Complex Optimization Problems Research Articles

Adaptive multi-stage evolutionary search for constrained multi-objective optimization

AbstractIn this paper, we propose a multi-stage evolutionary framework with adaptive selection (MSEFAS) for efficiently handling constrained multi-objective optimization problems (CMOPs). MSEFAS has two stages of optimization in its early phase of evolutionary search: one stage that encourages promising infeasible solutions to approach the feasible region and increases diversity, and the other stage that enables the population to span large infeasible regions and accelerates convergence. To adaptively determine the execution order of these two stages in the early process, MSEFAS treats the optimization stage with higher validity of selected solutions as the first stage and the other as the second one. In addition, at the late phase of evolutionary search, MSEFAS introduces a third stage to efficiently handle the various characteristics of CMOPs by considering the relationship between the constrained Pareto fronts (CPF) and unconstrained Pareto fronts. We compare the proposed framework with eleven state-of-the-art constrained multi-objective evolutionary algorithms on 56 benchmark CMOPs. Our results demonstrate the effectiveness of the proposed framework in handling a wide range of CMOPs, showcasing its potential for solving complex optimization problems.

An efficient multi-level thresholding method for breast thermograms analysis based on an improved BWO algorithm

Breast cancer is a prevalent disease and the second leading cause of death in women globally. Various imaging techniques, including mammography, ultrasonography, X-ray, and magnetic resonance, are employed for detection. Thermography shows significant promise for early breast disease detection, offering advantages such as being non-ionizing, non-invasive, cost-effective, and providing real-time results. Medical image segmentation is crucial in image analysis, and this study introduces a thermographic image segmentation algorithm using the improved Black Widow Optimization Algorithm (IBWOA). While the standard BWOA is effective for complex optimization problems, it has issues with stagnation and balancing exploration and exploitation. The proposed method enhances exploration with Levy flights and improves exploitation with quasi-opposition-based learning. Comparing IBWOA with other algorithms like Harris Hawks Optimization (HHO), Linear Success-History based Adaptive Differential Evolution (LSHADE), and the whale optimization algorithm (WOA), sine cosine algorithm (SCA), and black widow optimization (BWO) using otsu and Kapur's entropy method. Results show IBWOA delivers superior performance in both qualitative and quantitative analyses including visual inspection and metrics such as fitness value, threshold values, peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and feature similarity index (FSIM). Experimental results demonstrate the outperformance of the proposed IBWOA, validating its effectiveness and superiority.

A Survey on Manta Ray Foraging Optimization Algorithm of Variants and Applications

This review paper delves into the original MRFO and its variants, focusing on single-objective algorithms including but not limited to hybrid algorithms, learning strategies, multiple populations and dynamic parameter adjustment, highlighting the improvements made to enhance the algorithm's efficiency in global optimization, accelerate convergence rates, and improve its capacity to evade local optima. MRFO has emerged as an effective tool for solving complex optimization problems across various domains, including energy optimization, biomedical field, engineering problems, and others. A comprehensive analysis of applications of MRFO in different fields is provided, emphasizing its adaptability and efficacy. The paper concludes with a discussion on the challenges faced by MRFO and potential future research directions, aiming to consolidate the current research status and guide future investigations.

DMT-OMPA: Innovative applications of an efficient adversarial Marine Predators Algorithm based on dynamic matrix transformation in engineering design optimization

This paper introduces an innovative variant of the Marine Predators Algorithm (MPA), termed the Dynamic Matrix Transformation-based Oppositional Marine Predators Algorithm (DMT-OMPA), aimed at enhancing the efficiency of engineering optimization strategies. Traditional MPAs have several shortcomings, including insufficient solution diversity and coverage in the initialization phase, a tendency to become trapped in local optima, and inadequate search capabilities in the later stages of iteration, all of which negatively impact the algorithm’s efficiency and effectiveness. To address these issues, the DMT-OMPA incorporates oppositional learning mechanisms and dynamic matrix transformation strategies, significantly enhancing global search capabilities and accelerating convergence speed, particularly in handling complex multidimensional optimization problems.Experimental results on the CEC2013 and CEC2017 test suites demonstrate that DMT-OMPA outperforms other recent MPA variants, various classical algorithm variants, and newly proposed algorithms, verifying its advantages in precision and reliability. Furthermore, the application of this algorithm to various real-world engineering problems substantiates its broad applicability and high efficiency. The study’s findings not only deepen our understanding of swarm intelligence optimization algorithms but also provide a new efficient tool for solving complex engineering problems. The results indicate a promising potential for wider application in diverse fields, suggesting that the DMT-OMPA algorithm could become an effective tool for tackling complex optimization problems in the future.

