Complex Global Optimization Problems Research Articles

Harmonic Mean Optimizer (HMO) for global problems solving

This study introduces the Harmonic Mean Optimizer (HMO), a novel meta-heuristic algorithm designed to address complex global optimization problems. The primary objective of this research is to develop an optimization technique that effectively balances exploration and exploitation without requiring extensive parameter tuning, thereby simplifying the optimization process and enhancing its robustness across various problem domains. The HMO employs a unique dual-fitness index that leverages the harmonic mean to assess both the quality and diversity of candidate solutions dynamically. This approach ensures a balanced search process that avoids premature convergence and improves the ability to find global optima. The methodology involves extensive benchmarking of the HMO against a comprehensive set of test functions, including 23 traditional functions from the Congress on Evolutionary Computation (CEC) 2017 test suite. The performance of the HMO is compared with that of established meta-heuristic algorithms, such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO), to validate its efficacy in terms of convergence speed and solution accuracy. Additionally, the HMO is applied to several real-world engineering problems to demonstrate its practical utility. The results show that the HMO consistently outperforms the benchmark algorithms, achieving faster convergence and higher accuracy in finding optimal solutions across a diverse range of test problems. In practical applications, the HMO effectively optimized complex engineering tasks, achieving significant improvements in both solution quality and computational efficiency. These findings highlight the potential of the HMO as a versatile and powerful tool for global optimization tasks. the HMO offers a significant advancement in optimization methodologies by providing a robust, parameter-free approach that effectively balances exploration and exploitation. This study underscores the HMO’s applicability to a wide range of optimization challenges and sets the foundation for future research and development in enhancing and applying this innovative algorithm to more complex and diverse problem domains.

Modified snake optimizer based multi-level thresholding for color image segmentation of agricultural diseases

Image segmentation is crucial for early identification and diagnosis of crop diseases in agriculture. It helps identify disease areas and characteristics, laying the groundwork for disease diagnosis and treatment. However, color image thresholding segmentation method faces challenges in finding the optimal threshold as the number of thresholds increases, which affects segmentation quality. In this paper, a modified snake optimizer (MSO) is proposed to address the color image thresholding segmentation problem using Kapur’s entropy as the objective function. MSO incorporates a dynamic adaptive parameter adjustment method. The improved global position update formula introduces guidance from the optimal individual and disturbance from random individuals, effectively achieving a balance between global and local search capabilities. A dynamic parameter adjustment method is added to accelerate convergence speed during snake movement to food. Lévy flight is introduced to the Flight mode to help the algorithm escape local extremums. A balancing strategy is implemented in the Mating mode, incorporating guidance from the optimal individual and information exchange between sub-populations, enabling balanced exploration and local exploitation capabilities. The hill-climbing jump operation for the optimal individual is added to help the algorithm overcome local stagnation. The proposed MSO is evaluated on CEC 2017 test functions and color test images, and the obtained results are compared with other segmentation methods and other intelligent optimization algorithms. The results demonstrate that MSO exhibits stable and excellent performance in both complex global optimization problems and color image thresholding segmentation problems. Finally, MSO is applied to segment rice disease images, and the results reveal significantly better segmentation performance compared to other algorithms. MSO shows great potential in solving the thresholding segmentation problem for agricultural disease images, thereby assisting in the accurate identification, diagnosis, and treatment of agricultural diseases and insect pests.

An improved multi-operator differential evolution with two-phase migration strategy for numerical optimization

Over the last decade, the multi-operator differential evolution (MODE) has become one of the most popular research areas in the differential evolution (DE) family. Among these MODEs, an improved multi-operator differential evolution (IMODE) has achieved success as the winner in CEC2020. Despite its good performance, the random information sharing strategy may not efficiently handle the balance between exploration and exploitation for the complex numerical optimization. To address this limitation, we propose a two-phase migration strategy (TMS) to improve the performance of IMODE, called IMODE-TMS. In the first phase, the top-ranked individuals in each sub-population are retained for exploitation, and all the bottom-ranked individuals are assigned to three sub-populations to maintain diversity. Furthermore, the second phase plays a crucial role in eliminating stagnation. When a sub-population is identified as stagnant by the stagnation indicator, the optimal individual will migrate to that sub-population following the uni-directional ring structure. This process is mainly used to increase the off-trap capability on some problems with complex fitness landscapes. IMODE-TMS is tested on the CEC2020, CEC2021 and CEC2022 benchmark functions, and seven well-known complex global trajectory optimization problems (GTOP). The experimental results show that IMODE-TMS significantly outperforms not only IMODE but also other state-of-the-art comparison algorithms.

Human Evolutionary Optimization Algorithm

This paper introduces the Human Evolutionary Optimization Algorithm (HEOA), a metaheuristic algorithm inspired by human evolution. HEOA divides the global search process into two distinct phases: human exploration and human development. Logistic Chaos Mapping is employed for initialization. In the human exploration phase, an initial global search is conducted, followed by the human development phase, in which the population is categorized into leaders, explorers, followers, and losers, each utilizing distinct search strategies. The convergence speed and search accuracy of HEOA are evaluated using 23 well-established test functions. Furthermore, the algorithm's applicability in engineering optimization is assessed with four engineering problems. A comparative analysis with ten other algorithms highlights HEOA's effectiveness, as evidenced by various performance metrics and statistical measures. Consistently, the results demonstrate that HEOA surpasses most current state-of-the-art algorithms in approximating optimal solutions for complex global optimization problems. The MATLAB code for HEOA is available at https://github.com/junbolian/HEOA.git.

Theoretical research on the geometric structure and electronic properties of medium-sized LaHnq (n=2–20, q=0, 1) clusters

In cluster scientific research, determining the ground state structure is a fundamental aspect of investigating the properties and applications of clusters. However, the determination of the lowest-energy structure of clusters is not only a complex global optimization problem but also a crucial challenge in current cluster research. In the work the geometric structure and electronic properties of LaHn0/+ (n = 2–20) nanoclusters with potential for hydrogen storage are investigated using Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) method and Density Functional Theory (DFT). By calculating the average adsorption energy and hydrogen storage mass fraction, it is predicted that neutral LaH13 and cationic LaH14+ clusters exhibit high hydrogen storage densities of 8.6 wt% and 9.2 wt%, respectively. Furthermore, the molecular orbital composition and internal chemical bond binding mode were analyzed using adaptive natural density partition (AdNDP) and natural bond orbital (NBO). The results indicate that the strong hybridization between La 5d orbitals and H 1s orbitals is the primary factor contributing to the high stability of both neutral LaH13 and cationic LaH14+ clusters.

Enhanced crow search algorithm with multi-stage search integration for global optimization problems.

Crow search algorithm (CSA), as a new swarm intelligence algorithm that simulates the crows' behaviors of hiding and tracking food in nature, performs well in solving many optimization problems. However, while handling complex and high-dimensional global optimization problems, CSA is apt to fall into evolutionary stagnation and has slow convergence speed, low accuracy, and weak robustness. This is mainly because it only utilizes a single search stage, where position updating relies on random following among individuals or arbitrary flight of individuals. To address these deficiencies, a CSA with multi-stage search integration (MSCSA) is presented. Chaos and multiple opposition-based learning techniques are first introduced to improve original population quality and ergodicity. The free foraging stage based on normal random distribution and Lévy flight is designed to conduct local search for enhancing the solution accuracy. And the following stage using mixed guiding individuals is presented to perform global search for expanding the search space through tracing each other among individuals. Finally, the large-scale migration stage based on the best individual and mixed guiding individuals concentrates on increasing the population diversity and helping the population jump out of local optima by moving the population to a promising area. All of these strategies form multi-level and multi-granularity balances between global exploration and local exploitation throughout the evolution. The proposed MSCSA is compared with a range of other algorithms, including original CSA, three outstanding variants of CSA, two classical meta-heuristics, and six state-of-the-art meta-heuristics covering different categories. The experiments are conducted based on the complex and high-dimensional benchmark functions CEC 2017 and CEC 2010, respectively. The experimental and statistical results demonstrate that MSCSA is competitive for tackling large-scale complicated problems, and is significantly superior to the competitors.

MFO-SFR: An Enhanced Moth-Flame Optimization Algorithm Using an Effective Stagnation Finding and Replacing Strategy

Moth-flame optimization (MFO) is a prominent problem solver with a simple structure that is widely used to solve different optimization problems. However, MFO and its variants inherently suffer from poor population diversity, leading to premature convergence to local optima and losses in the quality of its solutions. To overcome these limitations, an enhanced moth-flame optimization algorithm named MFO-SFR was developed to solve global optimization problems. The MFO-SFR algorithm introduces an effective stagnation finding and replacing (SFR) strategy to effectively maintain population diversity throughout the optimization process. The SFR strategy can find stagnant solutions using a distance-based technique and replaces them with a selected solution from the archive constructed from the previous solutions. The effectiveness of the proposed MFO-SFR algorithm was extensively assessed in 30 and 50 dimensions using the CEC 2018 benchmark functions, which simulated unimodal, multimodal, hybrid, and composition problems. Then, the obtained results were compared with two sets of competitors. In the first comparative set, the MFO algorithm and its well-known variants, specifically LMFO, WCMFO, CMFO, ODSFMFO, SMFO, and WMFO, were considered. Five state-of-the-art metaheuristic algorithms, including PSO, KH, GWO, CSA, and HOA, were considered in the second comparative set. The results were then statistically analyzed through the Friedman test. Ultimately, the capacity of the proposed algorithm to solve mechanical engineering problems was evaluated with two problems from the latest CEC 2020 test-suite. The experimental results and statistical analysis confirmed that the proposed MFO-SFR algorithm was superior to the MFO variants and state-of-the-art metaheuristic algorithms for solving complex global optimization problems, with 91.38% effectiveness.

UCAV Path Planning for Avoiding Obstacles using Cooperative Co-evolution Spider Monkey Optimization

The unmanned combat aerial vehicle (UCAV) path planning problem is a complex global optimization problem that aims to seek an optimal flight route that avoids the threats and constraints on the battlefield. However, as the number and degree of the path threats increases, the recent UCAV path planning algorithms all suffer from being trapped into local optima with a low convergence rate, which leads to the poor performance. Therefore, to resolve these problems, we propose a Cooperative co-Evolution (CE)-based Spider Monkey Optimization (SMO) algorithm, named CESMO to address UCAV path planning problem for avoiding obstacles. First, a cooperative co-evolution strategy is proposed to prevent the algorithms from falling into local optima easily, enhancing the coherence of the path. After that, a further division is applied to the algorithm for diversifying the search direction of each individual in the sub-groups. Finally, the spider monkey optimization-based search mechanism is designed to further strengthen the search efficiency and boost the convergence rate. Experimental results demonstrate that our proposed method is more competitive than other state-of-the-art evolutionary algorithms for UCAV path planning problem considering the quality and stability of the final paths.

Esign and Application of Optimization Algorithm for Vegetable Planting and Distribution Based on Adaptive Differential Evolution Algorithm

Now, we have entered the "internet plus" era, and all industries are making use of information technology to seek a longer-term development. For vegetable distribution, we must rely on the power of information technology. Faced with complex global optimization problems, traditional optimization algorithms have many performance limitations, such as complex solution process and easy to fall into local optimization, which can't meet the needs of practical applications. This paper studies the design and application of optimization algorithm for vegetable planting and distribution based on adaptive differential evolution algorithm. The method adopted in this paper is adaptive differential evolution algorithm. In the original differential evolution algorithm, there are three undetermined parameters: population size (NP), variation factor (F) and crossover probability (CR). In the process of evolution, NP takes a fixed value, while the key control parameters F and CR, which affect the performance of the algorithm, will adaptively take different values on [0,1], and the values of F and CR will be recalculated for each individual in each generation. Let F and CR automatically adjust and change in the process of evolution. The research in this paper shows that the algorithm in this paper is effective and suitable for application.

Comprehensive learning Jaya algorithm for engineering design optimization problems

Jaya algorithm (JAYA) is a recently developed metaheuristic algorithm for global optimization problems. JAYA has a very simple structure and only needs the essential population size and terminal condition for solving optimization problems. However, JAYA is easy to get trapped in the local optimum for solving complex global optimization problems due to its single learning strategy. Motivated by this disadvantage of JAYA, this paper presents an improved JAYA, named comprehensive learning JAYA algorithm (CLJAYA), for solving engineering design optimization problems. The core idea of CLJAYA is the designed comprehensive learning mechanism by making full use of population information. The designed comprehensive learning mechanism consists of three different learning strategies to improve the global search ability of JAYA. To investigate the performance of CLJAYA, CLJAYA is first evaluated by the well-known CEC 2013 and CEC 2014 test suites, which include 50 multimodal test functions and eight unimodal test functions. Then CLJAYA is employed to solve five real-world engineering optimization problems. Experimental results demonstrate that CLJAYA can achieve better solutions for most test problems than JAYA and the other compared algorithms, which indicates the designed comprehensive learning mechanism is very effective. In addition, the source code of the proposed CLJAYA can be loaded from https://www.mathworks.com/matlabcentral/fileexchange/82134-the-source-code-for-cljaya .

Cooperation search algorithm: A novel metaheuristic evolutionary intelligence algorithm for numerical optimization and engineering optimization problems

This paper develops a novel population-based evolutionary method called cooperation search algorithm (CSA) to address the complex global optimization problem. Inspired by the team cooperation behaviors in modern enterprise, the CSA method randomly generates a set of candidate solutions in the problem space, and then three operators are repeatedly executed until the stopping criterion is met: the team communication operator is used to improve the global exploration and determine the promising search area; the reflective learning operator is used to achieve a comprise between exploration and exploitation; the internal competition operator is used to choose solutions with better performances for the next cycle. Firstly, three kinds of mathematical optimization problems (including 24 famous test functions, 25 CEC2005 test problems and 30 CEC2014 test problems) are used to test the convergence speed and search accuracy of the CSA method. Then, several famous engineering optimization problems (like Gear train design, Welded beam design and Speed reducer design) are chosen to testify the engineering practicality of the CSA method. The results in different scenarios demonstrate that as compared with several existing evolutionary algorithms, the CSA method can effectively explore the decision space and produce competitive results in terms of various performance evaluation indicators. Thus, an effective tool is provided for solving the complex global optimization problems.

Adaptive Differential Evolution Based on Successful Experience Information

As a powerful optimization algorithm for solving nonlinear, complex and tough global optimization problems, differential evolution (DE) has been widely applied in various science and engineering fields. In this article, considering that the evolution direction of each individual is not fully exploited to guide the search process in most DE algorithms, a new DE variant (named ADEwSE), which incorporates the successful experience of evolved individuals into classic “current-to-pbest/1” mutation strategy to reduce the randomness of search direction, is proposed. Moreover, crossover matrix sorting scheme based on real crossover rate, opposition learning of crossover rate and adaptive adjustment of top p% values are combined with the new mutation strategy to improve the global search ability. In addition, to improve the searching ability of ADEwSE further, an ADEwSE variant by introducing the linear reduction of population size is proposed. In order to verify and analyze the performance of ADEwSE, numerical experiments on a set of 29 test problems from CEC2017 benchmark for 30, 50 and 100 dimensions are executed. And the experimental results are compared with that of 21 state-of-art DE-based algorithms. Comparative analysis indicates that the ADEwSE and its improved version are competitive with these state-of-art DE variants in terms of solution quality obtained.

A Decentralized Solution for Transmission Expansion Planning: Getting Inspiration from Nature

Transmission expansion planning is a problem of considerable complexity where classical optimization techniques are unable to handle large case studies. Decomposition and divide-and-conquer strategies have been applied to this problem. We propose an alternative approach based on agent-based modeling (ABM) and inspired by the behavior of the Plasmodium mold, which builds efficient transportation networks as result of its search for food sources. Algorithms inspired by this mold have already been applied to road-network design. We modify an existing ABM for road-network design to include the idiosyncratic features of power systems and their related physics, and test it over an array of case studies. Our results show that the ABM can provide near-optimal designs in all the instances studied, possibly with some further interesting properties with respect to the robustness of the developed design. In addition, the model works in a decentralized manner, using mostly local information. This means that computational time will scale with size in a more benign way than global optimization approaches. Our work shows promise in applying ABMs to solve similarly complex global optimization problems in the energy landscape.

