Embedding a competitive ranking method in the artificial fish swarm algorithm for global optimization

Nonlinear programming problems are known to be difficult to solve, especially those that involve a multimodal objective function and/or non-convex and at the same time disjointed solution space. Heuristic methods that do not require derivative calculations have been used to solve this type of constrained problems. The most used constraint-handling technique has been the penalty method. This method converts the constrained optimization problem to a sequence of unconstrained problems by adding, to the objective function, terms that penalize constraint violation. The selection of the appropriate penalty parameter value is the main difficulty with this type of method. To address this issue, we use a global competitive ranking method. This method is embedded in a stochastic population based technique known as the artificial fish swarm (AFS) algorithm. The AFS search for better points is mainly based on four simulated movements: chasing, swarming, searching, and random. For each point, the movement that gives the best position is chosen. To assess the quality of each point in the population, the competitive ranking method is used to rank the points with respect to objective function and constraint violation independently. When points have equal constraint violations then the objective function values are used to define their relative fitness. The AFS algorithm also relies on a very simple and random local search to refine the search towards the global optimal solution in the solution space. A benchmarking set of global problems is used to assess this AFS algorithm performance.