Field Of Metaheuristics Research Articles

Learning tabu search algorithms: A scheduling application

Metaheuristics provide efficient approaches for many combinatorial problems. Research focused on improving the performance of metaheuristics has increasingly relied on either combining different metaheuristics, or leveraging methods that originate outside the field of metaheuristics. This paper presents a learning algorithm for improving tabu search by reducing its search space and evaluation effort. The learning tabu search algorithm uses classification methods in order to better motivate moves through the search space. The learning tabu search is compared to an enhanced version of tabu search that includes diversification, intensification and three neighborhoods in a physician scheduling application. We use the deterministic case to test the design of the algorithm (features and parameters) and as a proof of concept. We then solve the stochastic version of the problem. The experimental results demonstrate the benefit of using a learning mechanism under stochastic conditions.

Dynamic Random Walk and Dynamic Opposition Learning for Improving Aquila Optimizer: Solving Constrained Engineering Design Problems.

One of the most important tasks in handling real-world global optimization problems is to achieve a balance between exploration and exploitation in any nature-inspired optimization method. As a result, the search agents of an algorithm constantly strive to investigate the unexplored regions of a search space. Aquila Optimizer (AO) is a recent addition to the field of metaheuristics that finds the solution to an optimization problem using the hunting behavior of Aquila. However, in some cases, AO skips the true solutions and is trapped at sub-optimal solutions. These problems lead to premature convergence (stagnation), which is harmful in determining the global optima. Therefore, to solve the above-mentioned problem, the present study aims to establish comparatively better synergy between exploration and exploitation and to escape from local stagnation in AO. In this direction, firstly, the exploration ability of AO is improved by integrating Dynamic Random Walk (DRW), and, secondly, the balance between exploration and exploitation is maintained through Dynamic Oppositional Learning (DOL). Due to its dynamic search space and low complexity, the DOL-inspired DRW technique is more computationally efficient and has higher exploration potential for convergence to the best optimum. This allows the algorithm to be improved even further and prevents premature convergence. The proposed algorithm is named DAO. A well-known set of CEC2017 and CEC2019 benchmark functions as well as three engineering problems are used for the performance evaluation. The superior ability of the proposed DAO is demonstrated by the examination of the numerical data produced and its comparison with existing metaheuristic algorithms.

Analytical and Comparative Study for Optimization Problems

Finding an optimal solution to some problem, like minimizing and maximizing the objective function, is the goal of Single-Objective Optimization (SOP). Real-world problems, on the other hand, are more complicated and involve a wider range of objectives, several objectives should be maximized in such problems. No single solution could be enhanced in all objectives without deteriorating at least one other goal, which is the definition of Pareto-optimality. Understanding the idea of Multi-Objective Optimization (MOP) is thus necessary to find the optimum solution. Multi-objective evolutionary algorithm (MOEA) are made to simultaneously assess many objectives and find Pareto-optimal solutions, MOEA can resolve multi-objective and single-objective optimization problems. This paper aims to introduce a survey study for optimization problem solutions by comparing techniques, advantages, and disadvantages of SOP and MOP with metaheuristics and evolutionary algorithms. From this study, we conduct that the efficiency of MOP lies in the present more than one SOP, but it takes a longer time to process and train and is not suitable for all applications, While SOP is faster and more useful in stock and profit maximization applications. And the posterior techniques are considered the dominant approach to solving multi-objective problems by the use of the field of metaheuristics. Index Terms— Multi-Objective Evolutionary Algorithm, Multi-Objective Optimization, Optimization problem, Objective Function, Single-Objective Optimization.

Lessons from the Evolutionary Computation Bestiary.