Hybrid teaching–learning-based optimization and neural network algorithm for engineering design optimization problems

Neural network algorithm (NNA) is one of the newest meta-heuristic algorithms, which is inspired by biological nervous systems and artificial neural networks. Benefiting from the unique structure of artificial neural networks, NNA has good global search ability. However, slow convergence is its drawback that restricts its practical application. Teaching–learning-based optimization (TLBO) is an algorithm without any effort for fine tuning initial parameters, which has fast convergence speed while it is easy to fall into local optimum in solving complex global optimization problems. Considering the features of NNA and TLBO, an effective hybrid method based on TLBO and NNA, named TLNNA, is proposed for solving engineering optimization problems. The performance of TLNNA for 30 well-known unconstrained benchmark functions and 4 challenging engineering optimization problems is examined and the optimization results are compared with other competitive meta-heuristic algorithms. Such comparisons suggest that TLNNA has not only good global search ability of NNA but also fast convergence speed of TLBO and is more successful for most test problems in terms of solution quality and computational efficiency.

Hybrid parallel multimethod hyperheuristic for mixed-integer dynamic optimization problems in computational systems biology

This paper describes and assesses a parallel multimethod hyperheuristic for the solution of complex global optimization problems. In a multimethod hyperheuristic, different metaheuristics cooperate to outperform the results obtained by any of them isolated. The results obtained show that the cooperation of individual parallel searches modifies the systemic properties of the hyperheuristic, achieving significant performance improvements versus the sequential and the non-cooperative parallel solutions. Here we present and evaluate a hybrid parallel scheme of the multimethod, using both message-passing (MPI) and shared memory (OpenMP) models. The hybrid parallelization allows to achieve a better trade-off between performance and computational resources, through a compromise between diversity (number of islands) and intensity (number of threads per island). For the performance evaluation, we considered the general problem of reverse engineering nonlinear dynamic models in systems biology, which yields very large mixed-integer dynamic optimization problems. In particular, three very challenging problems from the domain of dynamic modeling of cell signaling were used as case studies. In addition, experiments have been carried out in a local cluster, a large supercomputer and a public cloud, to show the suitability of the proposed solution in different execution platforms.

A self-feedback strategy differential evolution with fitness landscape analysis

Differential evolution (DE) has been widely applied to complex global optimization problems. Different search strategies have been designed to find the optimum conditions in a fitness landscape. However, none of these strategies works well over all possible fitness landscapes. Since the fitness landscape associated with a complex global optimization problem usually consists of various local landscapes, each search strategy is efficient in a particular type of fitness landscape. A reasonable approach is to combine several search strategies and integrate their advantages to solve global optimization problems. This paper presents a new self-feedback strategy differential evolution (SFSDE) algorithm based on fitness landscape analysis of single-objective optimization problem. In the SFSDE algorithm, in the analysis of the fitness landscape features of fitness-distance correlation, a self-feedback operation is used to iteratively select and evaluate the mutation operators of the new SFSDE algorithm. Moreover, mixed strategies and self-feedback transfer are combined to design a more efficient DE algorithm and enhance the search range, convergence rate and solution accuracy. Finally, the proposed SFSDE algorithm is implemented to optimize soil water textures, and the experimental results show that the proposed SFSDE algorithm reduces the difficulty in estimating parameters, simplifies the solution process and provides a novel approach to calculate the parameters of the Van Genuchten equation. In addition, the proposed algorithm exhibits high accuracy and rapid convergence and can be widely used in the parameter estimation of such nonlinear optimization models.

Empirical study of particle swarm optimization inspired by Lotka–Volterra model in Ecology

Particle swarm optimization (PSO) has been proved to be an effective technique in solving complex global optimization problems. Many modified versions of the original PSO algorithm emerged during the last 15 years. Many of those existing methods employ all particles in a single population which adopts the similar monotonic strategy. The loss of diversity resulted in the premature convergence problem. In this paper, we proposed a suite of multi-swarm Lotka–Volterra model inspired particle swarm optimization algorithms (MSLVPSO) to address the premature convergence problem. The intraspecific and interspecific cooperation and competition strategy of the proposed model dramatically increased diversity of particles. As a result, it makes the particles more likely to break away from the local optimum. In addition, we derived the method to set parameters and developed several cooperative–competitive schemes. We evaluated the proposed MSLVPSO algorithms using a variety of benchmark functions. We also compared our proposed method with typical single-swarm PSO algorithms. Our experimental results show that the proposed MSLVPSO optimizers outperform other state-of-the-art algorithms.

