Design of Multi-Objective Optimization Problems

Multi-objective optimization (MOO) problems belong to programming approaches in which the decision-maker is faced with a multiplicity of conflicting objectives. This situation occurs with real-world problems involving engineering design, chemical processes, financial management, etc. This case means that achieving an optimum for one objective function requires some compromises on one or more of the other objectives. In such problems, we will obtain rather a set of equally good solutions, and not just one. The decision variables or parameters of MOO problems can be continuous, 0-1 binary or mixed-integer variables. The feasible region of a MOO problem is a dimensional space satisfying bounds on the variables, equalities, and inequalities. Equality constraints arise from mass, energy and momentum balances, and can be algebraic or differential equations. Inequality constraints come from possible requirements of the system, such as the temperature of a reactor that must not exceed a particular value, failure of the material, and other technical features. We begin by presenting a short history of global optimization. The development of multi-objective optimization techniques is due to the combined effects of new approaches and challenging applications. The new techniques are evolutionary algorithms inspired by Nature. There are some various real-world applications difficult to solve. A classification of MOO methods is based on two criteria, the number of Pareto solutions, and the decision-maker preferences. Examples illustrate the resolution of continuous and combinatorial problems from literature (e.g., minimum spanning tree, bicriteria knapsack problem).