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15 pages, 474 KiB

Open AccessArticle

The Meaning and Accuracy of the Improving Functions in the Solution of the CBQR by Krotov’s Method

by Ido Halperin

Mathematics 2024, 12(4), 611; https://doi.org/10.3390/math12040611 - 19 Feb 2024

Viewed by 770

Abstract

A new solution to the continuous-time bilinear quadratic regulator optimal control problem (CBQR) was recently developed using Krotov’s Method. This paper provides two theoretical results related to the properties of that solution. The first discusses the equivalent representation of the cost-to-go performance index. [...] Read more.

A new solution to the continuous-time bilinear quadratic regulator optimal control problem (CBQR) was recently developed using Krotov’s Method. This paper provides two theoretical results related to the properties of that solution. The first discusses the equivalent representation of the cost-to-go performance index. The second one breaks down this equivalence into smaller identities referencing the components of the performance index. The paper shows how these results can be used to verify the numerical accuracy of the computed solution. Additionally, the meaning of the improving function and the equivalent representation, which are the main elements in the discussed CBQR’s solution, are explained according to the derived notions. A numerical example of structural control application exemplifies the significance of these results and how they can be applied to a specific CBQR problem. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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24 pages, 2325 KiB

Open AccessArticle

A Hybrid Initialization and Effective Reproduction-Based Evolutionary Algorithm for Tackling Bi-Objective Large-Scale Feature Selection in Classification

by Hang Xu, Chaohui Huang, Hui Wen, Tao Yan, Yuanmo Lin and Ying Xie

Mathematics 2024, 12(4), 554; https://doi.org/10.3390/math12040554 - 12 Feb 2024

Cited by 2 | Viewed by 901

Abstract

Evolutionary algorithms have been widely used for tackling multi-objective optimization problems, while feature selection in classification can also be seen as a discrete bi-objective optimization problem that pursues minimizing both the classification error and the number of selected features. However, traditional multi-objective evolutionary [...] Read more.

Evolutionary algorithms have been widely used for tackling multi-objective optimization problems, while feature selection in classification can also be seen as a discrete bi-objective optimization problem that pursues minimizing both the classification error and the number of selected features. However, traditional multi-objective evolutionary algorithms (MOEAs) can encounter setbacks when the dimensionality of features explodes to a large scale, i.e., the curse of dimensionality. Thus, in this paper, we focus on designing an adaptive MOEA framework for solving bi-objective feature selection, especially on large-scale datasets, by adopting hybrid initialization and effective reproduction (called HIER). The former attempts to improve the starting state of evolution by composing a hybrid initial population, while the latter tries to generate more effective offspring by modifying the whole reproduction process. Moreover, the statistical experiment results suggest that HIER generally performs the best on most of the 20 test datasets, compared with six state-of-the-art MOEAs, in terms of multiple metrics covering both optimization and classification performances. Then, the component contribution of HIER is also studied, suggesting that each of its essential components has a positive effect. Finally, the computational time complexity of HIER is also analyzed, suggesting that HIER is not time-consuming at all and shows promising computational efficiency. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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30 pages, 3532 KiB

Open AccessArticle

A Synergistic MOEA Algorithm with GANs for Complex Data Analysis

by Weihua Qian, Hang Xu, Houjin Chen, Lvqing Yang, Yuanguo Lin, Rui Xu, Mulan Yang and Minghong Liao

Mathematics 2024, 12(2), 175; https://doi.org/10.3390/math12020175 - 5 Jan 2024

Cited by 1 | Viewed by 1332

Abstract

The multi-objective evolutionary algorithm optimization (MOEA) is a challenging but critical approach for tackling complex data analysis problems. However, prevailing MOEAs often rely on single strategies to obtain optimal solutions, leading to concerns such as premature convergence and insufficient population diversity, particularly in [...] Read more.

