Decomposability Conditions of Combinatorial Optimization Problems

Abstract

Combinatorial Optimization Problems (COP) are generally complex and difficult to solve as a single monolithic problem. Thus, the process to solve the main initial COP may pass through solving intermediate problems and then combining the obtained partial solutions to find initial problem’s global solutions. Such intermediate problems are supposed to be easier to handle than the initial problem. To be modeled using the hierarchical optimization framework, the master problem should satisfy a set of desirable conditions. These conditions are related to some characteristics of problems which are: multi-objectives problem, over constrained problems, conditions on data and problems with partial nested decisions. For each condition, we present supporting examples from the literature where it was applied. This paper aims to propose a new approach dealing with hard COPs particularly when the decomposition process leads to some well-known and canonical optimization sub-problems.