Multiobjective Optimization of Papermaking Wastewater Treatment Processes under Economic, Energy, and Environmental Goals.

Due to the heterogeneity of recycled paper materials and the production conditions, pollutants in papermaking wastewater fluctuate sharply over time. Quality control of the papermaking wastewater treatment process (PWTP) is challenging and costly. As regulations are also growing about the environmental effects of the PWTP on greenhouse gas (GHG) emission, energy consumption, etc., the PWTP formulates a complex multiobjective optimization problem. This research established a multiagent deep reinforcement learning framework to simultaneously optimize process cost, energy consumption, and GHG emission in the PWTP, subjected to the effluent quality, to realize economic, energy, and environmental (3E) goals. The biological treatment process of wastewater in paper mills was simulated using benchmark simulation model no. 1 (BSM1). The data generated based on the BSM manual was utilized for model training, and real data acquired from a local papermaking factory was used to estimate the model performance. The results show that the proposed method outperforms conventional techniques in identifying the best control strategies for multiple targets.

Development of an Information System for Wood Harvesting Planning

The article presents the results of developing a software system for production planning in the field of wood harvesting. The objects of research are the planning of harvesting operations, forest transport, construction, repair and maintenance of forest roads, as well as solving various related problems. The purpose of the work is to develop a native specialized software system for production planning in the field of wood harvesting, which is integrated with existing accounting and monitoring systems and is based on solving complex optimization problems of large dimensions using original specially developed methods and algorithms that take into account all the features of wood harvesting production in the Russian Federation. As a result of this work, an approach to creating such а system was developed, which includes a set of requirements for the software product, as well as formulations of the main tasks to be solved, listing the necessary initial data and information obtained as an output. The proposed approach was implemented by Russian IT-company Opti-Soft in the form of software product Opti-Wood — a multipurpose Decision Support System (DSS) designed for the use at forestry enterprises as a tool for optimizing production planning, management and control. The Opti-Wood system was developed in close contact with a large wood harvesting enterprise in the Republic of Karelia. The system is based on original algorithms for solving several optimization problems of increased complexity. Using the system allows one to increase the efficiency of logging processes by reducing costs in supply chains, the volume of warehouse stocks, the number of required vehicles; by mutual agreement of plans for harvesting operations, forest transport, road construction, etc., as well as by significantly reducing the time for taking management decisions. Increased profitability occurs due to the identification of additional options for the sale of products.

Incorporating machine learning and optimization techniques for assigning patients to operating rooms by considering fairness policies

Operating rooms (ORs) are key to a hospital's profitability, and increasing their benefits helps decrease surgical costs, minimize patient waiting times, and boost the number of patients admitted for surgery. This study presents a mixed-integer linear programming (MILP) model to address the issue of treating inpatients in operating rooms waiting for admission to the referral department. Moreover, it proposes a practical algorithm that minimizes overtime costs in operating rooms and increases patient satisfaction. Our model uses an integrated machine learning - tabu search (ML-TS) method. The proposed model uses differential ML and heuristic rules to achieve enhanced performance and scalability in solving complex optimization problems. A fairness policy is implemented, combined with an optimization method, to guide patient prioritization. This approach considers factors like urgency, waiting times, or specific patient needs and helps determine the order in which patients are scheduled for surgery. The outcomes imply that patient adaptability has led to savings ranging from 50% to 65% per surgery. Additionally, the Machine Learning-Tabu Search (ML-TS) algorithm has increased performance by about 35%. These algorithms also let the OR manager define the size of the uncertainty set and regulate overtime costs while accommodating surgeons' preferences as managerial implications insight. It adeptly navigates the solution space, identifies feasible solutions, and accelerates convergence.