The multi-objective evolutionary algorithm optimization (MOEA) is a challenging but critical approach for tackling complex data analysis problems. However, prevailing MOEAs often rely on single strategies to obtain optimal solutions, leading to concerns such as premature convergence and insufficient population diversity, particularly in high-dimensional data scenarios. In this paper, we propose a novel adversarial population generation algorithm, APG-SMOEA, which synergistically combines the benefits of MOEAs and Generative Adversarial Networks (GANs) to address these limitations. In order to balance the efficiency and quality of offspring selection, we introduce an adaptive population entropy strategy, which includes control parameters based on population entropy and a learning pool for storing and retrieving optimal solutions. Additionally, we attempt to alleviate the training complexity and model collapse problems common in GANs with APG-SMOEA. Experimental results on benchmarks demonstrate that the proposed algorithm is superior to the existing algorithms in terms of solution quality and diversity of low-dimensional or high-dimensional complex data. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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42 pages, 15274 KiB

Open AccessArticle

Evaluation and Analysis of Heuristic Intelligent Optimization Algorithms for PSO, WDO, GWO and OOBO

by Xiufeng Huang, Rongwu Xu, Wenjing Yu and Shiji Wu

Mathematics 2023, 11(21), 4531; https://doi.org/10.3390/math11214531 - 3 Nov 2023

Cited by 3 | Viewed by 1536

Abstract

In order to comprehensively evaluate and analyze the effectiveness of various heuristic intelligent optimization algorithms, this research employed particle swarm optimization, wind driven optimization, grey wolf optimization, and one-to-one-based optimizer as the basis. It applied 22 benchmark test functions to conduct a comparison [...] Read more.

In order to comprehensively evaluate and analyze the effectiveness of various heuristic intelligent optimization algorithms, this research employed particle swarm optimization, wind driven optimization, grey wolf optimization, and one-to-one-based optimizer as the basis. It applied 22 benchmark test functions to conduct a comparison and analysis of performance for these algorithms, considering descriptive statistics such as convergence speed, accuracy, and stability. Additionally, time and space complexity calculations were employed, alongside the nonparametric Friedman test, to further assess the algorithms. Furthermore, an investigation into the impact of control parameters on the algorithms’ output was conducted to compare and analyze the test results under different algorithms. The experimental findings demonstrate the efficacy of the aforementioned approaches in comprehensively analyzing and comparing the performance on different types of intelligent optimization algorithms. These results illustrate that algorithm performance can vary across different test functions. The one-to-one-based optimizer algorithm exhibited superior accuracy, stability, and relatively lower complexity. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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25 pages, 15461 KiB

Open AccessArticle

Non-Aggressive Adaptive Routing in Traffic

by Madhushini Narayana Prasad, Nedialko Dimitrov and Evdokia Nikolova

Mathematics 2023, 11(17), 3639; https://doi.org/10.3390/math11173639 - 23 Aug 2023

Viewed by 1131

Abstract

Routing a person through a traffic road network presents a tension between selecting a fixed route that is easy to navigate and selecting an aggressively adaptive route that minimizes travel time. In this paper, we propose a novel routing framework that strikes a [...] Read more.

Routing a person through a traffic road network presents a tension between selecting a fixed route that is easy to navigate and selecting an aggressively adaptive route that minimizes travel time. In this paper, we propose a novel routing framework that strikes a balance between adaptability and simplicity. Specifically, we propose to create non-aggressive adaptive routes that seek the best of both these extremes in the navigation world. These selected routes still adapt to changing traffic conditions, but we limit the number of adjustments made en route. This framework improves the driver experience by providing a continuum of options between saving travel time and reducing navigation stress. We design strategies to model single and multiple route adjustments, and investigate numerous techniques to solve these models for better route selection. To alleviate the intractability of handling real-life traffic data, we devise efficient algorithms with easily computable lower and upper bounds. We finally perform computational experiments on our algorithms to demonstrate the benefits of limited adaptability in terms of reducing the travel time. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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20 pages, 3060 KiB

Open AccessArticle

Design of Nonlinear Marine Predator Heuristics for Hammerstein Autoregressive Exogenous System Identification with Key-Term Separation

by Khizer Mehmood, Naveed Ishtiaq Chaudhary, Khalid Mehmood Cheema, Zeshan Aslam Khan, Muhammad Asif Zahoor Raja, Ahmad H. Milyani and Abdulellah Alsulami

Mathematics 2023, 11(11), 2512; https://doi.org/10.3390/math11112512 - 30 May 2023

Cited by 17 | Viewed by 1349

Abstract

Swarm-based metaheuristics have shown significant progress in solving different complex optimization problems, including the parameter identification of linear, as well as nonlinear, systems. Nonlinear systems are inherently stiff and difficult to optimize and, thus, require special attention to effectively estimate their parameters. This [...] Read more.

