A Comparative Study of Metaheuristic Optimization Algorithms for Solving Real-World Engineering Design Problems

Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.

Enhanced Butterfly Optimization Algorithm for Large-Scale Optimization Problems

To solve large-scale optimization problems,Fragrance coefficient and variant Particle Swarm local search Butterfly Optimization Algorithm(FPSBOA)is proposed.In the position update stage of Butterfly Optimization Algorithm(BOA),the fragrance coefficient is designed to balance the exploration and exploitation of BOA.The variant particle swarm local search strategy is proposed to improve the local search ability of the current optimal butterfly and prevent the algorithm from falling into local optimality.192000-dimensional functions and 201000-dimensional CEC 2010 large-scale functions are used to verify FPSBOA for complex large-scale optimization problems.The experimental results are statistically analyzed by Friedman test and Wilcoxon rank-sum test.All attained results demonstrated that FPSBOA can better solve more challenging scientific and industrial real-world problems with thousands of variables.Finally,four mechanical engineering problems and one ten-dimensional process synthesis and design problem are applied to FPSBOA,which shows FPSBOA has the feasibility and effectiveness in real-world application problems.

Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

Using Improved Particle Swarm Optimization Algorithm for Location Problem of Drone Logistics Hub

Drone logistics is a novel method of distribution that will become prevalent.The advantageous location of the logistics hub enables quicker customer deliveries and lower fuel consumption,resulting in cost savings for the company’s transportation operations.Logistics firms must discern the ideal location for establishing a logistics hub,which is challenging due to the simplicity of existing models and the intricate delivery factors.To simulate the drone logistics environment,this study presents a new mathematical model.The model not only retains the aspects of the current models,but also considers the degree of transportation difficulty from the logistics hub to the village,the capacity of drones for transportation,and the distribution of logistics hub locations.Moreover,this paper proposes an improved particle swarm optimization(PSO)algorithm which is a diversity-based hybrid PSO(DHPSO)algorithm to solve this model.In DHPSO,the Gaussian random walk can enhance global search in the model space,while the bubble-net attacking strategy can speed convergence.Besides,Archimedes spiral strategy is employed to overcome the local optima trap in the model and improve the exploitation of the algorithm.DHPSO maintains a balance between exploration and exploitation while better defining the distribution of logistics hub locations Numerical experiments show that the newly proposed model always achieves better locations than the current model.Comparing DHPSO with other state-of-the-art intelligent algorithms,the efficiency of the scheme can be improved by 42.58%.This means that logistics companies can reduce distribution costs and consumers can enjoy a more enjoyable shopping experience by using DHPSO’s location selection.All the results show the location of the drone logistics hub is solved by DHPSO effectively.

An Efficient Approach for Transforming Unbalanced Transportation Problems into Balanced Problems in Order to Find Optimal Solutions

In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.

Use the Power of a Genetic Algorithm to Maximize and Minimize Cases to Solve Capacity Supplying Optimization and Travelling Salesman in Nested Problems

Using Genetic Algorithms (GAs) is a powerful tool to get solution to large scale design optimization problems. This paper used GA to solve complicated design optimization problems in two different applications. The aims are to implement the genetic algorithm to solve these two different (nested) problems, and to get the best or optimization solutions.

Construction of Legal System of China's Farmland Protection under the Coexistence of Multiple Objectives:Historical Logic,Practical Problems and Optimization Paths

[Objectives]To explore the evolution of the legal system of farmland protection and explore the rules and characteristics of policy development based on the theory and logic of institutional change since China's reform and opening up,reveal the problems and deep-seated reasons of its legislation,clarify the direction of farmland protection in the new period,and solve the"non-agricultural""non-grain"and ecological problems of farmland.[Methods]Literature analysis and inductive deduction methods were used.[Results]The evolution of the farmland protection legal system has gone through the process of"national consciousness-policy guidelines-institutional system",the change from"single subject to multiple subjects";change from the use of"one-way administrative means to coordinated use of administrative,economic and technical means".The practical problems of the farmland protection legal system are mainly due to the insufficient systematization of the farmland protection legal system itself,the generalization of quantity protection,the transformation of quality protection,and the absence of ecological protection.[Conclusions]It is recommended to improve the existing farmland protection legal system from the establishment of the Farmland Protection Law,the improvement of the farmland protection public participation mechanism and supervision mechanism,the establishment of the farmland quality construction and improvement system,the differentiated farmland occupation and supplementation balance system,and the ecological restoration system.

