The purpose of this article is to review the literature on the topic of deterministic vehicle routing problem (VRP) and to give a review on the exact and approximate solution techniques. More specifically the approximate (Meta-heuristic) solution techniques are classified into: tabu search, simulated annealing, genetic algorithm, evolutionary algorithm, hybrid algorithm, and Ant Colony Optimization. Each of these solution techniques is briefly discussed and a case study from the literature is presented.

Task assignment problem (TAP) involves assigning a number of tasks to a number of processors in distributed computing systems and its objective is to minimize the sum of the total execution and communication costs, subject to all of the resource constraints. TAP is a combinatorial optimization problem and NP-complete. This paper proposes a hybrid Meta-heuristic algorithm for solving TAP in a heterogeneous distributed computing system. To compare our algorithm with previous ones, an extensive computational study on some benchmark problems was conducted. The results obtained from the computational study indicate that the proposed algorithm is a viable and effective approach for the TAP.

Investment decision making is one of the key issues in financial management. Selecting the appropriate tools and techniques that can make optimal portfolio is one of the main objectives of the investment world. This study tries to optimize the decision making in stock selection or the optimization of the portfolio by means of the artificial colony of honey bee algorithm. To determine the effectiveness of the algorithm, its sharp criteria was calculated and compared with the portfolio made up of genes and ant colony algorithms. The sample consisted of active firms listed on the Tehran Stock Exchange from 2005 to 2015. The sample selected by the systematic removal method. The findings show that artificial bee colony algorithm functions better than the genetic and ant colony algorithms in terms of portfolio formation.

In this paper, a new nature-inspired population-based Meta-heuristic algorithm is presented. The algorithm, called Cyclical Parthenogenesis Algorithm (CPA), is inspired by reproduction and social behavior of some zoological species like aphids, which can reproduce with and without mating. The algorithm considers each candidate solution as a living organism and iteratively improves the quality of solutions utilizing reproduction and displacement mechanisms. Mathematical and engineering design problems are employed in order to investigate the viability of the proposed algorithm. The results indicate that the performance of the newly proposed algorithm is comparable to other state-of-the-art Meta-heuristic algorithms.

This article presents a comprehensive review of chaos embedded Meta-heuristic optimization algorithms and describes the evolution of this algorithms along with some improvements, their combination with various methods as well as their applications. The reported results indicate that chaos embedded algorithms may handle engineering design problems efficiently in terms of precision and convergence and, in most cases; they outperform the results presented in the previous works. The main goal of this paper is to providing useful references to fundamental concepts accessible to the broad community of optimization practitioners.

Background and Objectives: The development of effective Meta-heuristic algorithms is crucial for solving complex optimization problems. This paper introduces the Society Deciling Process (SDP), a novel socio-inspired Meta-heuristic algorithm that simulates the social categorization into deciles based on metrics such as income, occupation, and education. The objective of this research is to introduce the SDP algorithm and evaluate its performance in terms of convergence speed and hit rate, comparing it with seven well-established Meta-heuristic algorithms to highlight its potential in optimization tasks.Methods: The SDP algorithm's efficacy was evaluated using a comprehensive set of 14 general test functions, including benchmarks from the CEC 2019 and CEC 2022 competitions. The performance of SDP was compared against seven established Meta-heuristic algorithms: Artificial Hummingbird Algorithm (AHA), Dwarf Mongoose Optimization algorithm (DMO), Reptile Search Algorithm (RSA), Snake Optimizer (SO), Prairie Dog Optimization (PDO), Fick’s Law Optimization (FLA), and Gazelle Optimization Algorithm (GOA). Statistical analysis was conducted using Friedman's rank and Wilcoxon signed-rank tests to assess the relative performance in terms of exploration, exploitation capabilities, and proximity to the optimum solution.Results: The results demonstrated that the SDP algorithm outperforms its counterparts in terms of convergence speed and hit rate across the selected test functions. In statistical tests, SDP showed significantly better performance in exploration and exploitation, leading to a higher proximity to the optimum solution compared to the other algorithms. Furthermore, when applied to five complex engineering design problems, the SDP algorithm exhibited superior performance, outmatching the state-of-the-art algorithms in terms of effectiveness and efficiency.Conclusion: The Society Deciling Process (SDP) algorithm introduces a novel and effective approach to optimization, inspired by societal structure dynamics. Its superior performance in convergence speed, exploration and exploitation capabilities, and application to complex engineering problems establishes SDP as a promising Meta-heuristic algorithm. This research not only demonstrates the potential of socio-inspired algorithms in optimization tasks but also opens avenues for further enhancements in Meta-heuristic algorithm designs.

This work introduces an innovative heuristic algorithm named "Competition and Collaboration in Evading Threat (CCET)". Inspired by the escape behavior of animals such as deer, buffalo, sheep, etc., from predators like lions, leopards, tigers, etc., and also drawing parallels with soldiers evading attacks in war zones involving missiles, cannons, tanks, enemy gunfire, etc., the algorithm has been devised. In this approach, it is assumed that soldiers in war zones or domesticated animals are fleeing from threats and, despite competing in their escape, they collaborate with each other to ensure their survival. Unlike existing heuristic algorithms that rely on convergence, this proposed algorithm focuses on a novel approach based on the concept of divergence. The optimal response is determined based on the divergence of prey from the threat of the predator. The algorithm undergoes testing on 23 well-known benchmark functions, including unimodal, multimodal, and fixed-dimensional functions. The performance of the proposed algorithm is validated against recognized heuristic algorithms. Comparative results indicate that the proposed algorithm significantly demonstrates the capability to compete with well-known and powerful algorithms.