Using semi-independent variables to enhance optimization search

In this study, the concept of a semi-independent variable (SIV) problem representation is investigated that embodies a set of expected or desired relationships among the original variables, with the goal of increasing search effectiveness and efficiency. The proposed approach intends to eliminate the generation of infeasible solutions associated with the known relationships among the variables and cutting the search space, thereby potentially improving a search algorithm's convergence rate and narrowing down the search space. However, this advantage does not come for free. The issue is the multiplicity of SIV formulations and their varying degree of complexity, especially with respect to variable interaction. In this paper, we propose the use of automatic variable interaction analysis methods to compare and contrast different SIV formulations. The performance of the proposed approach is demonstrated by implementing it within a number of classical and evolutionary optimization algorithms (namely, interior-point algorithm, simulated annealing, particle swarm optimization, genetic algorithm and differential evolution) in the application to several practical engineering problems. The case study results clearly show that the population-based algorithms can significantly benefit from the proposed SIV formulation resulting in better solutions with fewer function evaluations than in the original approach. The results also indicate that an automatic variable interaction analysis is capable of estimating the difficulty of the resultant SIV formulations prior to any optimization attempt.