The field of metaheuristics has a long history of finding inspiration in natural systems, starting from evolution strategies, genetic algorithms, and ant colony optimization in the second half of the 20th century. In the last decades, however, the field has experienced an explosion of metaphor-centered methods claiming to be inspired by increasingly absurd natural (and even supernatural) phenomena-several different types of birds, mammals, fish and invertebrates, soccer and volleyball, reincarnation, zombies, and gods. Although metaphors can be powerful inspiration tools, the emergence of hundreds of barely discernible algorithmic variants under different labels and nomenclatures has been counterproductive to the scientific progress of the field, as it neither improves our ability to understand and simulate biological systems nor contributes generalizable knowledge or design principles for global optimization approaches. In this article we discuss some of the possible causes of this trend, its negative consequences for the field, and some efforts aimed at moving the area of metaheuristics toward a better balance between inspiration and scientific soundness.

Initialization of metaheuristics: comprehensive review, critical analysis, and research directions

AbstractInitialization of metaheuristics is a crucial topic that lacks a comprehensive and systematic review of the state of the art. Providing such a review requires in‐depth study and knowledge of the advances and challenges in the broader field of metaheuristics, especially with regard to diversification strategies, in order to assess the proposed methods and provide insights for initialization. Motivated by the aforementioned research gap, we provide a related review and begin by describing the main metaheuristic methods and their diversification mechanisms. Then, we review and analyze the existing initialization approaches while proposing a new categorization of them. Next, we focus on challenging optimization problems, namely constrained and discrete optimization. Lastly, we give insights on the initialization of local search approaches.

A qualitative systematic review of metaheuristics applied to tension/compression spring design problem: Current situation, recommendations, and research direction

New metaheuristic algorithms have soared over the past ten years. A common practice in proposing a new algorithm is validating it on several benchmark functions and engineering problems. Although CEC benchmark problems are specifically designed to validate the performance of new meta-heuristics, engineering design problems from pressure vessels to springs have been used in hundreds of papers to prove algorithm efficiency. To date, no benchmark practices have been established yet, i.e., researchers design their own benchmark to validate their algorithm. Thus, the high number of new algorithms combined with the high number of different benchmarking setups complicates the comparing and validating processes. In this paper, we study benchmark practices related to engineering applications. In particular, our exhaustive qualitative systematic review focuses on metaheuristics applied to the tension/compression spring design problem (TCSDP). The aim of this study is threefold: (i) evaluate where the field stands in regards of algorithm performance on the TCSDP, (ii) evaluate benchmarking practices, and (iii) facilitate future algorithm comparison. For these purposes, we first review all the existing metaheuristics applied to the TCSDP in their first publication. For each paper, we gather the data regarding the problem definition, the simulation setup, and the optimized design. We evaluated the data through several metrics to find the best-optimized design so far. Our findings and analysis concluded that the field of metaheuristics and its benchmarking practice have not reached maturity yet. Thus, we recommend some actions to address the issues and provide future research directions.

A survey of recently developed metaheuristics and their comparative analysis

The aim of this study was to gather, discuss, and compare recently developed metaheuristics to understand the pace of development in the field of metaheuristics and make some recommendations for the research community and practitioners. By thoroughly and comprehensively searching the literature and narrowing the search results, we created with a list of 57 novel metaheuristic algorithms. Based on the availability of the source code, we reviewed and analysed the optimization capability of 26 of these algorithms through a series of experiments. We also evaluated the exploitation and exploration capabilities of these metaheuristics by using 50 unimodal functions and 50 multimodal functions, respectively. In addition, we assessed the capability of these algorithms to balance exploration and exploitation by using 29 shifted, rotated, composite, and hybrid CEC-BC-2017 benchmark functions. Moreover, we evaluated the applicability of these metaheuristics on four real-world constrained engineering optimization problems. To rank the algorithms, we performed a nonparametric statistical test, the Friedman mean rank test. Based on the statistical results for the unimodal and multimodal functions, we declared that the GBO, PO, and MRFO algorithms have better exploration and exploitation capabilities. Based on the results for the CEC-BC-2017 benchmark functions, we found the MPA, FBI, and HBO algorithms to be the most balanced. Finally, based on the results for the constrained engineering optimization problems, we declared that the HBO, GBO, and MA algorithms are the most suitable. Collectively, we confidently recommend the GBO, MPA, PO, and HBO algorithms for real-world optimization problems.

