A New Non-dominated Sorting Genetic Algorithm for Multi-Objective Optimization 85 A New Non-dominated Sorting Genetic Algorithm for Multi-Objective Optimization

Multi-objective optimization (MO) is a highly demanding research topic because many realworld optimization problems consist of contradictory criteria or objectives. Considering these competing objectives concurrently, a multi-objective optimization problem (MOP) can be formulated as finding the best possible solutions that satisfy these objectives under different tradeoff situations. A family of solutions in the feasible solution space forms a Pareto-optimal front, which describes the tradeoff among several contradictory objectives of an MOP. Generally, there are two goals in finding the Pareto-optimal front of a MOP: 1) to converge solutions as near as possible to the Pareto-optimal front; and 2) to distribute solutions as diverse as possible over the obtained non-dominated front. These two goals cause enormous search space in MOPs and let deterministic algorithms feel difficult to obtain the Pareto-optimal solutions. Therefore, satisfying these two goals simultaneously is a principal challenge for any algorithm to deal with MOPs (Dias & Vasconcelos, 2002). In recent years, several evolutionary algorithms (EAs) have been proposed to solve MOPs. For example, the strength Pareto evolutionary algorithm (SPEA) (Zitzler et al., 2000) and the revised non-dominated sorting genetic algorithm (NSGA-II) (Deb et al., 2002) are two most famous algorithms. Several extensions of genetic algorithms (GAs) for dealing with MOPs are also proposed, such as the niche Pareto genetic algorithm (NPGA) (Horn et al., 1994), the chaos-genetic algorithm (CGA) (Qi et al., 2006), and the real jumping gene genetic algorithm (RJGGA) (Ripon et al., 2007). However, most existing GAs only evaluate each chromosome by its fitness value regardless of the schema structure, which is a gene pattern defined by fixing the values of specific gene loci within a chromosome. The schemata theorem proved by Goldberg in 1989 is a central result of GA’s theory in which a larger of effective genomes implies a more efficient of searching ability for a GA (Goldberg, 1989). Inspired by the outstanding literature of Kalyanmoy Deb, this study proposes an evaluative crossover operator to incorporate with the original NSGA-II. The proposed evaluative version of NSGA-II, named E-NSGA-II, can further enhance the advantages of the fast nondominated sorting and the diversity preservation of the NSGA-II for improving the quality of the Pareto-optimal solutions in MOPs. The proposed evaluative crossover imitates the gene-therapy process at the forefront of medicine and therefore integrates a new gene6