Handling Complex Optimization Problems Research Articles

A novel hybrid genetic algorithm and Nelder-Mead approach and it’s application for parameter estimation

Background Traditional optimization methods often struggle to balance global exploration and local refinement, particularly in complex real-world problems. To address this challenge, we introduce a novel hybrid optimization strategy that integrates the Nelder-Mead (NM) technique and the Genetic Algorithm (GA), named the Genetic and Nelder-Mead Algorithm (GANMA). This hybrid approach aims to enhance performance across various benchmark functions and parameter estimation tasks. Methods GANMA combines the global search capabilities of GA with the local refinement strength of NM. It is first tested on 15 benchmark functions commonly used to evaluate optimization strategies. The effectiveness of GANMA is also demonstrated through its application to parameter estimation problems, showcasing its practical utility in real-world scenarios. Results GANMA outperforms traditional optimization methods in terms of robustness, convergence speed, and solution quality. The hybrid algorithm excels across different function landscapes, including those with high dimensionality and multimodality, which are often encountered in real-world optimization issues. Additionally, GANMA improves model accuracy and interpretability in parameter estimation tasks, enhancing both model fitting and prediction. Conclusions GANMA proves to be a flexible and powerful optimization method suitable for both benchmark optimization and real-world parameter estimation challenges. Its capability to efficiently explore parameter spaces and refine solutions makes it a promising tool for scientific, engineering, and economic applications. GANMA offers a valuable solution for improving model performance and effectively handling complex optimization problems.

Multi-threshold image segmentation using new strategies enhanced whale optimization for lupus nephritis pathological images

Lupus Nephritis (LN) has been considered as the most prevalent form of systemic lupus erythematosus. Medical imaging plays an important role in diagnosing and treating LN, which can help doctors accurately assess the extent and extent of the lesion. However, relying solely on visual observation and judgment can introduce subjectivity and errors, especially for complex pathological images. Image segmentation techniques are used to differentiate various tissues and structures in medical images to assist doctors in diagnosis. Multi-threshold Image Segmentation (MIS) has gained widespread recognition for its direct and practical application. However, existing MIS methods still have some issues. Therefore, this study combines non-local means, 2D histogram, and 2D Renyi’s entropy to improve the performance of MIS methods. Additionally, this study introduces an improved variant of the Whale Optimization Algorithm (GTMWOA) to optimize the aforementioned MIS methods and reduce algorithm complexity. The GTMWOA fusions Gaussian Exploration (GE), Topology Mapping (TM), and Magnetic Liquid Climbing (MLC). The GE effectively amplifies the algorithm’s proficiency in local exploration and quickens the convergence rate. The TM facilitates the algorithm in escaping local optima, while the MLC mechanism emulates the physical phenomenon of MLC, refining the algorithm’s convergence precision. This study conducted an extensive series of tests using the IEEE CEC 2017 benchmark functions to demonstrate the superior performance of GTMWOA in addressing intricate optimization problems. Furthermore, this study executed an experiment using Berkeley images and LN images to verify the superiority of GTMWOA in MIS. The ultimate outcomes of the MIS experiments substantiate the algorithm’s advanced capabilities and robustness in handling complex optimization problems.

Voronoi Tessellations based simple optimizer

Population diversity holds significant importance in determining the success of any evolutionary algorithm. It helps the algorithm in efficiently exploring the search space and identifying the promising region(s) containing global optimal solution(s). However, during the optimization procedure the population may lose its diversity, causing premature convergence in the algorithm and resulting in approximations to the sub-optimal solution(s). This paper proposes a Voronoi Tessellations based Simple Optimizer (VTSO) algorithm that utilizes a niche concept of Voronoi Tessellations (VTs) from the field of computational geometry to ensure a well-distributed population throughout the optimization procedure. It proposed an elite sampling mechanism that utilizes Lévy flights to aggressively explore the search space for locating potential optimal region(s), and the Differential Evolution (DE) algorithm to exploit these regions in order to approximate the global optimal solution(s). In addition, a population diameter-based switch is devised which activates itself when the algorithm detects premature convergence in the algorithm. Experiments are conducted on CEC14 and CEC17 benchmark test suit, and the proposed algorithm is compared with the existing state-of-the-art evolutionary algorithms. The results are competitive to recommend the VTSO algorithm as a new efficient and accurate optimizer for handling complex optimization problems.

