Application of chaotic mutation strategies-based single candidate optimization algorithms in engineering design problems

Heuristic search algorithms are a widely used methodology for addressing complex optimization problems. Typically, these algorithms are based on swarm or population-based approaches with the goal of converging to the optimal solution by navigating through a set of potential solutions across the search space. However, most of these approaches have shortcomings such as the requirement of a significant number of parameters, high computational cost, premature convergence and the inability to guarantee a global solution. In this thesis, we consider a new heuristic search strategy, the Single Candidate Optimization (SCO) algorithm, which, in contrast to swarm-based methodologies, uses a single candidate solution throughout the optimization process. SCO uses a two-stage methodology for updating the position of the candidate solution. In the first stage, the candidate searches various regions of the search space utilizing its own internal knowledge. In the second stage, the candidate searches for the optimal solution within its region using local search methods. In this way, the SCO algorithm strikes a balance between exploration and exploitation capabilities. The SCO algorithm offers several advantages such as simplicity, limited number of parameters, low computational cost and high performance. However, the SCO algorithm is not without potential shortcomings. These include the limited exploration capability of a single candidate solution, the risk of getting caught in local minima, and the possibility of getting stuck in suboptimal regions. While SCO's exploration mechanism can quickly lead a candidate solution to zero, this can prevent SCO from converging to a solution for problems with non-zero solutions. Various methods can be proposed to address these limitations and improve the performance of the SCO algorithm. In this thesis, a new mutation technique based on chaotic functions such as Chaucy, Gauss and Levy is proposed to improve the efficiency of the SCO algorithm and overcome the mentioned handicaps. This mutation operator improves the exploration capability by making the candidate solution traverse different regions of the search space while updating its position. The proposed Chaotic mutation based Single Candidate Optimizer (CSCO) algorithm is evaluated against the original SCO algorithm for 23 different benchmark functions obtained from the literature. In addition, the performance of the CSCO algorithm is evaluated by analyzing various engineering design problems identified in the literature. These include Welded Beam Design (WBD), Compression Spring Design (CSD) and Pressure Vessel Design (PVD). In addition to the original SCO algorithm, popular heuristic algorithms frequently used in the literature were also used in the comparisons. The results show a significant improvement in the performance of CSCO using different mutation techniques. First of all, in the comparison of 23 benchmark functions, the CSCO algorithm outperformed the original SCO algorithm by 73.91% for the best metric values. Likewise, when comparing the worst metric values, CSCO outperforms the original SCO algorithm by 56.52% for the benchmark functions. Furthermore, CSCO shows a 56.52% more effective median metric performance than SCO in 13 functions and a 43.48% more effective mean metric performance in 10 functions. It is also noteworthy that CSCO exhibits a smoother and more stable behavior across test functions, with a standard deviation 69.57% lower than SCO. These observations confirm that CSCO has a superior capability in optimizing test functions compared to SCO. In addition, when the convergence curves of SCO and CSCO algorithms for 10 engineering design problems are analyzed, it is seen that in 9 out of 10 problems, the CSCO algorithm converges to the solution point in fewer iterations without getting stuck in local minima. In engineering design problems, the CSCO algorithm demonstrates the efficiency of the improvements made with a 90% success rate.