Swarm-based metaheuristics have shown significant progress in solving different complex optimization problems, including the parameter identification of linear, as well as nonlinear, systems. Nonlinear systems are inherently stiff and difficult to optimize and, thus, require special attention to effectively estimate their parameters. This study investigates the parameter identification of an input nonlinear autoregressive exogenous (IN-ARX) model through swarm intelligence knacks of the nonlinear marine predators’ algorithm (NMPA). A detailed comparative analysis of the NMPA with other recently introduced metaheuristics, such as Aquila optimizer, prairie dog optimization, reptile search algorithm, sine cosine algorithm, and whale optimization algorithm, established the superiority of the proposed scheme in terms of accurate, robust, and convergent performances for different noise and generation variations. The statistics generated through multiple autonomous executions represent box and whisker plots, along with the Wilcoxon rank-sum test, further confirming the reliability and stability of the NMPA for parameter estimation of IN-ARX systems. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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15 pages, 1947 KiB

Open AccessArticle

The Moving Firefighter Problem

by Bruno R. Gutiérrez-De-La-Paz, Jesús García-Díaz, Rolando Menchaca-Méndez, Mauro A. Montenegro-Meza, Ricardo Menchaca-Méndez and Omar A. Gutiérrez-De-La-Paz

Mathematics 2023, 11(1), 179; https://doi.org/10.3390/math11010179 - 29 Dec 2022

Cited by 1 | Viewed by 3011

Abstract

The original formulation of the firefighter problem defines a discrete-time process where a fire starts at a designated subset of the vertices of a graph G. At each subsequent discrete time unit, the fire propagates from each burnt vertex to all of [...] Read more.

The original formulation of the firefighter problem defines a discrete-time process where a fire starts at a designated subset of the vertices of a graph G. At each subsequent discrete time unit, the fire propagates from each burnt vertex to all of its neighbors unless they are defended by a firefighter that can move between any pair of vertices in a single time unit. Once a vertex is burnt or defended, it remains in that state, and the process terminates when the fire can no longer spread. In this work, we present the moving firefighter problem, which is a generalization of the firefighter problem where the time it takes a firefighter to move from a vertex u to defend vertex v is determined by a function

τ

. This new formulation models situations such as a wildfire or a flood, where firefighters have to physically move from their current position to the location of an entity they intend to defend. It also incorporates the notion that entities modeled by the vertices are not necessarily instantaneously defended upon the arrival of a firefighter. We present a mixed-integer quadratically constrained program (MIQCP) for the optimization version of the moving firefighter problem that minimizes the number of burnt vertices for the case of general finite graphs, an arbitrary set

F \subset V

of vertices where the fire breaks out, a single firefighter, and metric time functions

τ

. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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33 pages, 3587 KiB

Open AccessArticle

Energy-Aware Cloud-Edge Collaborative Task Offloading with Adjustable Base Station Radii in Smart Cities

by Qian Su, Qinghui Zhang and Xuejie Zhang

Mathematics 2022, 10(21), 3992; https://doi.org/10.3390/math10213992 - 27 Oct 2022

Cited by 2 | Viewed by 1583

Abstract

In smart cities, the computing power and battery life of terminal devices (TDs) can be effectively enhanced by offloading tasks to nearby base stations (BSs) with richer resources. With the goal of TDs being fully served and achieving low-carbon energy savings for the [...] Read more.

