Restructuring in Combinatorial Optimization

TL;DR

This paper introduces a restructuring approach for combinatorial optimization problems, focusing on solution modification costs and proximity to target solutions, applicable to various problems like knapsack, assignment, and spanning trees.

Contribution

It proposes a new restructuring framework for combinatorial problems, addressing solution redesign with cost and closeness measures, and demonstrates its application across multiple problem types.

Findings

Restructuring methods effectively modify solutions with controlled costs.

The approach improves solution adaptation in modular systems.

Examples demonstrate practical application and benefits.

Abstract

The paper addresses a new class of combinatorial problems which consist in restructuring of solutions (as 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. This problem corresponds to redesign (improvement, upgrade) of modular systems or solutions. The restructuring approach is described and illustrated for the following combinatorial optimization problems: knapsack problem, multiple choice problem, assignment problem, spanning tree problems. Examples illustrate the restructuring processes.