Analysis of Chaotic Maps for Global Optimization and a Hybrid Chaotic Pattern Search Algorithm for Optimizing the Reliability of a Bank

Abstract

Optimization is an imperative feature in almost all fields of Engineering, Economics, and Sciences. Due to the advent of high-end computers and the gradual increase in the complexity of optimization problems, algorithms for numerical optimization have been developed. Numerous existing numerical optimization algorithms suffer from premature convergence, poor local/global search abilities, and high computational complexity. A chaotic optimization algorithm and a chaotic map could help overcome most of these setbacks. This paper offers a detailed study and analysis of five chaotic maps used for global Optimization, namely Chebyshev, Cubic, ICMIC, Neuron, and Sine maps. This work also proposes a pioneering global optimization method, Hybrid Chaotic Pattern Search Algorithm (HCPSA), for finding the global minimum for multivariable unconstrained optimization problems. Numerical results over 12 benchmark functions and comparative results (comparison of accuracy and computational time) with some popular algorithms evidence the effectiveness of the proposed algorithm for higher dimensional non-linear functions. The efficient usage of chaotic maps has helped reduce the computational time to evaluate the optimum for higher dimensional non-linear functions. To showcase the use of HCPSA in a real-world problem, we have taken the problem of analyzing financial ratios for predicting bankruptcy. Banks predict bankruptcy from the start of their businesses to determine their financial stability. In this work, we initially perform Logistic Regression (LR) on the data obtained from the banks to get the reliability function with financial ratios as decision variables. After this, the function is maximized using HCPSA and a Chebyshev map. This methodology is beneficial for decision-makers within a bank to maximize the reliability of the financial ratios and, most essential, to protect the bank from disasters. Comparative results of reliability prediction using HCPSA and PSO and a non-parametric statistical test proves that the proposed algorithm is better in terms of accuracy.