In smart cities, the computing power and battery life of terminal devices (TDs) can be effectively enhanced by offloading tasks to nearby base stations (BSs) with richer resources. With the goal of TDs being fully served and achieving low-carbon energy savings for the system, this paper investigates task offloading in cloud-edge collaborative heterogeneous scenarios with multiple BSs and TDs. According to the proportional relationship between the energy and coverage radii of BSs, a complete coverage task offloading model with adjustable BS radii is proposed. The task offloading problem is formulated as an integer linear program with multidimensional resource constraints to minimize the sum of energy consumption of BS coverage, offloading tasks to BSs and the cloud data center (CC). Since this task offloading problem is NP-hard, two approximate algorithms with polynomial time complexity are designed based on the greedy strategy of seeking the most energy-effective disk and the primal–dual method of constructing primal feasible solutions according to dual feasible solutions. Experimental results show that both the greedy and primal–dual algorithms can achieve good approximation performance, but each of them has its own advantages due to different design principles. The former is superior in execution time and energy consumption, while the latter has advantages in balancing loads among BSs and alleviating core network bandwidth pressure. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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21 pages, 4198 KiB

Open AccessArticle

Dwarf Mongoose Optimization Metaheuristics for Autoregressive Exogenous Model Identification

by Khizer Mehmood, Naveed Ishtiaq Chaudhary, Zeshan Aslam Khan, Khalid Mehmood Cheema, Muhammad Asif Zahoor Raja, Ahmad H. Milyani and Abdullah Ahmed Azhari

Mathematics 2022, 10(20), 3821; https://doi.org/10.3390/math10203821 - 16 Oct 2022

Cited by 34 | Viewed by 1857

Abstract

Nature-inspired metaheuristic algorithms have gained great attention over the last decade due to their potential for finding optimal solutions to different optimization problems. In this study, a metaheuristic based on the dwarf mongoose optimization algorithm (DMOA) is presented for the parameter estimation of [...] Read more.

Nature-inspired metaheuristic algorithms have gained great attention over the last decade due to their potential for finding optimal solutions to different optimization problems. In this study, a metaheuristic based on the dwarf mongoose optimization algorithm (DMOA) is presented for the parameter estimation of an autoregressive exogenous (ARX) model. In the DMOA, the set of candidate solutions were stochastically created and improved using only one tuning parameter. The performance of the DMOA for ARX identification was deeply investigated in terms of its convergence speed, estimation accuracy, robustness and reliability. Furthermore, comparative analyses with other recent state-of-the-art metaheuristics based on Aquila Optimizer, the Sine Cosine Algorithm, the Arithmetic Optimization Algorithm and the Reptile Search algorithm—using a nonparametric Kruskal–Wallis test—endorsed the consistent, accurate performance of the proposed metaheuristic for ARX identification. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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21 pages, 1101 KiB

Open AccessArticle

An Improved Gray Wolf Optimization Algorithm with a Novel Initialization Method for Community Detection

by Yan Kang, Zhongming Xu, Haining Wang, Yanchong Yuan, Xuekun Yang and Kang Pu

Mathematics 2022, 10(20), 3805; https://doi.org/10.3390/math10203805 - 15 Oct 2022

Cited by 3 | Viewed by 2158

Abstract

Community discovery (CD) under complex networks is a hot discussion issue in network science research. Recently, many evolutionary methods have been introduced to detect communities of networks. However, evolutionary optimization-based community discovery still suffers from two problems. First, the initialization population quality of [...] Read more.

Community discovery (CD) under complex networks is a hot discussion issue in network science research. Recently, many evolutionary methods have been introduced to detect communities of networks. However, evolutionary optimization-based community discovery still suffers from two problems. First, the initialization population quality of the current evolutionary algorithm is not good, resulting in slow convergence speed, and the final performance needs to be further improved. Another important issue is that current methods of CD have inconsistent network detection performance at different scales, showing a dramatic drop as the network scale increases. To address such issues, this paper proposes an algorithm based on the novel initial method and improved gray wolf optimization (NIGWO) to tackle the above two problems at the same time. In this paper, a novel initialization strategy is proposed to generate a high-quality initial population and greatly accelerate the convergence speed of population evolution. The strategy effectively fused the elite substructure of the community and different features based on the dependency and other features among nodes. Moreover, an improved GWO is presented with two new search strategies. An improved hunting prey stage is proposed to retain the excellent substructures of populations and quickly improve the community structure. Furthermore, new mutation strategies from node level to community level are designed in an improved encircling prey stage. Specifically, boundary nodes are mutated according to a proposed function to improve the search efficiency and save the computation assumption. Numerous experiments have proven our method obtains more excellent performance in most networks compared with 11 state-of-the-art algorithms. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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18 pages, 3725 KiB

