When an optimization problem involves only one objective function, it is a single-objective optimization. Most engineering problems require the designer to optimize a number of conflicting objectives. The objectives are in conflict with each other if an improvement in one objective leads to deterioration in another. Multiobjective problems in which there is competition between objectives may have no single, unique optimal solution. Multiobjective optimization problems are also referred to as multicriteria or vector optimization problems. We can formulate a multiobjective optimization problem as follows: Find a decision variable that satisfies the given constraints and optimizes a vector function whose components are objective functions. Formally, the multiobjective optimization problem is stated as follows:
where f : n → and Ω ⊂ n. For example, the constraint set Ω can have the form
In general, we may have three different ...