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Constrained optimization problems constitute an important fraction of optimization problems in the mechanical engineering domain. It is not uncommon for these problems to be highly-constrained where a specialized approach that aims to improve constraint satisfaction level of the whole population as well as finding the optimum is deemed useful especially when the objective functions are very costly. A new algorithm called Feasibility Enhanced Particle Swarm Optimization (FEPSO), which treats feasible and infeasible particles differently, is introduced. Infeasible particles in FEPSO do not need to evaluate objective functions and fly only based on social attraction depending on a single violated constraint, called the activated constraint, which is selected at each iteration based on constraint priorities and flight occurs only along dimensions of the search space to which the activated constraint is sensitive. To ensure progressive improvement of constraint satisfaction, particles are not allowed to violate a satisfied constraint in FEPSO. The highly-constrained four-stage gear train problem and its two variants introduced in this paper are used to assess the effectiveness of FEPSO. The results suggest that FEPSO is effective and consistent in obtaining feasible points, finding good solutions, and improving the constraint satisfaction level of the swarm as a whole.

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Highlights:Graphical/Tabular Abstract  Multi-objective and singleobjective feasibility enhanced particle swarm optimization  Pareto optimality based multi-objective optimization approach  Fixed weight linearly aggregated objective functions Figure A. Solutions obtained by the multi-objective approach provides design alternatives in the solution domain whereas the single objective approach gives a single solution for the given criteriaPurpose: Comparison of a Pareto based multi-objective feasibility enhanced particle swarm optimization approach with fixed weight linearly aggregated single-objective optimization using a variant of the same algorithm. Evaluation of the advantages presented by the multi-objective approach. Theory and Methods:Solutions for three separate multi-objective constrained problems were obtained using two different approaches: Pareto based multi-objective feasibility enhanced particle swarm optimization Singleobjective feasibility enhanced particle swarm optimization using fixed weight linearly aggregated singleobjective variants of the problems. Results:Comparisons involving three problems (two of which were highly constrained) revealed that optimizations performed using the multi-objective approach resulted in solutions that were also suitable for all singleobjective criteria. Results obtained by a single multi-objective optimization run were found to be at least as good as results obtained by separate aggregated-objective runs for each aggregated criterion. Conclusion:In Pareto optimality based optimization algorithms a Pareto front consisting of many non-dominated solutions are found in each run instead of a single solution. Therefore: The designer can choose from these non-dominated solutions with a clear trade-off between known values of all objectives. This approach allows performing the trade-off without requiring rerunning the optimization with new objective weights. If efficient Pareto optimality based multi-objective optimization algorithms are available, it is unnecessary to employ single-objective approaches by combining the objectives with presumably biased weights assigned with insufficient information related with the problem.

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