New Method for Constructing a Visibility Graph-Network in 3D Space and a New Hybrid System of Modeling

This paper describes a new method for constructing a visibility graph in 3D space. We use a method for predicting porosity of hardened specimens. We also use an intelligent system method to predict porosity of hardened specimens. Visibility graphs have many applications, one of which is the analysis of trend lines of market graphs. It is possible to use 2D visibility graphs for such analysis and the construction for 2D visibility graphs is well known; however, in this paper, we will present a new method for the construction of 3D visibility graphs. 3D visibility computations are central to any computer graphics application. Drawing graphs as nodes connected by links in 3D space is visually compelling but computationally difficult. Thus, the construction of 3D visibility graphs is highly complex and requires professional computers or supercomputers. This article describes a new method for analysing 3D visibility graphs. We develop new method for draws 3D visibility graphs for analysing microstructure pictures of robot laser-hardened specimens. The microstructure of robot laser-hardened specimens is very complex; however, we can present it using 3D visibility graphs. New method for the construction of 3D visibility graphs is very useful in many cases, including: illumination and rendering, motion planning, pattern recognition, computer graphics, computational geometry and sensor networks and the military and automotive industries. We use this new algorithm for determination complexity of porosity of the microstructure of robot laser-hardened specimens. For predicting surface porosity of hardened specimens we use neural network, genetic algorithm and multiple regression. With intelligent system we increase production of process of laser hardening, because we decrease time of process and increase topographical property of materials. Hybrid evolutionary computation is a generic, flexible, robust, and versatile method for solving complex global optimization problems and can also be used in practical applications. This paper explores the use of an intelligent system with such a hybrid method to improve existing hybrids. It describes a new hybrid method based on the cycle integration method.

Bat Algorithm: A Survey of the State-of-the-Art

The area of metaheuristic optimization algorithms has been attracting researchers for many years. These algorithms have built in capability to explore a large region of the solution space, are computationally robust, efficient and can avoid premature convergence. They have been extensively tested and applied on many hard optimization problems where conventional computing techniques perform unsatisfactorily. They are capable of solving general N-dimensional, linear, nonlinear and complex global optimization problems. One of the latest entrants in this field is the Bat algorithm which is based on the echolocation behaviour of bats. It has been proven to have good convergence properties on different benchmark functions and seems promising for dealing with optimization problems. The aim of this paper is to provide a survey of the state of the art on Bat algorithm. A concise effort has been made so that the readers get a rapid insight into some of the applications upon which bat algorithm has been applied till date in specialized fields of science and engineering. Some of the variants of the bat algorithm as reported in the literature have also been discussed.

Adaptive hierarchical artificial immune system and its application in RFID reader collision avoidance

This paper proposes an efficient adaptive hierarchical artificial immune system (AHAIS) for complex global optimization problems. In the proposed AHAIS optimization, a hierarchy with top-bottom levels is used to construct the antibody population, where some antibodies with higher affinity become the top-level elitist antibodies and the other antibodies with lower affinity become the bottom-level common antibodies. The elitist antibodies experience different evolutionary operators from those common antibodies, and a well-designed dynamic updating strategy is used to guide the evolution and retrogradation of antibodies between two levels. In detail, the elitist antibodies focus on self-learning and local searching while the common antibodies emphasize elitist-learning and global searching. In addition, an adaptive searching step length adjustment mechanism is proposed to capture more accurate solutions. The suppression operator introduces an upper limit of the similarity-based threshold by considering the concentration of the candidate antibodies. To evaluate the effectiveness and the efficiency of algorithms, a series of comparative numerical simulations are arranged among the proposed AHAIS, DE, PSO, opt-aiNet and IA-AIS, where eight benchmark functions are selected as testbeds. The simulation results prove that the proposed AHAIS is an efficient method and outperforms DE, PSO, opt-aiNet and IA-AIS in convergence speed and solution accuracy. Moreover, an industrial application in RFID reader collision avoidance also demonstrates the searching capability and practical value of the proposed AHAIS optimization.