Synergistic Swarm Optimization Algorithm

This research paper presents a novel optimization method called the Synergistic Swarm Optimization Algorithm(SSOA).The SSOA combines the principles of swarmintelligence and synergistic cooperation to search for optimal solutions efficiently.A synergistic cooperation mechanism is employed,where particles exchange information and learn from each other to improve their search behaviors.This cooperation enhances the exploitation of promising regions in the search space while maintaining exploration capabilities.Furthermore,adaptive mechanisms,such as dynamic parameter adjustment and diversification strategies,are incorporated to balance exploration and exploitation.By leveraging the collaborative nature of swarm intelligence and integrating synergistic cooperation,the SSOAmethod aims to achieve superior convergence speed and solution quality performance compared to other optimization algorithms.The effectiveness of the proposed SSOA is investigated in solving the 23 benchmark functions and various engineering design problems.The experimental results highlight the effectiveness and potential of the SSOA method in addressing challenging optimization problems,making it a promising tool for a wide range of applications in engineering and beyond.Matlab codes of SSOA are available at:https://www.mathworks.com/matlabcentral/fileexchange/153466-synergistic-swarm-optimization-algorithm.

Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

Even Search in a Promising Region for Constrained Multi-Objective Optimization

In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.

Optimizing Grey Wolf Optimization: A Novel Agents’ Positions Updating Technique for Enhanced Efficiency and Performance

Grey Wolf Optimization (GWO) is a nature-inspired metaheuristic algorithm that has gained popularity for solving optimization problems. In GWO, the success of the algorithm heavily relies on the efficient updating of the agents’ positions relative to the leader wolves. In this paper, we provide a brief overview of the Grey Wolf Optimization technique and its significance in solving complex optimization problems. Building upon the foundation of GWO, we introduce a novel technique for updating agents’ positions, which aims to enhance the algorithm’s effectiveness and efficiency. To evaluate the performance of our proposed approach, we conduct comprehensive experiments and compare the results with the original Grey Wolf Optimization technique. Our comparative analysis demonstrates that the proposed technique achieves superior optimization outcomes. These findings underscore the potential of our approach in addressing optimization challenges effectively and efficiently, making it a valuable contribution to the field of optimization algorithms.

A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem

In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H1 and L2 norms. Finally, some numerical experiments are carried out to support the theoretical results.

Learning-Based Metaheuristic Approach for Home Healthcare Optimization Problem

This research focuses on the home health care optimization problem that involves staff routing and scheduling problems.The considered problem is an extension of multiple travelling salesman problem.It consists of finding the shortest path for a set of caregivers visiting a set of patients at their homes in order to perform various tasks during a given horizon.Thus,a mixed-integer linear programming model is proposed to minimize the overall service time performed by all caregivers while respecting the workload balancing constraint.Nevertheless,when the time horizon become large,practical-sized instances become very difficult to solve in a reasonable computational time.Therefore,a new Learning Genetic Algorithm for mTSP(LGA-mTSP)is proposed to solve the problem.LGA-mTSP is composed of a new genetic algorithm for mTSP,combined with a learning approach,called learning curves.Learning refers to that caregivers’productivity increases as they gain more experience.Learning curves approach is considered as a way to save time and costs.Simulation results show the efficiency of the proposed approach and the impact of learning curve strategy to reduce service times.