Open AccessArticle

A Weld Surface Defect Recognition Method Based on Improved MobileNetV2 Algorithm

by Kai Ding, Zhangqi Niu, Jizhuang Hui, Xueliang Zhou and Felix T. S. Chan

Mathematics 2022, 10(19), 3678; https://doi.org/10.3390/math10193678 - 8 Oct 2022

Cited by 11 | Viewed by 2553

Abstract

Traditional welding quality inspection methods for pipelines and pressure vessels are time-consuming, labor-intensive, and suffer from false and missed inspection problems. With the development of smart manufacturing, there is a need for fast and accurate in-situ inspection of welding quality. Therefore, detection models [...] Read more.

Traditional welding quality inspection methods for pipelines and pressure vessels are time-consuming, labor-intensive, and suffer from false and missed inspection problems. With the development of smart manufacturing, there is a need for fast and accurate in-situ inspection of welding quality. Therefore, detection models with higher accuracy and lower computational complexity are required for technical support. Based on that, an in-situ weld surface defect recognition method is proposed in this paper based on an improved lightweight MobileNetV2 algorithm. It builds a defect classification model with MobileNetV2 as the backbone of the network, embeds a Convolutional Block Attention Module (CBAM) to refine the image feature information, and reduces the network width factor to cut down the number of model parameters and computational complexity. The experimental results show that the proposed weld surface defect recognition method has advantages in both recognition accuracy and computational efficiency. In summary, the method in this paper overcomes the limitations of traditional methods and achieves the goal of reducing labor intensity, saving time, and improving accuracy. It meets the actual needs of in-situ weld surface defect recognition for pipelines, pressure vessels, and other industrial complex products. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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23 pages, 4087 KiB

Open AccessArticle

A Vehicular Edge Computing-Based Architecture and Task Scheduling Scheme for Cooperative Perception in Autonomous Driving

by Yuankui Wei and Jixian Zhang

Mathematics 2022, 10(18), 3328; https://doi.org/10.3390/math10183328 - 14 Sep 2022

Cited by 3 | Viewed by 2099

Abstract

Cooperative perception is an important domain of autonomous driving that helps to improve road safety and traffic efficiency. Nevertheless, the large amount of sensed data and complicated algorithms make storage and computation for autonomous vehicles (AVs) challenging. Furthermore, not every AV needs to [...] Read more.

Cooperative perception is an important domain of autonomous driving that helps to improve road safety and traffic efficiency. Nevertheless, the large amount of sensed data and complicated algorithms make storage and computation for autonomous vehicles (AVs) challenging. Furthermore, not every AV needs to individually process all sensed data from other AVs because the environmental information is the same in a small region. Inspired by vehicular edge computing (VEC), where AVs are interconnected with the help of roadside units (RSUs) for better storage and computation capabilities, we propose a VEC-based architecture for cooperative perception and design a key task scheduling algorithm for the above challenges. Specifically, a time slot-based VEC architecture with the help of an RSU is designed, and the task scheduling problem in the proposed architecture is formulated as a multitask multitarget scheduling problem with assignment restrictions. A two-stage heuristic scheme (TSHS) is designed for the problem. Finally, extensive simulations indicate that the proposed architecture with the TSHS can enable cooperative perception, with a fast running speed and advanced performance, that is superior to that of the benchmarks, especially when most AVs face limitations in terms of storage and computation. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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13 pages, 288 KiB

Open AccessArticle

A Decision Model to Plan Optimally Production-Distribution of Seafood Product with Multiple Locations

by Firmansyah Firmansyah, Herman Mawengkang, Abdul Mujib and Devy Mathelinea

Mathematics 2022, 10(18), 3240; https://doi.org/10.3390/math10183240 - 6 Sep 2022

Cited by 2 | Viewed by 1681

Abstract

This study examines a multi-product fish production and distribution system in which multi-fish products are produced simultaneously from a wide range of raw resource classes. The objective of environmentally sustainable production planning is to meet market demand in accordance with environmental constraints. This [...] Read more.

