Island-based Crow Search Algorithm for solving optimal control problems

Abstract

Crow Search Algorithm (CROW) is one of the members of recently developed swarm-based metaheuristic algorithms. Literature includes different applications of this algorithm on engineering design problems. However, this optimization method suffers from some drawbacks such as premature convergence and trapping into local optima at the early phase of iterations. In order to conquer this algorithm specific inabilities, many research studies have been conducted in the literature dealing with the improvements and enhancements on the search mechanism of CROW. Structured population mechanism plays a vital role in preserving and controlling diversity, and thus increases the solution efficiency in evolutionary algorithms. Among the different types of methods used in structured algorithms, the island model is one of the widely applied solution strategies, in which the population individuals are subdivided into a predefined number of subpopulations. Migration mechanism is the key factor increasing population diversity, which takes place between independently running subpopulations during iterations to exchange valuable and useful solution information. This study embeds the fundamentals of the island model concepts into the Crow Search Algorithm to improve its probing capabilities of the search domain, by means of the periodically interacting subpopulations on the course of iterations. In addition, four different hierarchical migration topologies have been proposed, and their search effectiveness have been evaluated and compared over 45 optimization test functions. The optimization function test set includes classic benchmark optimization problems and CEC 2015 benchmark functions. Furthermore, each hierarchical island model is applied for solving six different optimal control problems in order to investigate their efficiencies on multi-dimensional real world optimization problems. The investigated optimal control problems are parallel reaction, continuous stirred tank reactor, batch reactor consecutive reaction, nonlinear constrained mathematical system, nonlinear continuous stirred tank reactor and nonlinear crane container problems. It is found out that the island model concepts improved the optimization performance of CROW. The proposed island models outperformed or showed similar performance compared to the six selected literature optimizers for 27–29 classic benchmark optimization problems. Moreover, incorporating the master sub-population to the island model improved the optimization capability of the algorithm further in most cases. The island models that employ the master sub-population came up with more favorable results compared to their non-master sub-population peers in all optimal control problems. The island model that includes the master sub-population and has the migration topology entitled “82” found the most desirable solutions for 4–6 optimal control problems.