A Scheme Library-Based Ant Colony Optimization with 2-Opt Local Search for Dynamic Traveling Salesman Problem

The dynamic traveling salesman problem(DTSP)is significant in logistics distribution in real-world applications in smart cities,but it is uncertain and difficult to solve.This paper proposes a scheme library-based ant colony optimization(ACO)with a two-optimization(2-opt)strategy to solve the DTSP efficiently.The work is novel and contributes to three aspects:problemmodel,optimization framework,and algorithmdesign.Firstly,in the problem model,traditional DTSP models often consider the change of travel distance between two nodes over time,while this paper focuses on a special DTSP model in that the node locations change dynamically over time.Secondly,in the optimization framework,the ACO algorithm is carried out in an offline optimization and online application framework to efficiently reuse the historical information to help fast respond to the dynamic environment.The framework of offline optimization and online application is proposed due to the fact that the environmental change inDTSPis caused by the change of node location,and therefore the newenvironment is somehowsimilar to certain previous environments.This way,in the offline optimization,the solutions for possible environmental changes are optimized in advance,and are stored in a mode scheme library.In the online application,when an environmental change is detected,the candidate solutions stored in the mode scheme library are reused via ACO to improve search efficiency and reduce computational complexity.Thirdly,in the algorithm design,the ACO cooperates with the 2-opt strategy to enhance search efficiency.To evaluate the performance of ACO with 2-opt,we design two challenging DTSP cases with up to 200 and 1379 nodes and compare them with other ACO and genetic algorithms.The experimental results show that ACO with 2-opt can solve the DTSPs effectively.

Analysis of the Impact of Optimal Solutions to the Transportation Problems for Variations in Cost Using Two Reliable Approaches

In this paper, we have used two reliable approaches (theorems) to find the optimal solutions to transportation problems, using variations in costs. In real-life scenarios, transportation costs can fluctuate due to different factors. Finding optimal solutions to the transportation problem in the context of variations in cost is vital for ensuring cost efficiency, resource allocation, customer satisfaction, competitive advantage, environmental responsibility, risk mitigation, and operational fortitude in practical situations. This paper opens up new directions for the solution of transportation problems by introducing two key theorems. By using these theorems, we can develop an algorithm for identifying the optimal solution attributes and permitting accurate quantification of changes in overall transportation costs through the addition or subtraction of constants to specific rows or columns, as well as multiplication by constants inside the cost matrix. It is anticipated that the two reliable techniques presented in this study will provide theoretical insights and practical solutions to enhance the efficiency and cost-effectiveness of transportation systems. Finally, numerical illustrations are presented to verify the proposed approaches.

A Survey of Evolutionary Algorithms for Multi-Objective Optimization Problems With Irregular Pareto Fronts

Evolutionary algorithms have been shown to be very successful in solving multi-objective optimization problems(MOPs).However,their performance often deteriorates when solving MOPs with irregular Pareto fronts.To remedy this issue,a large body of research has been performed in recent years and many new algorithms have been proposed.This paper provides a comprehensive survey of the research on MOPs with irregular Pareto fronts.We start with a brief introduction to the basic concepts,followed by a summary of the benchmark test problems with irregular problems,an analysis of the causes of the irregularity,and real-world optimization problems with irregular Pareto fronts.Then,a taxonomy of the existing methodologies for handling irregular problems is given and representative algorithms are reviewed with a discussion of their strengths and weaknesses.Finally,open challenges are pointed out and a few promising future directions are suggested.

On vector variational-like inequalities and vector optimization problems with (G, α)-invexity

The aim of this paper is to study the relationship among Minty vector variationallike inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving(G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem,Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of(G, α)-invex functions. Examples are provided to elucidate our results.

On the Well-Posedness for Optimization Problems: A Theoretical Investigation

In this paper, some theoretical notions of well-posedness and of well-posedness in the generalized sense for scalar optimization problems are presented and some important results are analysed. Similar notions of well-posedness, respectively for a vector optimization problem and for a variational inequality of differential type, are discussed subsequently and, among the various vector well-posedness notions known in the literature, the attention is focused on the concept of pointwise well-posedness. Moreover, after a review of well-posedness properties, the study is further extended to a scalarizing procedure that preserves well-posedness of the notions listed, namely to a result, obtained with a special scalarizing function, which links the notion of pontwise well-posedness to the well-posedness of a suitable scalar variational inequality of differential type.

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.

A Bi-population Cooperative Optimization Algorithm Assisted by an Autoencoder for Medium-scale Expensive Problems

This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.