IOOA: A multi-strategy fusion improved Osprey Optimization Algorithm for global optimization

<abstract><p>With the widespread application of metaheuristic algorithms in engineering and scientific research, finding algorithms with efficient global search capabilities and precise local search performance has become a hot topic in research. The osprey optimization algorithm (OOA) was first proposed in 2023, characterized by its simple structure and strong optimization capability. However, practical tests have revealed that the OOA algorithm inevitably encounters common issues faced by metaheuristic algorithms, such as the tendency to fall into local optima and reduced population diversity in the later stages of the algorithm's iterations. To address these issues, a multi-strategy fusion improved osprey optimization algorithm is proposed (IOOA). First, the characteristics of various chaotic mappings were thoroughly explored, and the adoption of Circle chaotic mapping to replace pseudo-random numbers for population initialization improvement was proposed, increasing initial population diversity and improving the quality of initial solutions. Second, a dynamically adjustable elite guidance mechanism was proposed to dynamically adjust the position updating method according to different stages of the algorithm's iteration, ensuring the algorithm maintains good global search capabilities while significantly increasing the convergence speed of the algorithm. Lastly, a dynamic chaotic weight factor was designed and applied in the development stage of the original algorithm to enhance the algorithm's local search capability and improve the convergence accuracy of the algorithm. To fully verify the effectiveness and practical engineering applicability of the IOOA algorithm, simulation experiments were conducted using 21 benchmark test functions and the CEC-2022 benchmark functions, and the IOOA algorithm was applied to the LSTM power load forecasting problem as well as two engineering design problems. The experimental results show that the IOOA algorithm possesses outstanding global optimization performance in handling complex optimization problems and broad applicability in practical engineering applications.</p></abstract>

Multi-Objective Routing Optimization in Electric and Flying Vehicles: A Genetic Algorithm Perspective

The advent of electric and flying vehicles (EnFVs) has brought significant advancements to the transportation industry, offering improved sustainability, reduced congestion, and enhanced mobility. However, the efficient routing of messages in EnFVs presents unique challenges that demand specialized algorithms to address their specific constraints and objectives. This study analyzes several case studies that investigate the effectiveness of genetic algorithms (GAs) in optimizing routing for EnFVs. The major contributions of this research lie in demonstrating the capability of GAs to handle complex optimization problems with multiple objectives, enabling the simultaneous consideration of factors like energy efficiency, travel time, and vehicle utilization. Moreover, GAs offer a flexible and adaptive approach to finding near-optimal solutions in dynamic transportation systems, making them suitable for real-world EnFV networks. While GAs show promise, there are also limitations, such as computational complexity, difficulty in capturing real-world constraints, and potential sub-optimal solutions. Addressing these challenges, the study highlights several future research directions, including the integration of real-time data and dynamic routing updates, hybrid approaches with other optimization techniques, consideration of uncertainty and risk management, scalability for large-scale routing problems, and enhancing energy efficiency and sustainability in routing. By exploring these avenues, researchers can further improve the efficiency and effectiveness of routing algorithms for EnFVs, paving the way for their seamless integration into modern transportation systems.