Diversified sine–cosine algorithm based on differential evolution for multidimensional knapsack problem

The sine–cosine algorithm (SCA) is one of the simplest and efficient stochastic search algorithms in the field of metaheuristics. It has shown its efficacy in solving several real-life applications. However, in some cases, it shows stagnation at local optima and premature convergence issues due to low exploitation ability and insufficient diversity skills. To overcome these issues from the SCA, its enhanced version named ISCA is developed in this paper. The proposed ISCA is designed based on modifying the original search mechanism of the SCA and hybridizing it with a differential evolution (DE) algorithm. The search procedure in the ISCA switches between the modified search mechanism of the SCA and DE based on the evolutionary states of candidate solutions and a parameter called the switch parameter. The modified SCA enhances the exploitation ability and convergence speed, while the DE maintains the diversity of the population to avoid local optimal solutions. The parameters of the ISCA are tuned in such as way that they could balance the exploration and exploitation features. Validation of the ISCA is conducted on a benchmark set of 23 continuous optimization problems through different performance measures, which reveals its effectiveness as a better optimizer for continuous optimization problems. Furthermore, the proposed ISCA is extended to develop its efficient binary version named BISCA for solving multidimensional knapsack problems. A benchmark collection of 49 instances is used for the performance evaluation of the BISCA. Comparison of results produced by the BISCA with other algorithms and previous studies indicates its better search efficiency and verifies it as an effective alternative for solving the MKP.

A reinforcement learning-Variable neighborhood search method for the capacitated Vehicle Routing Problem

Finding the best sequence of local search operators that yields the optimal performance of Variable Neighborhood Search (VNS) is an important open research question in the field of metaheuristics. This paper proposes a Reinforcement Learning method to address this question. We introduce a new hyperheuristic scheme, termed Bandit VNS, inspired by the Multi-Armed Bandit (MAB), a particular type of a single state reinforcement learning problem. In Bandit VNS, we utilize the General Variable Neighborhood Search metaheuristic and enhance it by a hyperheuristic strategy. We examine several variations of the Upper Confidence Bound algorithm to create a reliable strategy for adaptive neighborhood selection. Furthermore, we utilize Adaptive Windowing, a state of the art algorithm to estimate and detect changes in the data stream. Bandit VNS is designed for effective parallelization and encourages cooperation between agents to produce the best solution quality. We demonstrate this concept’s advantages in accuracy and speed by extensive experimentation using the Capacitated Vehicle Routing Problem. We compare the novel scheme’s performance against the conventional General Variable Neighborhood Search metaheuristic in terms of the CPU time and solution quality. The Bandit VNS method shows excellent results and reaches significantly higher performance metrics when applied to well-known benchmark instances. Our experiments show that, our approach achieves an improvement of more than 25% in solution quality when compared to the General Variable Neighborhood Search method using standard library instances of medium and large size.

Exposing the grey wolf, moth‐flame, whale, firefly, bat, and antlion algorithms: six misleading optimization techniques inspired bybestialmetaphors

AbstractWe present a rigorous, component‐based analysis of six widespread metaphor‐based algorithms for tackling continuous optimization problems. In addition to deconstructing the six algorithms into their components and relating them with equivalent components proposed in well‐established techniques, such asparticle swarm optimizationandevolutionary algorithms, we analyze the use of the metaphors that inspired these algorithms to understand whether their usage has brought any novel and useful concepts to the field of metaheuristics. Our result is that the ideas proposed in the six studied algorithms have been in the literature of metaheuristics for years and that the only novelty in these self‐proclaimednovelalgorithms is six different terminologies derived from the use of new metaphors. We discuss the reasons why the metaphors that inspired these algorithms are misleading and ultimately useless as a source of inspiration to design effective optimization tools. Finally, we discuss the rationale often presented by the authors of metaphor‐based algorithms as their motivation to propose more algorithms of this type, which is based on a wrong understanding of the no‐free‐lunch theorems for optimization.

