Stochastic Algorithms for Practical Optimization

Abstract

Stochastic is a research area that delivers general purpose high quality optimization algorithms, proved effectual in dealing with complex practical optimization problems. Success of stochastic greatly depends on their aptitude to establish equilibrium between their essential characters like diversification and Intensification. But in 1995 No Free Lunch Theorems by Wolpert and Macready established a general opinion that all algorithms perform equally when averaged over the whole function space and hence none of them can be claimed to be the best over the entire function space. For this reason, the basic algorithms require essential refinements and further developments. The main goal of this thesis is to develop new effective hybrid stochastics strategies and then to apply the developed hybrid stochastic algorithms to complex practical problems. Generally, hybridization is carried out by integrating powerful components of different algorithms, possibly of different natures. The first hybrid stochastic algorithm proposed in this work is Evolutionary Simplex Adaptive Hooke-Jeeves (𝐸𝑆𝐴𝐻𝐽) Algorithm which is a combination of Genetic Algorithm and modified Hooke-Jeeves method. The second proposed hybrid optimization algorithm is based on Differential Evolution (𝐷𝐸), Gradient Evolution (𝐺𝐸) and Jumping Technique named as Differential Gradient Evolution Plus (DGE+). The proposed algorithm hybridizes the above mentioned algorithms with the help of an improvised probability distribution, additionally provides a new shake off method to avoid premature convergence towards local optima. The third hybrid technique is implemented with the collaboration of Differential Evolution with Padé Approximation and named as Evolutionary Padé Approximation (𝐸𝑃𝐴) scheme. The last approach has been developed based on modified 𝑇𝑂𝑃𝑆𝐼𝑆 named Rank Based 𝑇𝑂𝑃𝑆𝐼𝑆 (RB-TOPSIS) for the multi-criteria decision making for Congress on Evolutionary Computation 2017 competition. The efficacies of developed hybrid stochastic techniques are validated theoretically as well as empirically. The computational efficiency of 𝐸𝑆𝐴𝐻𝐽 algorithm is tested by applying it to a collection of six diversified benchmark functions and five large scale economic load dispatch problems with valve point loading effects. Based on simulation results, the XXI solution quality, computational efficiency and consistency show the superiority of the 𝐸𝑆𝐴𝐻𝐽 algorithm over most of the other approaches. To evaluate the efficiency of DGE+ it has been applied on thirteen unconstrained test problems, four complex constrained non-linear chemical optimization problems and eight complex engineering design problems. The comparison revealed that DGE+ is able to provide very competitive and promising results. A general computational framework based on hybrid 𝐸𝑃𝐴 scheme for solving epidemiological dynamical models has been implemented. This framework is applied for numerical treatments of smoking model, Measles model and 𝐻𝐼𝑉/𝐴𝐼𝐷𝑆 model with vertical transmission. The 𝐸𝑃𝐴 scheme has provided convergence solution regarding relationship among the different population compartments for diseases free equilibrium, it has been observed that the results of 𝐸𝑃𝐴 scheme are more reliable and significant when a comparison is drawn with non-standardized finite difference (𝑁𝑆𝐹𝐷) numerical scheme. In the last study the results obtained by RB-TOPSIS are compared with the results of well known 12 algorithms presented in CEC 2017 to make decision about the best algorithm. The experimental results demonstrate that RB-TOPSIS not only overcomes the computational cost but also has better segmentation accuracy.