A Variable Search Space Strategy Based on Sequential Trust Region Determination Technique

The complexity of an optimization problem is determined by its decision and objective spaces. Over the past few decades, a large number of works have focused on the performance improvement of metaheuristic algorithms via the objective space, whereas studies related to the decision space have attracted little attentions. Moreover, metaheuristic algorithms may not obtain satisfactory results within an entire feasible region, even if sufficient computational resources are available. Therefore, reducing the search space (i.e., finding a trust region) may be an effective method to ensure that the convergence is sufficiently close to the global optimal region. However, inappropriate subspace size may also weaken the performance of algorithms except for ones with a sufficiently small search space. To alleviate aforementioned problems, a variable search space (VSS) strategy based on a sequential trust region determination approach is proposed in this paper. In the VSS, the entire optimization process is divided into two stages: the first stage is to use an optimization approach for sequentially finding the trust domain of each variable and then determine the best-matched subspace; the second stage is to employ the optimization method for searching an optimal/near-optimal solution within the found trust region. The effectiveness of the VSS is evaluated using two widely used test suites, that is, IEEE CEC2014 and BBOB2012. Experimental results indicate that improving the algorithm performance is an important method for tackling problems, but locating a trust region is also beneficial for metaheuristic algorithms to improve the solution precision, especially for complex optimization problems.