Novel Hybrid Crayfish Optimization Algorithm and Self-Adaptive Differential Evolution for Solving Complex Optimization Problems

Novel Hybrid Crayfish Optimization Algorithm and Self-Adaptive Differential Evolution for Solving Complex Optimization Problems

Approximate dynamic programming for liner shipping network design

AbstractThe global containerised trade heavily relies on liner shipping services, facilitating the worldwide movement of large cargo volumes along fixed routes and schedules. The profitability of shipping companies hinges on how efficiently they design their shipping network; a complex optimization problem known as the liner shipping network design problem (LSNDP). In recent years, approximate dynamic programming (ADP), also known as reinforcement learning, has emerged as a promising approach for large-scale optimisation. This paper introduces a novel Markov decision process for the LSNDP and investigates the potential of ADP. We show that ADP methods based on value iteration produce optimal solutions to small instances, but their scalability is hindered by high memory demands. An ADP method based on a deep neural network requires less memory and successfully obtains feasible solutions. The quality of solutions, however, declines for larger instances, possibly due to the discrete nature of high-dimensional state and action spaces.

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.

Per-Instance Algorithm Configuration in Homogeneous Instance Spaces: A Use Case in Reconfigurable Assembly Systems

The physical capabilities of a reconfigurable assembly system (RAS) increase the agility and responsiveness of the system in highly volatile market conditions. However, achieving optimal RAS utilization entails solving complex optimization problems effectively and efficiently. These optimizations often define homogenous sets of problem instances. While algorithm configuration in such homogeneous contexts traditionally adopts a “one-size-fits-all” approach, recent studies have shown the potential of per-instance algorithm configuration (PIAC) methods in these settings. In this work, we evaluate and compare the performance of different PIAC methods in this context, namely Hydra—a state-of-the-art PIAC method—and a simpler case-based reasoning (CBR) approach. We evaluate the impact of the tuning time budget and/or the number of unique problem instances used for training on each of the method’s performance and robustness. Our experiments show that whilst Hydra fails to improve upon the default algorithm configuration, the CBR method can lead to 16% performance increase using as few as 100 training instances. Following these findings, we evaluate Hydra’s methodology when applied to homogenous instance spaces. This analysis shows the limitations of Hydra’s inference mechanisms in these settings and showcases the advantages of distance-based approaches used in CBR.

Assisted Active Learning for Model-Based Method Development in Liquid Chromatography.

In recent decades, there has been a growing interest in fully automated methods for tackling complex optimization problems across various fields. Active learning (AL) and its variant, assisted active learning (AAL), incorporating guidance or assistance from external sources into the learning process, play key roles in this automation by enabling the autonomous selection of optimal experimental conditions to efficiently explore the problem space. These approaches are particularly valuable in situations wherein experimentation is costly or time-consuming. This study explores the application of AAL in model-based method development (MD) for liquid chromatography (LC) by using Bayesian statistics to incorporate historical data and analyte information for the generation of initial retention models. The process involves updating the model parameters based on new experiments, coupled with an active data selection method to choose the most informative experiment to run in a subsequent step. This iterative process balances model exploitation and experimental exploration until a satisfactory separation is achieved. The effectiveness of this approach is demonstrated via two practical examples, resulting in optimized separations in a limited number of experiments by optimizing the gradient slope. It is shown that the ability of AAL to leverage past knowledge and compound information to improve accuracy and reduce experimental runs offers a flexible alternative approach to fixed design methods.

Reinforcement learning-trained optimisers and Bayesian optimisation for online particle accelerator tuning

Online tuning of particle accelerators is a complex optimisation problem that continues to require manual intervention by experienced human operators. Autonomous tuning is a rapidly expanding field of research, where learning-based methods like Bayesian optimisation (BO) hold great promise in improving plant performance and reducing tuning times. At the same time, reinforcement learning (RL) is a capable method of learning intelligent controllers, and recent work shows that RL can also be used to train domain-specialised optimisers in so-called reinforcement learning-trained optimisation (RLO). In parallel efforts, both algorithms have found successful adoption in particle accelerator tuning. Here we present a comparative case study, assessing the performance of both algorithms while providing a nuanced analysis of the merits and the practical challenges involved in deploying them to real-world facilities. Our results will help practitioners choose a suitable learning-based tuning algorithm for their tuning tasks, accelerating the adoption of autonomous tuning algorithms, ultimately improving the availability of particle accelerators and pushing their operational limits.