This study examines a multi-product fish production and distribution system in which multi-fish products are produced simultaneously from a wide range of raw resource classes. The objective of environmentally sustainable production planning is to meet market demand in accordance with environmental constraints. This paper sets out a management model that converts fisheries into multiple marine objects and moves them to various dispensing centers. It also incorporates a model to improve production and distribution planning at the same time. The problem is formulated as a mixed integer programming model. Then, we addressed a strategy of releasing non-basic variables from their bounds to force basic non-integer variables to take integer value. As an implementation, we solved a fish production planning problem faced by an industry located in Kisaran city, North Sumatra province, Indonesia. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

34 pages, 8730 KiB

Open AccessArticle

Elite Chaotic Manta Ray Algorithm Integrated with Chaotic Initialization and Opposition-Based Learning

by Jianwei Yang, Zhen Liu, Xin Zhang and Gang Hu

Mathematics 2022, 10(16), 2960; https://doi.org/10.3390/math10162960 - 16 Aug 2022

Cited by 10 | Viewed by 2204

Abstract

The manta ray foraging optimizer (MRFO) is a novel nature-inspired optimization algorithm that simulates the foraging strategy and behavior of manta ray groups, i.e., chain, spiral, and somersault foraging. Although the native MRFO has revealed good competitive capability with popular meta-heuristic algorithms, it [...] Read more.

The manta ray foraging optimizer (MRFO) is a novel nature-inspired optimization algorithm that simulates the foraging strategy and behavior of manta ray groups, i.e., chain, spiral, and somersault foraging. Although the native MRFO has revealed good competitive capability with popular meta-heuristic algorithms, it still falls into local optima and slows the convergence rate in dealing with some complex problems. In order to ameliorate these deficiencies of the MRFO, a new elite chaotic MRFO, termed the CMRFO algorithm, integrated with chaotic initialization of population and an opposition-based learning strategy, is developed in this paper. Fourteen kinds of chaotic maps with different properties are used to initialize the population. Thereby, the chaotic map with the best effect is selected; meanwhile, the sensitivity analysis of an elite selection ratio in an elite chaotic searching strategy to the CMRFO is discussed. These strategies collaborate to enhance the MRFO in accelerating overall performance. In addition, the superiority of the presented CMRFO is comprehensively demonstrated by comparing it with a native MRFO, a modified MRFO, and several state-of-the-art algorithms using (1) 23 benchmark test functions, (2) the well-known IEEE CEC 2020 test suite, and (3) three optimization problems in the engineering field, respectively. Furthermore, the practicability of the CMRFO is illustrated by solving a real-world application of shape optimization of cubic generalized Ball (CG-Ball) curves. By minimizing the curvature variation in these curves, the shape optimization model of CG-Ball ones is established. Then, the CMRFO algorithm is applied to handle the established model compared with some advanced meta-heuristic algorithms. The experimental results demonstrate that the CMRFO is a powerful and attractive alternative for solving engineering optimization problems. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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39 pages, 15488 KiB

Open AccessArticle

An Improved Reptile Search Algorithm Based on Lévy Flight and Interactive Crossover Strategy to Engineering Application

by Liqiong Huang, Yuanyuan Wang, Yuxuan Guo and Gang Hu

Mathematics 2022, 10(13), 2329; https://doi.org/10.3390/math10132329 - 3 Jul 2022

Cited by 17 | Viewed by 2140

Abstract

In this paper, we propose a reptile search algorithm based on Lévy flight and interactive crossover strategy (LICRSA), and the improved algorithm is employed to improve the problems of poor convergence accuracy and slow iteration speed of the reptile search algorithm. First, the [...] Read more.

