Evolving test instances of the Hamiltonian completion problem

Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is usually no standard set of instances to benchmark performance. Second, using existing graph generators results in a restricted spectrum of difficulty and the resulting graphs are usually not diverse enough to draw sound conclusions. That is why recent work proposes a new methodology to generate a diverse set of instances by using an evolutionary algorithm. We can then analyze the resulting graphs and get key insights into which attributes are most related to algorithm performance. We can also fill observed gaps in the instance space in order to generate graphs with previously unseen combinations of features. This methodology is applied to the instance space of the Hamiltonian completion problem using two different solvers, namely the Concorde TSP Solver and a multi-start local search algorithm.Comment: 12 pages, 12 figures, minor revisions in section

Exploring search space trees using an adapted version of Monte Carlo tree search for combinatorial optimization problems

In this article, a novel approach to solve combinatorial optimization problems is proposed. This approach makes use of a heuristic algorithm to explore the search space tree of a problem instance. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is used to explore game trees. By leveraging the combinatorial structure of a problem, several enhancements to the algorithm are proposed. These enhancements aim to efficiently explore the search space tree by pruning subtrees, using a heuristic simulation policy, reducing the domains of variables by eliminating dominated value assignments and using a beam width. They are demonstrated for two specific combinatorial optimization problems: the quay crane scheduling problem with non-crossing constraints and the 0-1 knapsack problem. Computational results show that the algorithm achieves promising results for both problems and eight new best solutions for a benchmark set of instances are found for the former problem. These results indicate that the algorithm is competitive with the state-of-the-art. Apart from this, the results also show evidence that the algorithm is able to learn to correct the incorrect choices made by constructive heuristics

The Second International Nurse Rostering Competition

This paper reports on the Second International Nurse Rostering Competition (INRC-II). Its contributions are (1) a new problem formulation which, differently from INRC-I, is a multi-stage procedure, (2) a competition environment that, as in INRC-I, will continue to serve as a growing testbed for search approaches to the INRC-II problem, and (3) final results of the competition. We discuss also the competition environment, which is an infrastructure including problem and instance definitions, testbeds, validation/simulation tools and rules. The hardness of the competition instances has been evaluated through the behaviour of our own solvers, and confirmed by the solvers of the participants. Finally, we discuss general issues about both nurse rostering problems and optimisation competitions in general.PostprintPeer reviewe