Parallel Multi-Criterion Genetic Algorithms: Review and Comprehensive Study

2. Multi-Objectives Genetic Algorithms

Multi-objective optimization methods are based on the idea of finding optimal solutions to problems having multiple objectives (Coello, C. A. 1999; Coello, C. A. 2000; Zydallis 2003). Hence, for this type of problems the user is never satisfied by finding one solution that is optimized with respect to a single criterion. The principle of a multi-criteria optimization procedure is different from that of a single criterion optimization. In a single criterion the main objective is to find a globally optimal solution. However, in a multi-criteria optimization problem, there is more than one objective function, each of which may have a different individual optimal solution. The objective functions are said to be conflicting if there exists an adequate distinction in the optimal solutions corresponding to different objectives, this presents a set of optimal solutions, instead of one optimal solution known as Pareto-optimal solutions (Coello, C. A. 2001 & 2006; Deb 1999; Schaffer 1985; Veldhuizen & Lamont 2000)

A multi-objective problem can be defined having x objectives (say f_i, i = 1, 2, …, x and x>1). Any two solutions S¹ and S² (having ’m’ decision variables, each) can have one, two possibilities -one dominates the other or none dominates the other’. Solution S¹ is said to dominate the other solution, S², if the following conditions are true: