Solving Complex Optimization Problems Research Articles

Revolutionizing sustainable supply chain management: A review of metaheuristics

This paper reviews the application of metaheuristics for optimized sustainable supply chain management (SSCM). This paper explores the potential of metaheuristics to improve the supply chain’s sustainability while enhancing its efficiency and competitiveness. The paper provides an overview of the principles of SSCM and the challenges businesses face in achieving sustainable supply chain management. It then introduces the concept of metaheuristics and describes their use in solving complex optimization problems. The paper reviews various metaheuristics algorithms applied to sustainable supply chain management and analyzes their effectiveness in addressing the challenges of SSCM. The paper also identifies the key factors that influence the success of using metaheuristics for SSCM, such as the choice of algorithm, problem complexity, and data quality. Finally, the paper provides recommendations for future research in this area and highlights the potential of metaheuristics to promote sustainable supply chain management. The review suggests that metaheuristics can be a valuable tool for optimizing sustainable supply chain management and improving supply chain operations’ sustainability, efficiency, and competitiveness.

Research Progress of Nature-Inspired Metaheuristic Algorithms in Mobile Robot Path Planning

The research of mobile robot path planning has shifted from the static environment to the dynamic environment, from the two-dimensional environment to the high-dimensional environment, and from the single-robot system to the multi-robot system. As the core technology for mobile robots to realize autonomous positioning and navigation, path-planning technology should plan collision-free and smooth paths for mobile robots in obstructed environments, which requires path-planning algorithms with a certain degree of intelligence. Metaheuristic algorithms are widely used in various optimization problems due to their algorithmic intelligence, and they have become the most effective algorithm to solve complex optimization problems in the field of mobile robot path planning. Based on a comprehensive analysis of existing path-planning algorithms, this paper proposes a new algorithm classification. Based on this classification, we focus on the firefly algorithm (FA) and the cuckoo search algorithm (CS), complemented by the dragonfly algorithm (DA), the whale optimization algorithm (WOA), and the sparrow search algorithm (SSA). During the analysis of the above algorithms, this paper summarizes the current research results of mobile robot path planning and proposes the future development trend of mobile robot path planning.

A Modified Binary Arithmetic Optimization Algorithm for Feature Selection

Feature selection chooses the optimal subset from the feature set without scarifying the information carried by the dataset. It is considered a complex combinatorial problem, so classical optimization techniques fail to solve it when the feature set becomes larger. Meta-heuristic approaches are well known to solve complex optimization problems; hence these algorithms have been successfully applied to extract optimal feature subsets. The arithmetic Optimization Algorithm is a newly proposed mathematics-based meta-heuristic search algorithm successfully applied to solve optimization problems. However, it has been observed that AOA experiences a poor exploration phase. Hence in the present work, a Modified Binary Arithmetic Optimization Algorithm (MB-AOA) is proposed, which solves the poor exploration problem of standard AOA. In the MB-AOA, instead of utilizing a single best solution, an optimal solution set that gradually shrinks after each successive iteration is applied for better exploration during initial iterations. Also, instead of a fixed search parameter (μ), the MB-AOA utilizes a variable parameter suitable for binary optimization problems. The proposed method is evaluated over seven real-life datasets from the UCI repository as a feature selection wrapper method and compared with standard AOA over two performance metrics, Average Accuracy, F-score, and the generated feature subset size. MB-AOA has performed better in six datasets regarding F-score and average accuracy. The obtained results from the simulation process demonstrate that the MB-AOA can select the relevant features, thus improving the classification task’s overall accuracy levels.

A Compact Snake Optimization Algorithm in the Application of WKNN Fingerprint Localization.

Indoor localization has broad application prospects, but accurately obtaining the location of test points (TPs) in narrow indoor spaces is a challenge. The weighted K-nearest neighbor algorithm (WKNN) is a powerful localization algorithm that can improve the localization accuracy of TPs. In recent years, with the rapid development of metaheuristic algorithms, it has shown efficiency in solving complex optimization problems. The main research purpose of this article is to study how to use metaheuristic algorithms to improve indoor positioning accuracy and verify the effectiveness of heuristic algorithms in indoor positioning. This paper presents a new algorithm called compact snake optimization (cSO). The novel algorithm introduces a compact strategy to the snake optimization (SO) algorithm, which ensures optimal performance in situations with limited computing and memory resources. The performance of cSO is evaluated on 28 test functions of CEC2013 and compared with several intelligent computing algorithms. The results demonstrate that cSO outperforms these algorithms. Furthermore, we combine the cSO algorithm with WKNN fingerprint positioning and RSSI positioning. The simulation experiments demonstrate that the cSO algorithm can effectively reduce positioning errors.

