Swarm Optimization
Evolutionary algorithms have been used to solve multi-objective optimization problems of two or three objectives giving results that both converge to the optimal front and are diverse along that front. However, once the number of objectives rises to four and above, the Pareto dominance concept that most of these algorithms are based on loses selection pressure, recombination operations are ineffective as individuals in populations are not close in the problem space and the evaluation of performance measures such as hyper-volume becomes computationally expensive.
To overcome the loss in selection pressure, recent evolutionary algorithms adopt a number of techniques which include modifying the dominance relation to increase selection pressure as done with ε-dominance, α-dominance and dominance area control, using a secondary selection mechanism such as the shift-based density estimator, grid-based fitness metric or knee-point driven analysis to filter individuals and decomposing the so-called many objective problems into sub- problems to simultaneously solve.
The controlling dominance area of solutions, CDAS technique has been found to be effective in generating solutions that converge to the optimal front but leads to a loss in the diversity of the generated solutions. In this paper, we propose an extension to the speed-constrained particle swarm optimizer that uses a relaxed form of dominance, CDAS and the shift-based density estimator as secondary selection mechanism to increase diversity of solutions obtained. Also, the particles in the swarm will have an archive of personal bests from which the selection will be done using the weighted sum approach. Finally, the performance of the algorithm will be compared with state of the art algorithms such as NSGA-III and MOEA/DD using the DTLZ benchmark functions.