Bi-preference linkage-driven artificial bee colony algorithm with multi-operator fusion

The artificial bee colony algorithm (ABC) struggles in handling complex optimization problems with high dimensions in light of its search operators’ strong exploration and weak exploitation properties. To tackle this situation, in this study, we propose a bi-preference linkage-driven ABC algorithm with multi-operator fusion, named BPLABC. BPLABC couples a preference-free stochastic search operator with a global best-guided search operator in the employed bee phase to maintain the population diversity while enhancing the population quality. During the onlooker bee phase, a tailored bi-type elite-guided exploitation mechanism is employed to regulate the exploitation intensity of the promising elite nectar sources selected via a new roulette selection probability calculation paradigm. To discourage the onlooker bees from slipping into local traps, after the scout bee phase, an auxiliary adversarial search operator is assembled to tug certain promising elite solutions away from the present pseudo-global best solution. To illustrate the effectiveness and efficiency of BPLABC, two sets of test suits consisting of 23 benchmark problems, 30 complex CEC2014 functions, and two real-world problems are picked for testing. Experimental results showed that BPLABC can achieve superior or equivalent performance to several representative ABC variants on the majority of the tested problems.

An improved artificial electric field algorithm and its application in neural network optimization

Artificial electric field (AEF) algorithm is a newly developed meta-heuristic optimization technique inspired by the Coulomb's law of electrostatic force. As so far, AEF algorithm has been successfully applied in some scientific research and engineering fields, but it still has the defects of premature convergence and poor search ability in handling complex optimization problems. To address such issues, a novel Coulomb's constant generation scheme is explored to calculate the electrostatic force, and then an improved AEF (IAEF) algorithm is developed to strengthen the global exploration capability. Subsequently, 18 popular test functions with different dimensions are selected as benchmarks for performance evaluation. Furthermore, two nonlinear problems of neural network optimization are employed to further investigate the effectiveness and superiority of IAEF algorithm. Experimental results demonstrate that the proposed IAEF is efficient and effective optimization method in comparison with the conventional AEF and several famous evolutionary algorithms.

Weighted iterated local branching for mathematical programming problems with binary variables

Local search algorithms are frequently used to handle complex optimization problems involving binary decision variables. One way of implementing a local search procedure is by using a mixed-integer programming solver to explore a neighborhood defined through a constraint that limits the number of binary variables whose values are allowed to change in a given iteration. Recognizing that not all variables are equally promising to change when searching for better neighboring solutions, we propose a weighted iterated local branching heuristic. This new procedure differs from similar existing methods since it considers groups of binary variables and associates with each group a limit on the number of variables that can change. The groups of variables are defined using weights that indicate the expected contribution of flipping the variables when trying to identify improving solutions in the current neighborhood. When the mixed-integer programming solver fails to identify an improving solution in a given iteration, the proposed heuristic may force the search into new regions of the search space by utilizing the group of variables that are least promising to flip. The weighted iterated local branching heuristic is tested on benchmark instances of the optimum satisfiability problem, and computational results show that the weighted method is superior to an alternative method without weights.

Multi-objective equilibrium optimizer: framework and development for solving multi-objective optimization problems

ABSTRACT This paper proposes a new Multi-Objective Equilibrium Optimizer (MOEO) to handle complex optimization problems, including real-world engineering design optimization problems. The Equilibrium Optimizer (EO) is a recently reported physics-based metaheuristic algorithm, and it has been inspired by the models used to predict equilibrium state and dynamic state. A similar procedure is utilized in MOEO by combining models in a different target search space. The crowding distance mechanism is employed in the MOEO algorithm to balance exploitation and exploration phases as the search progresses. In addition, a non-dominated sorting strategy is also merged with the MOEO algorithm to preserve the population diversity and it has been considered as a crucial problem in multi-objective metaheuristic algorithms. An archive with an update function is used to uphold and improve the coverage of Pareto with optimal solutions. The performance of MOEO is validated for 33 contextual problems with 6 constrained, 12 unconstrained, and 15 practical constrained engineering design problems, including non-linear problems. The result obtained by the proposed MOEO algorithm is compared with other state-of-the-art multi-objective optimization algorithms. The quantitative and qualitative results indicate that the proposed MOEO provides more competitive outcomes than the different algorithms. From the results obtained for all 33 benchmark optimization problems, the efficiency, robustness, and exploration ability to solve multi-objective problems of the MOEO algorithm are well defined and clarified. The paper is further supported with extra online service and guideline at https://premkumarmanoharan.wixsite.com/mysite.