A multi-leader Harris hawks optimizer with adaptive mutation and its application for modeling of silicon content in liquid iron of blast furnace

Aiming at the problem that Harris hawks optimizer (HHO) has poor population diversity and is easy to fall into local optimum when solving complex optimization problems, a multi-leader Harris Hawks optimizer with adaptive mutation (MLHHO-AM) is proposed, in which multiple leaders are used to guide the Harris hawks to improve the population diversity. An adaptive mutation is introduced to enhance the ability of the algorithm to jump out of the local optimum. The key feature of the strategy is that Gaussian mutation occurs in some dimensions of the optimal solution, and the number of mutation dimensions is adaptively changed. To verify the numerical optimization performance of MLHHO-AM, the parameter sensitivity, the role of two improved mechanisms, and population diversity are analyzed based on 23 classical test functions. Then, MLHHO-AM is compared with 12 state-of-the-art variants and 11 basic metaheuristic algorithms on IEEE CEC2017 and IEEE CEC2022 benchmark suites. The above test results show that the proposed MLHHO-AM is an effective algorithm with better numerical optimization performance than most competitors. In order to verify ability of MLHHO-AM to handle the practical problem, the parameters of the Elman neural network (ENN) used to build the prediction model of silicon content in liquid iron of blast furnace are optimized by MLHHO-AM. The simulation results based on actual data show that the ENN prediction model based on MLHHO-AM has higher prediction accuracy with R2=0.7563 and RMSE=0.0598. Therefore, the proposed MLHHO-AM has excellent numerical optimization performance and can be used to predict the silicon content in liquid iron of blast furnace.

A novel chaotic chimp sine cosine algorithm Part-I: For solving optimization problem

In the realm of solving complex optimization problems, it becomes crucial to fulfill multiple objectives to achieve optimal system performance while adhering to various conditions and limitations. Traditional optimization methods often face challenges such as sluggish convergence speed and confinement to local optima, making it difficult to find satisfactory solution. To tackle this challenge, the development of multi-objective programming is directed towards satisfying physical constraints. In line of the above problems and limitations, this work aims to contribute by proposing a hybrid optimization technique that can effectively address such optimization issues. The proposed algorithm, called the chaotic chimp sine cosine (C-CHOA-SC) algorithm, combines the chimp optimization algorithm (CHOA) and the sine cosine algorithm (SCA) to overcome problems of slow convergence and getting stuck in local optima. It does this by using the SCA after the CHOA and incorporating chaos to explore and exploit the search space effectively. This hybrid approach aims to improve the algorithm's performance (offers enhanced exploration capabilities, efficient exploitation of the search space, and improved convergence speed) and find better solutions to optimization problems. These features make the C-CHOA-SC algorithm well-suited for solving complex optimization problems with multiple objectives, providing a contemporary and effective solution. To evaluate the performance of the proposed C-CHOA-SC algorithm, three phases of analysis are conducted. In the first phase, the exploration, exploitation, and avoidance of local optima are tested using the CEC 2019 benchmark problems. The second phase involves tracking and validating the performance of C-CHOA-SC using multiple performance metrics on two-dimensional test functions. Finally, non-parametric alternative test i.e., the Wilcoxon rank sum test and Friedman test are performed. The results demonstrate that the proposed technique exhibits significantly better performance compared to other methods, with a 95 % significance level. As concerned to Friedman test, the C-CHOA-SC algorithm obtains a lower rank, it implies that it outperforms the other competing algorithms in terms of its overall performance.

Variational quantum non-orthogonal optimization

Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum optimization scheme where discrete classical variables are encoded in non-orthogonal states of the quantum system. We develop the case of non-orthogonal qubit states, with individual qubits on the quantum computer handling more than one bit classical variable. Combining this idea with Variational Quantum Eigensolvers (VQE) and quantum state tomography, we show that it is possible to significantly reduce the number of qubits required by quantum hardware to solve complex optimization problems. We benchmark our algorithm by successfully optimizing a polynomial of degree 8 and 15 variables using only 15 qubits. Our proposal opens the path towards solving real-life useful optimization problems in today’s limited quantum hardware.

Improved Teaching Learning Algorithm with Laplacian operator for solving nonlinear engineering optimization problems

Teaching Learning Algorithm (TLA) is a recently developed nature-inspired optimization technique applicable to complex optimization problems. This paper proposes an improved TLA version using the Laplacian operator of the Genetic Algorithm (GA), named LX-TLA. The proposed algorithm is tested on benchmark optimization problems, including unimodal and multimodal problems. The numerical results are obtained in the form of objective function values, and a t-test is applied to compare the performance of LX-TLA and basic TLA. Convergence plots are given to provide insight into the convergence behavior of LX-TLA. The results reveal that proposed algorithm provides effective and efficient performance in solving benchmark test functions. The proposed algorithm is also applied to engineering design problems, such as Tuned Mass Damper (TMD), truss structure, welded beam, tension string, and pressure vessel. The results obtained using LX-TLA are compared with other nature-inspired optimization algorithms. The results demonstrate that the proposed algorithm is a robust and effective tool for solving complex optimization problems.

Fast random opposition-based learning Golden Jackal Optimization algorithm

Nowadays, optimization techniques are required in various engineering domains in order to find optimal solutions for complex problems. As a result, there is a growing tendency among scientists to enhance existing nature-inspired algorithms using various evolutionary strategies and to develop new nature-inspired optimization methods that can properly explore the feature space. The recently designed nature-inspired metaheuristic, named the Golden Jackal Optimization​ (GJO) algorithm, was inspired by the collaborative hunting actions of the golden jackal in nature to solve various challenging problems. However, like other approaches, the GJO has the limitations of poor exploitation ability, ease to get stuck in a local optimal region, and an improper balancing of exploration and exploitation. To overcome these limitations, this paper proposes a novel contribution to GJO based on a new technique, namely the fast random opposition-based learning Golden Jackal Optimization algorithm (FROBL-GJO). The FROBL technique is mainly inspired by opposition-based learning (OBL) and random opposition-based learning (ROBL) techniques to enhance the optimization precision and convergence speed of the GJO algorithm. Furthermore, two other models, such as OBL-GJO and ROBL-GJO, are also proposed for comparison purposes. To examine the proficiency of the newly proposed FROBL-GJO algorithm, it has been examined with several well-known existing meta-heuristic algorithms while solving the CEC-2005 and CEC-2019 benchmark test functions and real-life engineering problems. The experimental outcomes and statistical tests reveal the superior performance of the proposed FROBL-GJO in solving both global optimization and engineering design problems. Hence, the findings of benchmark functions and engineering problems endorse that the proposed FROBL-GJO algorithm can be considered a promising method for solving complex optimization problems.

Neural Network Algorithm With Reinforcement Learning for Parameters Extraction of Photovoltaic Models.

This research focuses on the application of artificial neural networks (ANNs) on parameters extraction of photovoltaic (PV) models. Extracting parameters of the PV models accurately is crucial to control and optimize PV systems. Although many algorithms have been proposed to address this issue, how to extract the parameters of the PV models accurately and reliably is still a great challenge. Neural network algorithm (NNA) is a recently reported metaheuristic algorithm. NNA is inspired by ANNs. Benefiting from the unique structure of ANNs, NNA shows excellent global search ability. However, NNA faces the challenge of slow convergence rate and local optima stagnation in solving complex optimization problems. This article presents an improved NNA, named neural network algorithm with reinforcement learning (RLNNA), for extracting parameters of the PV models. In RLNNA, three strategies, namely modification factor with reinforcement learning (RL), transfer operator with historical population, and feedback operator, are designed to overcome the challenge of NNA. To verify the performance of RLNNA, it is employed to extract the parameters of the three PV models. Experimental results show that RLNNA can extract the parameters of the considered PV models with higher accuracy and stronger stability compared with NNA and the other 12 powerful algorithms, which fully indicates the effectiveness of the improved strategies.

An Improved Differential Evolution Algorithm for Numerical Optimization Problems

The differential evolution algorithm has gained popularity for solving complex optimization problems because of its simplicity and efficiency. However, it has several drawbacks, such as a slow convergence rate, high sensitivity to the values of control parameters, and the ease of getting trapped in local optima. In order to overcome these drawbacks, this paper integrates three novel strategies into the original differential evolution. First, a population improvement strategy based on a multi-level sampling mechanism is used to accelerate convergence and increase the diversity of the population. Second, a new self-adaptive mutation strategy balances the exploration and exploitation abilities of the algorithm by dynamically determining an appropriate value of the mutation parameters; this improves the search ability and helps the algorithm escape from local optima when it gets stuck. Third, a new selection strategy guides the search to avoid local optima. Twelve benchmark functions of different characteristics are used to validate the performance of the proposed algorithm. The experimental results show that the proposed algorithm performs significantly better than the original DE in terms of the ability to locate the global optimum, convergence speed, and scalability. In addition, the proposed algorithm is able to find the global optimal solutions on 8 out of 12 benchmark functions, while 7 other well-established metaheuristic algorithms, namely NBOLDE, ODE, DE, SaDE, JADE, PSO, and GA, can obtain only 6, 2, 1, 1, 1, 1, and 1 functions, respectively. Doi: 10.28991/HIJ-2023-04-02-014 Full Text: PDF

Significance of Linear Programming for Optimization

Linear programming (LP) is a powerful mathematical technique that has revolutionized optimization problems across various fields. This abstract highlights the significance of linear programming in optimization and its profound impact on decision-making, resource allocation, and efficiency enhancement. The primary objective of linear programming is to maximize or minimize a linear objective function, subject to a set of linear constraints. LP provides a systematic framework for modeling and solving complex optimization problems, enabling decision-makers to make informed choices and allocate resources optimally. The significance of linear programming lies in its ability to address a wide range of real-world challenges efficiently and effectively. In the realm of operations research, linear programming has found extensive applications in supply chain management, production planning, scheduling, and logistics optimization. By formulating decision problems into mathematical models, LP allows organizations to streamline their processes, minimize costs, optimize resource utilization, and maximize overall productivity. Linear programming has also made significant contributions in the field of economics. It has enabled economists to analyze and optimize economic systems, such as determining the optimal production levels for different goods, optimizing resource allocation in a market, and solving complex pricing problems. LP provides a quantitative framework for economic decision-making, facilitating the identification of optimal solutions and supporting policy development. Furthermore, linear programming plays a crucial role in the field of transportation and network optimization. It aids in solving problems related to route optimization, facility location, network design, and capacity planning. By efficiently allocating resources and optimizing transportation networks, LP helps reduce costs, improve service levels, and enhance overall efficiency in the transportation sector. In summary, the significance of linear programming for optimization is evident in its wide-ranging applications and its ability to tackle complex decision problems in various domains. By employing mathematical modeling and optimization techniques, LP allows decision-makers to make informed choices, allocate resources optimally, and achieve desired objectives. The ongoing advancements in LP algorithms and computing technologies further enhance its applicability and make it an indispensable tool for optimization in today's dynamic and competitive world.

Quantum-behaved particle swarm optimization with dynamic grouping searching strategy

The quantum-behaved particle swarm optimization (QPSO) algorithm, a variant of particle swarm optimization (PSO), has been proven to be an effective tool to solve various of optimization problems. However, like other PSO variants, it often suffers a premature convergence, especially when solving complex optimization problems. Considering this issue, this paper proposes a hybrid QPSO with dynamic grouping searching strategy, named QPSO-DGS. During the search process, the particle swarm is dynamically grouped into two subpopulations, which are assigned to implement the exploration and exploitation search, respectively. In each subpopulation, a comprehensive learning strategy is used for each particle to adjust its personal best position with a certain probability. Besides, a modified opposition-based computation is employed to improve the swarm diversity. The experimental comparison is conducted between the QPSO-DGS and other seven state-of-art PSO variants on the CEC’2013 test suit. The experimental results show that QPSO-DGS has a promising performance in terms of the solution accuracy and the convergence speed on the majority of these test functions, and especially on multimodal problems.