Permutation Tests for Metaheuristic Algorithms

Many metaheuristic approaches are inherently stochastic. In order to compare such methods, statistical tests are needed. However, choosing an appropriate test is not trivial, given that each test has some assumptions about the distribution of the underlying data that must be true before it can be used. Permutation tests (P-Tests) are statistical tests with minimal number of assumptions. These tests are simple, intuitive and nonparametric. In this paper, we argue researchers in the field of metaheuristics to adopt P-Tests to compare their algorithms. We define two statistic tests and then present an algorithm that uses them to compute the p-value. The proposed process is used to compare 5 metaheuristic algorithms on 10 benchmark functions. The resulting p-values are compared with the p-values of two widely used statistical tests. The results show that the proposed P-test is generally consistent with the classical tests, but more conservative in few cases.

DSGWO: An improved grey wolf optimizer with diversity enhanced strategy based on group-stage competition and balance mechanisms

Grey wolf optimizer (GWO) is a popular algorithm in the field of meta-heuristics with fast convergence speed and strong exploitation ability for solving different types of optimization problems. However, there are two problems presented in the optimization process of GWO. Problem (1): GWO algorithm uses three leading wolves to direct the population for search, resulting in poor population diversity. Problem (2): Individuals selected in the optimization process of GWO have the current optimal fitness value, resulting in poor global search capabilities of the algorithm, and the population may tend to converge prematurely and fall into local optimum. In order to solve the above problems, this paper proposes the Diversity enhanced Strategy based Grey Wolf Optimizer (DSGWO), which combines two mechanisms to improve the performance of the GWO algorithm, including the group-stage competition mechanism and the exploration–exploitation balance mechanism. The experimental results are evaluated by using IEEE CEC 2014 benchmark functions and two engineering problems. The Wilcoxon rank-sum test is also conducted to measure the performance of DSGWO. The results demonstrate that the DSGWO algorithm can efficiently obtain the optimal solution of the dataset used in this paper, preserve more population diversity, and enhance the global search capability. In addition, through the application of two engineering problems, it is verified that DSGWO is suitable for solving engineering design problems.

PopDMMO: A general framework of population-based stochastic search algorithms for dynamic multimodal optimization

Dynamic multimodal optimization problems (DMMOPs) are a class of problems consisting of two characteristics, i.e., dynamic and multimodal natures. The former characteristic reveals that the properties of DMMOPs change over time, which is derived from dynamic optimization problems (DOPs). The latter one indicates that there exist multiple global or acceptable local optima, which comes from the multimodal optimization problems (MMOPs). Although there has been much attention to both DOPs and MMOPs in the field of meta-heuristics, there is little work devoting to the connection between the dynamic and multimodal natures in DMMOPs. To solve DMMOPs, the strategies dealing with dynamic and multimodal natures in the algorithms should cooperate with each other. Before looking deeply into the connections between two natures, there is necessary to measure the performances of the methods dealing with two natures in DMMOPs. In this paper, first, considering the dynamic and multimodal natures of DMMOPs, we design a set of benchmark problems to simulate various dynamic and multimodal environments. Then, we propose the optimization framework called PopDMMO containing several popular algorithms and methods to test and compare the performances of these algorithms, which gives a general view of solving DMMOPs.

Attraction Basins in Metaheuristics: A Systematic Mapping Study

Context: In this study, we report on a Systematic Mapping Study (SMS) for attraction basins in the domain of metaheuristics. Objective: To identify research trends, potential issues, and proposed solutions on attraction basins in the field of metaheuristics. Research goals were inspired by the previous paper, published in 2021, where attraction basins were used to measure exploration and exploitation. Method: We conducted the SMS in the following steps: Defining research questions, conducting the search in the ISI Web of Science and Scopus databases, full-text screening, iterative forward and backward snowballing (with ongoing full-text screening), classifying, and data extraction. Results: Attraction basins within discrete domains are understood far better than those within continuous domains. Attraction basins on dynamic problems have hardly been investigated. Multi-objective problems are investigated poorly in both domains, although slightly more often within a continuous domain. There is a lack of parallel and scalable algorithms to compute attraction basins and a general framework that would unite all different definitions/implementations used for attraction basins. Conclusions: Findings regarding attraction basins in the field of metaheuristics reveal that the concept alone is poorly exploited, as well as identify open issues where researchers may improve their research.

