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TopMultiple Objective Optimization
Multiple objective optimization refers to the solution of problems with two or more objectives to be satisfied simultaneously. Often, such objectives are in conflict with each other and are expressed in different units. Because of their nature, multiple objective optimization problems normally have, not one, but a set of solutions, which are called Pareto-optimal solutions or nondominated solutions (Chankong & Haimes, 1983; Hans, 1988). When such solutions are represented in the objective function space, the graph produced is called the Pareto front or the Pareto-optimal set of the problem.
In general, there are two primary approaches for the solution of a multiple objective problem. The first approach involves determining the relative importance of the attributes, and aggregating the attributes into some kind of overall composite objective function (sometimes called a value or utility function); while the second approach involves populating a number of feasible solutions along a Pareto frontier and the final solution is a set of non-dominated solutions. MOEAs are the most notable methods from this second approach.
A general formulation of a multiple objective optimization problem consists of a number of objectives with a number of inequality and equality constraints. Mathematically, the problem can be written as in Equation 1 (Rao, 1991):minimize / maximize f(x) (1) subject to:
j = 1, 2, …, J
k = 1, 2, …, Kwhere,