A Modified Simulated Annealing (MSA) Algorithm to Solve the Supplier Selection and Order Quantity Allocation Problem with Non-Linear Freight Rates

Economic Order Quantity (EOQ) is an important optimization problem for inventory management with an impact on various industries; however, their mathematical models may be complex with non-convex, non-linear, and non-differentiable objective functions. Metaheuristic algorithms have emerged as powerful tools for solving complex optimization problems (including EOQ). They are iterative search techniques that can efficiently explore large solution spaces and obtain near-optimal solutions. Simulated Annealing (SA) is a widely used metaheuristic method able to avoid local suboptimal solutions. The traditional SA algorithm is based on a single agent, which may result in a low convergence rate for complex problems. This article proposes a modified multiple-agent (population-based) adaptive SA algorithm; the adaptive algorithm imposes a slight attraction of all agents to the current best solution. As a proof of concept, the proposed algorithm was tested on a particular EOQ problem (recently studied in the literature and interesting by itself) in which the objective function is non-linear, non-convex, and non-differentiable. With these new mechanisms, the algorithm allows for the exploration of different regions of the solution space and determines the global optimum in a faster manner. The analysis showed that the proposed algorithm performed well in finding good solutions in a reasonably short amount of time.

Epigenetic opportunities for evolutionary computation

Evolutionary computation is a group of biologically inspired algorithms used to solve complex optimization problems. It can be split into evolutionary algorithms, which take inspiration from genetic inheritance, and swarm intelligence algorithms, that take inspiration from cultural inheritance. However, much of the modern evolutionary literature remains relatively unexplored. To understand which evolutionary mechanisms have been considered, and which have been overlooked, this paper breaks down successful bioinspired algorithms under a contemporary biological framework based on the extended evolutionary synthesis, an extension of the classical, genetics focused, modern synthesis. Although the idea of the extended evolutionary synthesis has not been fully accepted in evolutionary theory, it presents many interesting concepts that could provide benefits to evolutionary computation. The analysis shows that Darwinism and the modern synthesis have been incorporated into evolutionary computation but the extended evolutionary synthesis has been broadly ignored beyond: cultural inheritance, incorporated in the sub-set of swarm intelligence algorithms, evolvability, through covariance matrix adaptation evolution strategy (CMA-ES), and multilevel selection, through multilevel selection genetic algorithm (MLSGA). The framework shows a gap in epigenetic inheritance for evolutionary computation, despite being a key building block in modern interpretations of evolution. This leaves a diverse range of biologically inspired mechanisms as low hanging fruit that should be explored further within evolutionary computation and illustrates the potential of epigenetic based approaches through the recent benchmarks in the literature.

Distributed Differential Evolution With Adaptive Resource Allocation.

Distributed differential evolution (DDE) is an efficient paradigm that adopts multiple populations for cooperatively solving complex optimization problems. However, how to allocate fitness evaluation (FE) budget resources among the distributed multiple populations can greatly influence the optimization ability of DDE. Therefore, this article proposes a novel three-layer DDE framework with adaptive resource allocation (DDE-ARA), including the algorithm layer for evolving various differential evolution (DE) populations, the dispatch layer for dispatching the individuals in the DE populations to different distributed machines, and the machine layer for accommodating distributed computers. In the DDE-ARA framework, three novel methods are further proposed. First, a general performance indicator (GPI) method is proposed to measure the performance of different DEs. Second, based on the GPI, a FE allocation (FEA) method is proposed to adaptively allocate the FE budget resources from poorly performing DEs to well-performing DEs for better search efficiency. This way, the GPI and FEA methods achieve the ARA in the algorithm layer. Third, a load balance strategy is proposed in the dispatch layer to balance the FE burden of different computers in the machine layer for improving load balance and algorithm speedup. Moreover, theoretical analyses are provided to show why the proposed DDE-ARA framework can be effective and to discuss the lower bound of its optimization error. Extensive experiments are conducted on all the 30 functions of CEC 2014 competitions at 10, 30, 50, and 100 dimensions, and some state-of-the-art DDE algorithms are adopted for comparisons. The results show the great effectiveness and efficiency of the proposed framework and the three novel methods.