Optimal Allocation of Water Resources Using Agro-Economic Development and Colony Optimization Algorithm

Water is an irreplaceable commodity with a high economic value. Today, water scarcity is the biggest challenge in the world, and the crises arising from lack of freshwater resources are serious threats to sustainable environmental development and human health and welfare. As the problems grow in complexity and dimensions, it becomes less possible to solve them with conventional optimization methods or explicit computational methods in a proper amount of time and with the currently limited computation memory, making it very difficult to achieve an optimal absolute solution. In this regard, metaheuristic algorithms that are generally inspired by nature are used in complex optimization problems. The Pishin Dam is an important dam in the eastern basin of Iran in the south of Sistan and Baluchestan province. This region faces severe water stress due to very low precipitation and very high evaporation on the one hand and the growing increase in urban, agricultural, and industrial demand on the other hand. The water development plans executed by the Ministry of Energy in the studied region influence water supply and demand profoundly. This research investigated the optimal allocation of water resources of this dam under management scenarios using the metaheuristic technique of the ant colony optimization algorithm (ACO). The results showed that the best value of the objective function was 82.3658 million m3. When applying the scenario of developing the cultivation area, the best value was obtained at 67.1258, which was significantly different from the base state. The results show that the ACO algorithm is suitable for the water resources of the Pishin Dam and can be used in planning and policymaking.

A rhinopithecus swarm optimization algorithm for complex optimization problem

This paper introduces a novel meta-heuristic algorithm named Rhinopithecus Swarm Optimization (RSO) to address optimization problems, particularly those involving high dimensions. The proposed algorithm is inspired by the social behaviors of different groups within the rhinopithecus swarm. RSO categorizes the swarm into mature, adolescent, and infancy individuals. Due to this division of labor, each category of individuals employs unique search methods, including vertical migration, concerted search, and mimicry. To evaluate the effectiveness of RSO, we conducted experiments using the CEC2017 test set and three constrained engineering problems. Each function in the test set was independently executed 36 times. Additionally, we used the Wilcoxon signed-rank test and the Friedman test to analyze the performance of RSO compared to eight well-known optimization algorithms: Dung Beetle Optimizer (DBO), Beluga Whale Optimization (BWO), Salp Swarm Algorithm (SSA), African Vultures Optimization Algorithm (AVOA), Whale Optimization Algorithm (WOA), Atomic Retrospective Learning Bare Bone Particle Swarm Optimization (ARBBPSO), Artificial Gorilla Troops Optimizer (GTO), and Harris Hawks Optimization (HHO). The results indicate that RSO exhibited outstanding performance on the CEC2017 test set for both 30 and 100 dimension. Moreover, RSO ranked first in both dimensions, surpassing the mean rank of the second-ranked algorithms by 7.69% and 42.85%, respectively. Across the three classical engineering design problems, RSO consistently achieves the best results. Overall, it can be concluded that RSO is particularly effective for solving high-dimensional optimization problems.

Metaheuristics-guided active learning for optimizing reaction conditions of high-performance methane conversion

Converting greenhouse gases into value-added chemical compounds has been widely studied in chemical science for sustainable industry. In particular, nonoxidative coupling of methane (NOCM) that transforms methane into useful chemical compounds has received great interests because methane is a naturally abundant greenhouse gas. NOCM has received significant attention in sustainable industry for addressing the climate crisis. However, there are complex optimization problems in maximizing the efficiency of the nonoxidative methane conversion. Although conventional data-driven methods have been successfully applied to various engineering problems, a data-driven optimization of NOCM remains a challenging problem because expensive chemical experiments should be performed to collect prior data for model training. To avoid the expensive costs of chemical experiments, we propose an active learning method that performs training data augmentation and model re-training without pre-defined unlabeled experimental data. To this end, we combine active learning with metaheuristic algorithms to perform active learning with statistically augmented data. We applied the proposed method to a high-throughput screening task to discover new reaction conditions of high-performance NOCM, and the high-throughput screening error was significantly reduced by 69.11%.

