sergio, Pardo, Eduardo G., Laguna, Manuel, Duarte, Abraham
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.02.2021; Pergamon Press Inc
• Subjects: Apexes; Circular embedding; Cyclic cutwidth; Graph layout problem; Graph theory; Lower bounds; Multistart search; Operations research; Optimization; Searching; Statistical tests; Tabu Search; Circular embedding; Tabu Search; Multistart search; Cyclic cutwidth; Graph layout problem
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2020.105116

•Multistart Tabu Search for the Cyclic Cutwidth Minimization Problem (CCMP).•New search properties of the CCMP useful for other similar graph layout problems•New Lower Bound for the CCMP.•Favorably empirical comparison with previous heuristic approaches.•Non-parametric statistical tests to assess the merit of our proposal. The Cyclic Cutwidth Minimization Problem (CCMP) is a Graph Layout Problem that consists of finding an embedding of the vertices of a candidate graph in a host graph, in order to minimize the maximum cut of a host edge. In this case, the host graph is restricted to be a cycle. In this paper, we identify a new lower bound for the problem, and also a property which allows search procedures to drastically reduce the neighborhood size during the search. Additionally, we propose the use of an alternative objective function for min–max optimization problems, never used before in the context of the CCMP. These strategies have been combined within a multistart search procedure for this problem. The obtained method is compared with the state of the art for the CCMP using sets of problem instances previously published. Statistical tests indicate the merit of our proposal.