Multiobjective combinatorial optimization: some approaches

There have been many developments in multiple criteria decision‐making (MCDM) during the last 50 years. Researchers from different areas have also recognized the multiple‐criteria nature of problems in their application areas and tried to address these issues. Unfortunately, there has not always been sufficient information flow between the researchers in the MCDM area and the researchers applying MCDM to their problems. More recently, multiobjective combinatorial optimization (MOCO) and multiobjective metaheuristic areas have been enjoying substantial developments. These problems are hard to solve. Many researchers addressed the problem of finding all nondominated solutions. This is a difficult task for MOCO problems. This difficulty limits many of the studies to concentrate on bicriteria problems. In this paper, I review some MCDM approaches that aim to find only the preferred solutions of the decision maker (DM). I argue that this is especially important for MOCO problems. I discuss several of our approaches that incorporate DM's preferences into the solution process of MOCO problems and argue that there is a need for more work to be done in this area.