Constraint-based robust single- and multi-objective optimization

Finding optimal solutions for real-world problems requires the handling of many difficulties: multiple objectives, constraints, a dynamic search space, uncertainty, expensive objective functions, noisy fitness function, etc. Regardless of how good a solution is, its quality might substantially degrade in the case of uncertainty in any part of the solution obtained by an algorithm. An optimization algorithm therefore should search for robust solutions to minimize the negative consequences of uncertainties. This thesis aims to propose a reliable and computationally cheap technique to ensure robust solutions by introducing a new constraint and designing robust algorithms for solving single-objective and multi-objective optimization problems. The thesis first proposes a constraint to improve the reliability of robust optimization algorithms that utilize implicit averaging methods. In the proposed approach, the number of previously sampled points in the neighbourhood of a solution are counted and used to check how reliable the robustness measure of a solution is while searching for the robust optimum solution. Several constraint-based relational operators and algorithms are proposed using the proposed constraint and leveraging it on Particle Swarm Optimization and Grasshopper Optimization Algorithm. A reliable Pareto optimal dominance technique is then developed to compare solutions in multi-objective problems. In this technique, one solution reliably dominates another if it complies with the conditions of the regular Pareto optimal dominance and there are a certain minimum number of sampled points around the two solutions involved in the comparison. Using this method, constraint-based robust variants of Multi-Objective Particle Swarm Optimization and Multi-objective Grasshopper Optimization Algorithms are proposed. A large number of case studies with single and multiple objectives are solved in this thesis, including optimization test functions and marine propeller design problems. The statistical results and in-depth analysis show the merits of the proposed robust optimization technique when using evolutionary algorithms in this thesis.