3.4Experiments & Results :-. A.Benchmark Functions. The
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3.4 Experiments & results :-
A. Benchmark Functions
The most challenging issue in validation of an Evolutionary Multi-objective Optimization (EMOO) algorithm is to identify the right benchmark functions with diverse characteristics such as multi-modality, deception, isolation and particularly location of true Pareto-optimal front in the surface to resemble complicated real life problems. Traditional benchmark functions ,  usually have the global optimum lying either in the centre of the search range or on the bounds. Naturally, these benchmark functions are inadequate to exhaustively test the performance of a MOO algorithm. In order to overcome the above problem, a set of recommended benchmark functions  was proposed in the…show more content… Here two repositories are maintained in addition to the search population. One contains a single local best for each member of the swarm and the second one is the external archive . This archive uses the method from  to separate the objective function space into a number of hypercubes (an adaptive grid) to generate well-distributed Pareto fronts . Those hypercubes containing more than one particle are assigned a fitness score equal to the result of dividing 10 by the number of the resident particles in that hypercube . Thus a more densely populated hypercube is given a lower score. Next the primary population uses its local best and global best particle positions (from the external archive) to update their velocities. The global best is selected by first choosing a hypercube (according to its score) using the roulette-wheel selection and then opting for a particle randomly from such hypercube. After that mutation operators are used to enhance the exploratory capabilities of the swarm.
2) Non-dominated Sorting Genetic Algorithm-II (NSGA-II)
Non-dominated Sorting Genetic Algorithm-II (NSGA-II) starts with a parent population set PG of randomly initialized solutions of size. Then an iterative process begins, where genetic operations like tournament selection, crossover and mutation are done on the parent set to obtain the child population QG also of size