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).