Comparison of Centralized and Distributed Intelligent Particle Multi-Swarm Optimization on Search Performance

In recent years, the technology of particle swarm optimization (PSO) is expanding remarkably. Especially, the technical development of particle multi-swarm optimization (PMSO) attracts attention, and it is expected to handle complex optimization problems. In this paper, we propose two kinds of search methods of PMSO for pattern classification. The crucial idea, here, is how to handle the given parity problems by using these search methods of centralized and distributed intelligent particle multi-swarm optimization (i.e., CIPMSO and DIPMSO). Due to accomplish the hard task of obtaining the high-performance and high-efficiency of PMSO technology, many computer experiments are carried out to handle the 2-bit, 3-bit and 4-bit parity problems under different search situations. Therefore, the obtained experimental results are analyzed and compared, respectively, the search performance and characteristics of the search methods of both CIPMSO and DIPMSO are clarified. Based on the obtained information and know-how, it will further improve the search efficiency and act in conformity of PMSO technology.

Modified Particle Swarm Optimization With Effective Guides

Despite of its simplicity, the conventional learning strategy of canonical particle swarm optimization (PSO) is inefficient to handle complex optimization problems due to its tendency of overemphasizing the fitness information of global best position without considering the diversity information of swarm. In this article, a modified particle swarm optimization with effective guides (MPSOEG) is proposed, aiming to improve the algorithm's search performances in handling the optimization problems with different characteristics. Depending on the search performance of algorithm, two types of exemplars can be generated by an optimal guide creation (OGC) module incorporated into MPSOEG by referring to the particles with valuable directional information. Particularly, a global exemplar is generated by OCG module to guide the swarm converging towards the promising solution regions of search space, whereas a unique local exemplar can be customized for each particle to enable it escaping from local or non-optimal solution regions. In contrary to global best particle, the exemplars generated by OGC module are able to guide all MPSOEG particles more effectively by considering both fitness and diversity information of swarm, hence can achieve better balancing of algorithm's exploration and exploitation searches. Another notable contribution of MPSOEG is the simplicity of its learning framework through the elimination of both inertia weight and acceleration coefficients parameters. Comprehensive simulation studies are conducted with 25 benchmark functions and the proposed MPSOEG is reported to outperform its six peer algorithms in terms of search accuracy, search reliability and search efficiency in most tested problems.

A New Artificial Bee Colony Based on Multiple Search Strategies and Dimension Selection

Artificial bee colony (ABC) algorithm is a popular optimization technique with strong search ability. Although ABC has the ability to handle complex optimization problems, it suffers from weak exploitation and slow convergence. In order to tackle this issue, a new ABC variant based on multiple search strategies and dimension selection (ABC-MSDS) is proposed in this paper. Firstly, multiple search strategies based on dual strategy pool are designed. Compared to other existing ABC with multiple search strategies, our approach constructs two strategy pools for employed and onlooker bees, respectively. Secondly, a new dimension selection method is used to replace the random dimension selection in the standard ABC. In the search process, each dimension is chosen one by one in terms of the quality of offspring. Finally, a modified scout bee phase is employed to accelerate the search. Experimental study is conducted on classical benchmark problems and CEC 2013 shifted and rotated problems. The performance of ABC-MSDS is compared with several recently published ABC variants. Computational results demonstrate the effectiveness of our approach.