In this paper, we propose a reptile search algorithm based on Lévy flight and interactive crossover strategy (LICRSA), and the improved algorithm is employed to improve the problems of poor convergence accuracy and slow iteration speed of the reptile search algorithm. First, the proposed algorithm increases the variety and flexibility of the people by introducing the Lévy flight strategy to prevent premature convergence and improve the robustness of the population. Secondly, an iteration-based interactive crossover strategy is proposed, inspired by the crossover operator and the difference operator. This strategy is applied to the reptile search algorithm (RSA), and the convergence accuracy of the algorithm is significantly improved. Finally, the improved algorithm is extensively tested using 2 test sets: 23 benchmark test functions and 10 CEC2020 functions, and 5 complex mechanical engineering optimization problems. The numerical results show that LICRSA outperforms RSA in 15 (65%) and 10 (100%) of the 2 test sets, respectively. In addition, LICRSA performs best in 10 (43%) and 4 (40%) among all algorithms. Meanwhile, the enhanced algorithm shows superiority and stability in handling engineering optimization. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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32 pages, 5257 KiB

Open AccessArticle

Enhanced Remora Optimization Algorithm for Solving Constrained Engineering Optimization Problems

by Shuang Wang, Abdelazim G. Hussien, Heming Jia, Laith Abualigah and Rong Zheng

Mathematics 2022, 10(10), 1696; https://doi.org/10.3390/math10101696 - 16 May 2022

Cited by 52 | Viewed by 3391

Abstract

Remora Optimization Algorithm (ROA) is a recent population-based algorithm that mimics the intelligent traveler behavior of Remora. However, the performance of ROA is barely satisfactory; it may be stuck in local optimal regions or has a slow convergence, especially in high dimensional complicated [...] Read more.

Remora Optimization Algorithm (ROA) is a recent population-based algorithm that mimics the intelligent traveler behavior of Remora. However, the performance of ROA is barely satisfactory; it may be stuck in local optimal regions or has a slow convergence, especially in high dimensional complicated problems. To overcome these limitations, this paper develops an improved version of ROA called Enhanced ROA (EROA) using three different techniques: adaptive dynamic probability, SFO with Levy flight, and restart strategy. The performance of EROA is tested using two different benchmarks and seven real-world engineering problems. The statistical analysis and experimental results show the efficiency of EROA. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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30 pages, 7010 KiB

Open AccessArticle

A Hybrid Arithmetic Optimization and Golden Sine Algorithm for Solving Industrial Engineering Design Problems

by Qingxin Liu, Ni Li, Heming Jia, Qi Qi, Laith Abualigah and Yuxiang Liu

Mathematics 2022, 10(9), 1567; https://doi.org/10.3390/math10091567 - 6 May 2022

Cited by 27 | Viewed by 3097

Abstract

Arithmetic Optimization Algorithm (AOA) is a physically inspired optimization algorithm that mimics arithmetic operators in mathematical calculation. Although the AOA has an acceptable exploration and exploitation ability, it also has some shortcomings such as low population diversity, premature convergence, and easy stagnation into [...] Read more.

Arithmetic Optimization Algorithm (AOA) is a physically inspired optimization algorithm that mimics arithmetic operators in mathematical calculation. Although the AOA has an acceptable exploration and exploitation ability, it also has some shortcomings such as low population diversity, premature convergence, and easy stagnation into local optimal solutions. The Golden Sine Algorithm (Gold-SA) has strong local searchability and fewer coefficients. To alleviate the above issues and improve the performance of AOA, in this paper, we present a hybrid AOA with Gold-SA called HAGSA for solving industrial engineering design problems. We divide the whole population into two subgroups and optimize them using AOA and Gold-SA during the searching process. By dividing these two subgroups, we can exchange and share profitable information and utilize their advantages to find a satisfactory global optimal solution. Furthermore, we used the Levy flight and proposed a new strategy called Brownian mutation to enhance the searchability of the hybrid algorithm. To evaluate the efficiency of the proposed work, HAGSA, we selected the CEC 2014 competition test suite as a benchmark function and compared HAGSA against other well-known algorithms. Moreover, five industrial engineering design problems were introduced to verify the ability of algorithms to solve real-world problems. The experimental results demonstrate that the proposed work HAGSA is significantly better than original AOA, Gold-SA, and other compared algorithms in terms of optimization accuracy and convergence speed. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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30 pages, 9665 KiB

