Diversity improvement of solutions in multiobjective genetic algorithms using pseudo function inverses

Diversity improvement methods generally implement niching and fitness sharing schemes. In this work we propose a general principle based on using the inverse mapping from objective space to decision space that allows for the creation of diverse solutions in a direct manner. When analytical forms of objective functions are known, we propose a method of generating set-valued inverse maps, in functional or algorithmic form, which when restricted to the feasible search range yield pseudo inverses of objectives. In the absence of analytical functional forms we propose the use of artificial neural networks (ANNs) in a novel configuration to directly learn the inverse map without network inversion procedures. We implement two diversity creation operators and use them in a standard binary multi-objective genetic algorithm (MOGA) to solve standard bi-objective optimization problems. We also propose a parameter less approach of fixing the number and desirable locations of solutions in sparse regions. Proposed algorithms are compared with NSGA-II and it is shown that the proposed algorithms achieve desired level of diversity in fewer function evaluations compared to NSGA-II.