A Novel Multi-Objective Competitive Swarm Optimization Algorithm

Introduction

The general form of a multi-objective problem can be represented as follows: subject to (1) where is decision variable in the search space . The objective vector maps the decision variable in to number of objective functions in the objective space .

In real life, many optimization problems as defined in (1) often need to optimize conflicting objectives simultaneously. Optimization of one objective often costs the other objectives due to the trade-offs between them. Hence, it is not possible to find a single solution to optimize all the objectives all together. These types of problems are called multi-objective optimization problems. The optimal trade-off solutions are called Pareto-optimal solutions. In real, it is not possible to collect all the pareto-optimal solutions, hence an approximation of all these pareto-optimal solution called the Pareto-front is formed. These problems are usually treated as a different type of optimization problem and there is always need of different techniques to handle these types of problems. The classical optimization techniques usually convert the whole multi-objective optimization problem into number of single objective optimization problems to solve them separately. It then collects one trade-off solution in each single objective problem to form the Pareto-front. The difficulty of the methodology is that it has to execute several times to collect different Pareto-optimal solutions in each run. Hence, it is always inspiring to bring together all the Pareto-optimal solutions in a single run. Therefore, evolutionary algorithms due to the population-based nature are one such positivity to bring all the Pareto-optimal solutions in a single simulation run.