Open AccessArticle

An Improved Wild Horse Optimizer for Solving Optimization Problems

by Rong Zheng, Abdelazim G. Hussien, He-Ming Jia, Laith Abualigah, Shuang Wang and Di Wu

Mathematics 2022, 10(8), 1311; https://doi.org/10.3390/math10081311 - 14 Apr 2022

Cited by 45 | Viewed by 4835

Abstract

Wild horse optimizer (WHO) is a recently proposed metaheuristic algorithm that simulates the social behavior of wild horses in nature. Although WHO shows competitive performance compared to some algorithms, it suffers from low exploitation capability and stagnation in local optima. This paper presents [...] Read more.

Wild horse optimizer (WHO) is a recently proposed metaheuristic algorithm that simulates the social behavior of wild horses in nature. Although WHO shows competitive performance compared to some algorithms, it suffers from low exploitation capability and stagnation in local optima. This paper presents an improved wild horse optimizer (IWHO), which incorporates three improvements to enhance optimizing capability. The main innovation of this paper is to put forward the random running strategy (RRS) and the competition for waterhole mechanism (CWHM). The random running strategy is employed to balance exploration and exploitation, and the competition for waterhole mechanism is proposed to boost exploitation behavior. Moreover, the dynamic inertia weight strategy (DIWS) is utilized to optimize the global solution. The proposed IWHO is evaluated using twenty-three classical benchmark functions, ten CEC 2021 test functions, and five real-world optimization problems. High-dimensional cases (D = 200, 500, 1000) are also tested. Comparing nine well-known algorithms, the experimental results of test functions demonstrate that the IWHO is very competitive in terms of convergence speed, precision, accuracy, and stability. Further, the practical capability of the proposed method is verified by the results of engineering design problems. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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Review

Jump to: Research

28 pages, 999 KiB

Open AccessReview

A Survey on Fair Allocation of Chores

by Hao Guo, Weidong Li and Bin Deng

Mathematics 2023, 11(16), 3616; https://doi.org/10.3390/math11163616 - 21 Aug 2023

Cited by 6 | Viewed by 2299

Abstract

Wherever there is group life, there has been a social division of labor and resource allocation, since ancient times. Examples include ant colonies, bee colonies, and wolf colonies. Different roles are responsible for different tasks. The same is true of human beings. Human [...] Read more.

Wherever there is group life, there has been a social division of labor and resource allocation, since ancient times. Examples include ant colonies, bee colonies, and wolf colonies. Different roles are responsible for different tasks. The same is true of human beings. Human beings are the largest social group in nature, among whom there are intricate social networks and interest networks between individuals. In such a complex relationship, how do decision makers allocate resources or tasks to individuals in a fair way? This is a topic worthy of further study. In recent decades, fair allocation has been at the core of research in economics, mathematics and other fields. The fair allocation problem is to assign a set of items to a set of agents so that each agent’s allocation is as fair as possible to satisfy each agent. The fairness measurements followed in current research include envy-freeness, proportionality, equitability, maximin share fairness, competitive equilibrium, maximum Nash social diswelfare, and so on. In this paper, the main concern is the allocation of chores. We discuss this problem in two parts: divisible and indivisible. We comprehensively review the existing results, algorithms, and approximations that meet various fairness criteria in chronological order. The relevant results of achieving fairness and efficiency are also discussed. In addition, we propose some open questions and future research directions for this problem based on existing research. Full article

(This article belongs to the Special Issue Optimisation Algorithms and Their Applications)

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