Effective integrations of constraint programming, integer programming and local search for two combinatorial optimisation problems

• Main Author: He, Fang
• Published: University of Nottingham 2012
• Subjects: 005.116; QA Mathematics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.575362

This thesis focuses on the construction of effective and efficient hybrid methods based on the integrations of Constraint Programming (CP), Integer Programming (IP) and local search (LS) to tackle two combinatorial optimisation problems from different application areas: the nurse rostering problems and the portfolio selection problems. The principle of designing hybrid methods in this thesis can be described as: for the combinatorial problems to be solved, the properties of the problems are investigated firstly and the problems are decomposed accordingly in certain ways; then the suitable solution techniques are integrated to solve the problem based on the properties of substructures/subproblems by taking the advantage of each technique. For the over-constrained nurse rostering problems with a large set of complex constraints, the problems are first decomposed by constraint. That is, only certain selected set of constraints is considered to generate feasible solutions at the first stage. Then the rest of constraints are tackled by a second stage local search method. Therefore, the hybrid methods based on this constraint decomposition can be represented by a two-stage framework “feasible solution + improvement”. Two integration methods are proposed and investigated under this framework. In the first integration method, namely a hybrid CP with Variable Neighourhood Search (VNS) approach, the generation of feasible initial solutions relies on the CP while the improvement of initial solutions is gained by a simple VNS in the second stage. In the second integration method, namely a constraint-directed local search, the local search is enhanced by using the information of constraints. The experimental results demonstrate the effectiveness of these hybrid approaches. Based on another decomposition method, Dantzig-Wolfe decomposition, in the third integration method, a CP based column generation, integrates the feasibility reasoning of CP with the relaxation and optimality reasoning of Linear Programming. The experimental results demonstrate the effectiveness of the methods as well as the knowledge of the quality of the solution. For the portfolio selection problems, two integration methods, which integrate Branch-and-Bound algorithm with heuristic search, are proposed and investigated. In layered Branch-and-Bound algorithm, the problem is decomposed into the subsets of variables which are considered at certain layers in the search tree according to their different features. Node selection heuristics, and branching rules, etc. are tailored to the individual layers, which speed up the search to the optimal solution in a given time limit. In local search branching Branch-and-Bound algorithm, the idea of local search is applied as the branching rule of Branch-and-Bound. The local search branching is applied to generate a sequence of subproblems. The procedure for solving these subproblems is accelerated by means of the solution information reusing. This close integration between local search and Branch-and-Bound improves the efficiency of the Branch-and-Bound algorithm according to the experimental results. The hybrid approaches benefit from each component which is selected according to the properties of the decomposed problems. The effectiveness and efficiency of all the hybrid approaches to the two application problems developed in this thesis are demonstrated. The idea of designing appropriate components in hybrid approach concerning properties of subproblems is a promising methodology with extensive potential applications in other real-world combinatorial optimisation problems.