Using Crowding Distance to Improve Multi-Objective PSO with Local Search

Biology inspired algorithms have been gaining popularity in recent decades and beyond. These methods are based on biological metaphor such as Darwinian evolution and swarm intelligence. One of the most recent algorithms in this category is the Particle Swarm Optimization (PSO). PSO is a population-based approach using a set of candidate solutions, called particles, which move within the search space. The trajectory followed by each particle is guided by its own experience as well as by its interaction with other particles. Specific methods of adjusting the trajectory are motivated by the observations in birds, fishes, or other organisms that move in swarms. Multi-objective optimization (MOO) is an important field to apply swarm intelligence metaheuristics because there is not only one solution for MOO ingeneral. The solution of a MOO problem is generally referred as a non-dominated solution, which is different from the optimal solution of single-objective optimization problem. A solution is said to be nondominated over another only if it has superior, at least no inferior, performance in all objectives. Hence, non-dominance means that the improvement of one objective could only be achieved at the expense of other objectives. This concept always gives not a single solution, but rather a set of solutions called the non-dominated set or non-dominated archive. Generally speaking, there are two approaches to MOO: classical methods and evolutionary methods. Classical methods first convert separate objective functions into a single objective function by weighted sum method, utility function method, or goal programming method, and then solve them by traditional optimization techniques. Such modelling puts the original problem in an inadequate manner, using a surrogate variable with incomplete information. Subsequent optimization techniques also contradicts our intuition that singleobjective optimization is a degenerate case of MOO (Deb, 2001). The result of classical approach is a compromise solution whose non-dominance can not be guaranteed (Liu et al., 2003). Lastly, but not the least, a single optimized solution could only be found in each simulation run of traditional optimization techniques such that it limits the choices available to the decision maker. Therefore, using a population of solutions to evolve towards several non-dominated solutions in each run makes evolutionary algorithms, such as swarm intelligence methods, popular in solving MOO problems.