Towards Integrated Glance To Restructuring in Combinatorial Optimization
This addresses redesign of modular systems in combinatorial optimization, but it appears incremental as it extends existing problems without major breakthroughs.
The paper tackles restructuring problems in combinatorial optimization, where solutions are redesigned with cost and closeness constraints, and it describes the approach for various problems like knapsack and spanning trees with numerical examples.
The paper focuses on a new class of combinatorial problems which consists in restructuring of solutions (as sets/structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the restructuring, (ii) a closeness to a goal solution. Three types of the restructuring problems are under study: (a) one-stage structuring, (b) multi-stage structuring, and (c) structuring over changed element set. One-criterion and multicriteria problem formulations can be considered. The restructuring problems correspond to redesign (improvement, upgrade) of modular systems or solutions. The restructuring approach is described and illustrated (problem statements, solving schemes, examples) for the following combinatorial optimization problems: knapsack problem, multiple choice problem, assignment problem, spanning tree problems, clustering problem, multicriteria ranking (sorting) problem, morphological clique problem. Numerical examples illustrate the restructuring problems and solving schemes.