Multi-Strategy Improved Flamingo Search Algorithm for Global Optimization

To overcome the limitations of the Flamingo Search Algorithm (FSA), such as a tendency to converge on local optima and improve solution accuracy, we present an improved algorithm known as the Multi-Strategy Improved Flamingo Search Algorithm (IFSA). The IFSA utilizes a cube chaotic mapping strategy to generate initial populations, which enhances the quality of the initial solution set. Moreover, the information feedback model strategy is improved to dynamically adjust the model based on the current fitness value, which enhances the information exchange between populations and the search capability of the algorithm itself. In addition, we introduce the Random Opposition Learning and Elite Position Greedy Selection strategies to constantly retain superior individuals while also reducing the probability of the algorithm falling into a local optimum, thereby further enhancing the convergence of the algorithm. We evaluate the performance of the IFSA using 23 benchmark functions and verify its optimization using the Wilcoxon rank-sum test. The compared experiment results indicate that the proposed IFSA can obtain higher convergence accuracy and better exploration abilities. It also provides a new optimization algorithm for solving complex optimization problems.

Overview of Metaheuristic Algorithms

Metaheuristic algorithms are optimization algorithms that are used to address complicated issues that cannot be solved using standard approaches. These algorithms are inspired by natural processes such as genetics, swarm behavior, and evolution, and they are used to explore a broad search space to identify the global optimum of a problem. Genetic algorithms, particle swarm optimization, ant colony optimization, simulated annealing, and tabu search are examples of popular metaheuristic algorithms. These algorithms have been widely utilized to address complicated issues in domains like as engineering, finance, and computer science. In general, the history of metaheuristic algorithms spans several decades and involves the development of various optimization algorithms that are inspired by natural systems. Metaheuristic algorithms have become a valuable tool in solving complex optimization problems in various fields, and they are likely to continue to play an important role in the development of new technologies and applications.

Progressive Learning Hill Climbing Algorithm with Energy-Map-Based Initialization for Image Reconstruction.

Image reconstruction is an interesting yet challenging optimization problem that has several potential applications. The task is to reconstruct an image using a fixed number of transparent polygons. Traditional gradient-based algorithms cannot be applied to the problem since the optimization objective has no explicit expression and cannot be represented by computational graphs. Metaheuristic search algorithms are powerful optimization techniques for solving complex optimization problems, especially in the context of incomplete information or limited computational capability. In this paper, we developed a novel metaheuristic search algorithm named progressive learning hill climbing (ProHC) for image reconstruction. Instead of placing all the polygons on a blank canvas at once, ProHC starts from one polygon and gradually adds new polygons to the canvas until reaching the number limit. Furthermore, an energy-map-based initialization operator was designed to facilitate the generation of new solutions. To assess the performance of the proposed algorithm, we constructed a benchmark problem set containing four different types of images. The experimental results demonstrated that ProHC was able to produce visually pleasing reconstructions of the benchmark images. Moreover, the time consumed by ProHC was much shorter than that of the existing approach.

Multistrategy-Boosted Carnivorous Plant Algorithm: Performance Analysis and Application in Engineering Designs

Many pivotal and knotty engineering problems in practical applications boil down to optimization problems, which are difficult to resolve using traditional mathematical optimization methods. Metaheuristics are efficient algorithms for solving complex optimization problems while keeping computational costs reasonable. The carnivorous plant algorithm (CPA) is a newly proposed metaheuristic algorithm, inspired by its foraging strategies of attraction, capture, digestion, and reproduction. However, the CPA is not without its shortcomings. In this paper, an enhanced multistrategy carnivorous plant algorithm called the UCDCPA is developed. In the proposed framework, a good point set, Cauchy mutation, and differential evolution are introduced to increase the algorithm's calculation precision and convergence speed as well as heighten the diversity of the population and avoid becoming trapped in local optima. The superiority and practicability of the UCDCPA are illustrated by comparing its experimental results with several algorithms against the CEC2014 and CEC2017 benchmark functions, and five engineering designs. Additionally, the results of the experiment are analyzed again from a statistical point of view using the Friedman and Wilcoxon rank-sum tests. The findings show that these introduced strategies provide some improvements in the performance of the CPA, and the accuracy and stability of the optimization results provided by the proposed UCDCPA are competitive against all algorithms. To conclude, the proposed UCDCPA offers a good alternative to solving optimization issues.