Nonlinear-based Chaotic Harris Hawks Optimizer: Algorithm and Internet of Vehicles application

Harris Hawks Optimizer (HHO) is one of the many recent algorithms in the field of metaheuristics. The HHO algorithm mimics the cooperative behavior of Harris Hawks and their foraging behavior in nature called surprise pounce. HHO benefits from a small number of controlling parameters setting, simplicity of implementation, and a high level of exploration and exploitation. To alleviate the drawbacks of this algorithm, a modified version called Nonlinear based Chaotic Harris Hawks Optimization (NCHHO) is proposed in this paper. NCHHO uses chaotic and nonlinear control parameters to improve HHO’s optimization performance. The main goal of using the chaotic maps in the proposed method is to improve the exploratory behavior of HHO. In addition, this paper introduces a nonlinear control parameter to adjust HHO’s exploratory and exploitative behaviors. The proposed NCHHO algorithm shows an improved performance using a variety of chaotic maps that were implemented to identify the most effective one, and tested on several well-known benchmark functions. The paper also considers solving an Internet of Vehicles (IoV) optimization problem that showcases the applicability of NCHHO in solving large-scale, real-world problems. The results demonstrate that the NCHHO algorithm is very competitive, and often superior, compared to the other algorithms. In particular, NCHHO provides 92% better results in average to solve the uni-modal and multi-modal functions with problem dimension sizes of D = 30 and 50, whereas, with respect to the higher dimension problem, our proposed algorithm shows 100% consistent improvement with D = 100 and 1000 compared to other algorithms. In solving the IoV problem, the success rate was 62.5%, which is substantially better in comparison with the state-of-the-art algorithms. To this end, the proposed NCHHO algorithm in this paper demonstrates a promising method to be widely used by different applications, which brings benefits to industries and businesses in solving their optimization problems experienced daily , such as resource allocation, information retrieval, finding the optimal path for sending data over networks, path planning, and so many other applications.

A comprehensive comparison of recent developed meta-heuristic algorithms for streamflow time series forecasting problem

Hydrological models play a crucial role in water planning and decision making. Machine Learning-based models showed several drawbacks for frequent high and a wide range of streamflow records. These models also experience problems during the training process such as over-fitting or trapping in searching for global optima To overcome these limitations, the current study attempts to hybridize the recently developed physics-inspired metaheuristic algorithms (MHAs) such as Equilibrium Optimization (EO), Henry Gases Solubility Optimization (HGSO), and Nuclear Reaction Optimization(NRO) with Multi-layer Perceptron (MLP). These models’ accuracy will be inspected to solve the streamflow forecasting problem where the streamflow dataset was collected through 130 years from a station located on the High Aswan Dam (HAD). The performance of proposed models then will be compared with two traditional neural network models(MLP and RNN), and nine well-known hybrid MLP-based models belong to the different branches of the metaheuristic field (evolutionary group, swarm group, and physics group). The internal parameters of the proposed models will be initialized and optimized. Different performance metrics will be used to examine the performance of the proposed models. The stability of the proposed models and the convergence speed will be evaluated. Finally, ranking these models based on different performance evaluations will be carried out. The results show that the models in the group of Physics-MLP are more reliable in capturing the streamflow patterns, followed by the Swarm-MLP group and then by the Evolutionary-MLP group. Finally, among the all employed methods, the NRO has the best accuracy with the lowest RMSE(2.35), MAE(1.356), MAPE(16.747), and the highest WI(0.957), R(0.924), and confidence in forecasting the streamflow of Aswan High Dam. It can be concluded that augmenting the NRO algorithm with MLP can be a reliable tool in forecasting the monthly streamflow with a high level of precision, speed convergence, and high constancy level.