Using Fuzzy Clustering Chaotic-based Differential Evolution to solve multiple resources leveling in the multiple projects scheduling problem

Project scheduling is an important part of construction project planning. Resource leveling is the process used within project scheduling to reduce fluctuations in resource usage over the period of project implementation. These fluctuations frequently create the untenable requirement of regularly hiring and firing temporary staff resources to meet short-term project needs. Construction project decision makers currently rely on experience-based methods to manage fluctuations. However, these methods lack consistency and may result in unnecessary wastage of resources or costly schedule overruns. This research introduces a novel optimization model called the Fuzzy Clustering Chaotic-based Differential Evolution for solving multiple resources leveling in the multiple projects scheduling problem (FCDE-MRLMP). The novel Fuzzy Clustering Chaotic-based Differential Evolution (FCDE) algorithm integrates fuzzy c-means clustering and chaotic techniques into the original Differential Evolution (DE) algorithm to handle complex optimization problems. The chaotic technique prevents the optimization algorithm from converging prematurely. The fuzzy c-means clustering technique acts as several multi-parent crossover operators in order to utilize population information efficiently and enhance convergence efficiency. Experiments run indicate that the proposed model obtains optimal results more reliably and efficiently than the benchmark algorithms considered. The proposed optimization model is a promising alternative approach to assist project managers to handle resource-leveling project scheduling problems effectively.

Orthogonal Multiobjective Chemical Reaction Optimization Approach for the Brushless DC Motor Design

The optimal design of a brushless direct-current motor (BLDCM) is a prevalent and practical issue in the field of magnetics. A major problem is to design a BLDCM so that it operates optimally in the sense of producing maximum efficiency with minimal material cost. Using the sizing model, a novel orthogonal multiobjective chemical reaction optimization (OMOCRO) algorithm is proposed to solve this problem. Chemical reaction optimization is a newly proposed heuristic algorithm, inspired by the interactions between molecules during chemical reactions. In our proposed OMOCRO, we employ a Pareto ranking scheme to deal with multiobjective optimization problems, and orthogonal experimental design is used in the initialization stage. Comparative experiments with nondominated sorting genetic algorithm and multiobjective particle swarm approach demonstrate that our proposed method is more competitive in handling complex optimization problems.

Probability Collectives with Collaborative Optimization (PCCO): A Novel Framework for Handling Complex Optimization Problems

In this paper, a novel framework as a combination of Probability Collectives (PC) and Collaborative Optimization (CO) is proposed and detailed illustrated. The framework has a two-level structure which is similar to that of CO, but with the system level replaced by distributed PC based agents. This formulation maintains the advantage of CO while enhances the optimization and coordination ability at the system level. For better implementation, some adaption and improvement has been made to the origin PC method. The resultant PCCO framework shows satisfied performance in handling complex optimization problems with both efficiency and accuracy.

Methods for Integrating and Handling Complex Optimization Problems in the Process Industries

A hot topic in the process systems engineering community is the so called integration of decision levels. Industrial process systems are operated at different levels of decisions; in the lowest level, actual process operating conditions are chosen, while at the intermediate and higher level production and planning are strategically scheduled. Modeling and optimization at each of the levels is often done sequentially and this leads to the question whether optimization of individual levels will result in a 'global optimum'. For this reason integration is applied. Integration could mean that targets are closer to their global optima, but it also encompasses the increasing complexity of the overall optimization problem. This is the reason, that for many industrially scaled optimization problems, the approach is still on the basis of a sequential approach. In this paper we discuss, on the basis on patent literature of the last 20 years, which tools are available to handle these complex integrated optimization problems.

Methods for Integrating and Handling Complex Optimization Problems in the Process Industries

A hot topic in the process systems engineering community is the so called integration of decision levels. Industrial process systems are operated at different levels of decisions; in the lowest level, actual process operating conditions are chosen, while at the intermediate and higher level production and planning are strategically scheduled. Modeling and optimization at each of the levels is often done sequentially and this leads to the question whether optimization of individual levels will result in a ‘global optimum’. For this reason integration is applied. Integration could mean that targets are closer to their global optima, but it also encompasses the increasing complexity of the overall optimization problem. This is the reason, that for many industrially scaled optimization problems, the approach is still on the basis of a sequential approach. In this paper we discuss, on the basis on patent literature of the last 20 years, which tools are available to handle these complex integrated optimization problems. Keywords: Systems integration, optimization, process industries