Improvised Artificial Electric Field Algorithms for Continuous and Discrete Optimization Problems

Abstract

Metaheuristic algorithms play a crucial role in solving complex optimization problems across various domains. Flexibility, scalability, robustness, a complementary role to exact methods, and ability to solve complex problems of practical applications are some primary reasons to use metaheuristics. Differential Evolution, Particle Swarm Optimization, Memetic Algorithms, and Artificial Electric Field Algorithm (AEFA) are some good examples of metaheuristics. This thesis is dedicated to the design and experiment of advanced versions of AEFA. The work carried out in this thesis aims to develop competent and efficient variants of AEFA for solving continuous and discrete optimization problems along with some practical applications in the areas of neural network training and medical image segmentation. A novel variant of AEFA, termed adaptive AEFA (iAEFA), incorporating a Com prehensive Learning (CL) strategy, is introduced specifically for continuous optimiza tion problems. The CL strategy is one of the most popular learning mechanisms, integrated in several metaheuristics for the identification of good individuals in the search space. This newly proposed iAEFA undergoes rigorous testing across twenty three benchmark problems, including the formidable 100-digit challenge benchmark problems of the CEC 2019 test suites, spanning dimensions 9, 10, 16, and 18. The performance of iAEFA is critically evaluated against seven leading-edge algorithms using a suite of metrics, complemented by statistical validation through the applica tion of appropriate statistical tests. A theoretical analysis is also performed to show its convergence ability using the linear recurrence method. Both theoretical and nu merical examinations underscore the proposed iAEFA’s efficiency and effectiveness in addressing continuous optimization problems. Another AEFA variant named PAEFA is developed, featuring a competition and collaboration-based multilevel structure designed to solve high-dimensional continuous optimization problems. PAEFA constructs a multilevel structure and places them in specific layers. The whole population is divided into two groups of winners and losers by pairwise comparison of their fitness in the same layer. Losers collaborate with their respective winners, whereas winners collaborate with individuals who are on the upper layers. In PAEFA, each individual has their own learning mechanism, which can learn from more than one exemplar, rather than only from the global best. With the knowledge of this structure, the diversity of the population increases, which strengthens the performance of PAEFA. To verify the adaptability of PAEFA, extensive experiments are performed on the CEC 2017 test suite at 30, 50, and 100 dimensions. We have studied the diversity factor of PAEFA using all three dimensions. These experiments suggest that PAEFA outperforms over thirty state-of-the-art algorithms in terms of accuracy, statistical results, and convergence speed while achieving comparable computational time in most cases and showing the validity of results. Moreover, two binary adaptations of AEFA designed to address continuous as well as discrete optimization problems. By transforming the search space into discrete segments, these binary variants of AEFA achieve rapid convergence, making them ex ceptionally suitable for real-life optimization tasks. Within this binary framework, posi tion parameters are encoded as binary digits (0 or 1), facilitating a distinct approach to problem-solving. The performance of these binary versions is rigorously tested against a spectrum of unimodal, multimodal, and discrete optimization problems, with their ef fectiveness benchmarked alongside seven state-of-the-art optimization algorithms. The comparative evaluations demonstrate the superior performance of these binary AEFA adaptations over competing algorithms. The use of the Wilcoxon signed-rank test, a non-parametric statistical technique, further establishes statistical significance of the experiments and dominance of the competing algorithms. Through an examination of time complexity and success rates, the robustness and efficiency of the proposed binary models are validated properly. Remarkably, the developed variants shine in its ability to solve large-scale knapsack problems with unprecedented accuracy, showcasing its optimization ability in solving complex optimization scenarios. AEFA variants are successfully applied to two practical optimization problems, showcasing their effectiveness and applicability. In the first case, AEFA is utilized to optimize multi-layer perceptrons (MLP) in Artificial Neural Networks, focusing on minimizing system weights and biases. This modified AEFA trained various datasets, including four classification and three approximation sets from the UCI Machine Learn ing Repository, alongside ten large-scale datasets. When compared against a range of metaheuristic and back propagation algorithms among others, the developed AEFA variants demonstrated superior performance across multiple metrics. The second application aims multilevel thresholding for image segmentation using Kapur’s entropy, highlighting thresholding’s importance in image segmentation. Nine intelligent AEFA models are assessed on COVID-19 dataset at thresholds of 3, 6, and 11, using metrics like MEAN, FSIM, and SSIM. The AEFA models compared to other metaheuristic models in producing superior segmented images at all thresholds, confirmed by statistical tests and demonstrating high accuracy. This underscores AEFA models’ advanced capability in tackling multilevel image thresholding, particularly in medical datasets.