Performance evaluation of firefly algorithm with unconstrained optimization issues

In this paper, we have investigated a new spectral Quasi-Newton (QN) algorithm. New search directions of the proposed algorithm increase its stability and increase the arrival to the optimum solution with a lowest cost value and our numerical applications on the standard Firefly Algorithm (FA)and the new proposed algorithm are powerful as in meta-heuristic field. Our new proposed algorithm has quite common uses in several sciences and engineering problems. Finally, our numerical results show that the proposed technique is the best and its accuracy higher than the accuracy of the standard FA. These numerical results are compared using statistical analysis to evaluate the efficiency and the robustness of new proposed algorithm.

Re-sampled inheritance compact optimization

Compact optimization is an alternative paradigm in the field of metaheuristics requiring a modest use of memory to optimize a problem. As opposed to population-based algorithms, which conduct the search by employing a set of candidate solutions, compact algorithms use a probabilistic model to describe how solutions are distributed over the search space. Compared to other Estimation of Distribution Algorithms, peculiar features such as the use of simple probabilistic models, in which variables are treated independently, and the need for a minimal number of solutions to be sampled to perform the search, make these algorithms suitable for those applications plagued by memory limitations. Compact algorithms show good results on different kinds of optimization problems but often prematurely converge and perform poorly on non-separable. In this paper, we attempt to overcome these limitations by combining compact algorithms with a restart mechanism named Re-Sampled Inheritance (RI) whose purpose is to avoid premature convergence while also inheriting parts of the variables from the best solution found so far. To assess the effect of the RI mechanism, we extensively test various existing compact algorithms, with and without RI, and compare the best RI-based compact algorithm against several competing algorithms on several optimization problems at different dimensionalities. We also evaluate the effect of the RI parameters on the overall algorithmic performance. Our numerical results not only show that RI consistently enhances the performances of compact algorithms, but also shed some light on the effectiveness of different compact logics at handling problems at different dimensionalities.

Sine cosine grey wolf optimizer to solve engineering design problems

Balancing the exploration and exploitation in any nature-inspired optimization algorithm is an essential task, while solving the real-world global optimization problems. Therefore, the search agents of an algorithm always try to explore the unvisited domains of a search space in a balanced manner. The sine cosine algorithm (SCA) is a recent addition to the field of metaheuristics that finds the solution of an optimization problem using the behavior of sine and cosine functions. However, in some cases, the SCA skips the true solutions and trapped at sub-optimal solutions. These problems lead to the premature convergence, which is harmful in determining the global optima. Therefore, in order to alleviate the above-mentioned issues, the present study aims to establish a comparatively better synergy between exploration and exploitation in the SCA. In this direction, firstly, the exploration ability of the SCA is improved by integrating the social and cognitive component, and secondly, the balance between exploration and exploitation is maintained through the grey wolf optimizer (GWO). The proposed algorithm is named as SC-GWO. For the performance evaluation, a well-known set of benchmark problems and engineering test problems are taken. The dimension of benchmark test problems is varied from 30 to 100 to observe the robustness of the SC-GWO on scalability of problems. In the paper, the SC-GWO is also used to determine the optimal setting for overcurrent relays. The analysis of obtained numerical results and its comparison with other metaheuristic algorithms demonstrate the superior ability of the proposed SC-GWO.

Levy Flights in Metaheuristics Optimization Algorithms – A Review

ABSTRACT In recent years, Levy flight (LF) is increasingly being employed as search mechanism in metaheuristics optimization algorithms (MOA) to solve complex real world problems. LF-based algorithms are found to exhibit superior or equivalent results to their non-LF counterparts and are expected to be advantageous in situations where no prior information is accessible, the targets are challenging to ascertain, and the distribution of targets is scarce. It has emerged as an alternative to Gaussian distribution (GD) to achieve randomization in MOA and have applications in diverse biological, chemical, and physical phenomena. The purpose of this article is to make the readers acquainted with the applicability of LF in some of the latest optimization algorithm applied in the field of metaheuristics. Also the present study deals with examination of basic underlying principle in the working of LF along with their related properties.