Revolutionizing optimization: An innovative nutcracker optimizer for single and multi-objective problems

Nutcracker Optimization Algorithm (NOA) is a recently proposed meta-heuristic algorithm inspired by foraging and storing behavior of nutcracker birds. NOA demonstrates strong performance across various test sets and optimization problems. However, it faces challenges in effectively balancing exploration and exploitation, particularly in high-dimensional and complex applications. In this paper, an improved variant of NOA based on Bernoulli map strategy and seasonal behavior strategy, called INOA, is proposed. Firstly, the Bernoulli map strategy enhances the quality of the initial population during the initialization process. Secondly, the seasonal behavior strategy is employed to balance the exploration and exploitation of NOA, enabling it to effectively handle high-dimensional problems by improving convergence and exploration capabilities. Additionally, this paper extends INOA to a multi-objective version called MONOA, enabling the algorithm to solve multi-objective problems.The proposed algorithm, INOA, undergoes evaluation using 30 classical benchmark problems, CEC-2014, CEC-2017, CEC-2019 test suites, and two real-world engineering design problems. INOA’s performance is compared with three categories of optimization methods: (1) recently-developed algorithms, i.e., NOA, BWO, DBO, RIME, MGO, HBA, and SO, (2) highly-cited algorithms, i.e., SMA, MPA, GWO, and (3) high-performing optimizers and winners of CEC competition, i.e., CJADE, L-SHADE-RSP, L-SHADE, and EBOwithCMAR. The proposed algorithm, MONOA, undergoes evaluation using well-known ZDT and DTLZ suites, as well as six constrained and engineering design problems. MONOA’s performance is compared with some state-of-the-art approaches such as MOPSO, NSSO, MOGOA, MOSMA, and MOMGA. Five performance indicators are employed for comparison purposes. Experimental results and comparisons affirm the efficacy of INOA in solving complex and higher-dimensional optimization problems. Similarly, the findings underscore the effectiveness of MONOA in solving diverse multi-objective problems with distinct characteristics.

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.

Neural population dynamics optimization algorithm: A novel brain-inspired meta-heuristic method

Meta-heuristic algorithms are popular for their efficiency in solving complex optimization problems. Although there are many known algorithms, identifying ways to improve their performance remains an important research area. This paper proposes a brain neuroscience-inspired meta-heuristic algorithm called the Neural Population Dynamics Optimization Algorithm (NPDOA). There are three strategies in NPDOA. (1) The attractor trending strategy drives neural populations towards optimal decisions, thereby ensuring exploitation capability. (2) The coupling disturbance strategy deviates neural populations from attractors by coupling with other neural populations, thus improving exploration ability. (3) The information projection strategy controls the communication between neural populations, enabling a transition from exploration to exploitation. The results of benchmark and practical problems verified the effectiveness of NPDOA.

Dynamic Harris hawks optimizer based on historical information and tournament strategy and its application in numerical optimization of blast furnace ingredients

Harris hawks optimizer (HHO) is a new meta-heuristic optimization algorithm, which is inspired by the cooperative behavior and chasing style of Harris hawks in nature. However, HHO can neither balance exploration and exploitation well nor fully use historical information in the face of complex optimization problems. In order to alleviate the shortcomings of HHO, a dynamic Harris hawks optimizer based on historical information and tournament strategy (DHHO-HITS) is proposed in this paper, in which a dynamic parameter is proposed to adjust the behavior of the Harris hawks in exploration and exploitation. The concept of “archive” is added to store the historical optimal solutions, and then a randomly selected historical optimal solution in the “archive” is used to guide the Harris hawk population, which improves the utilization rate of historical information and the accuracy of the solution. The tournament strategy is used to select a new generation of the population to avoid premature convergence. To verify the performance of DHHO-HITS, the CEC2020 benchmark suite is used to analyze the selection of parameters, the influence of the control parameters, the influence of three improved mechanisms, and the dynamic properties of the algorithm. Then, DHHO-HITS is compared with 20 other algorithms on multiple dimensions of the CEC2017 benchmark suite, CEC2020 benchmark suite, and CEC2021 benchmark suite. Further, the proposed DHHO-HITS is applied to three standard engineering problems. These test results show that DHHO-HITS outperforms most competitors in numerical optimization. Finally, DHHO-HITS is used to solve the numerical optimization of blast furnace ingredients. The simulation results based on actual data show that the optimized ingredient scheme can reduce the CO2 emissions of the blast furnace while meeting multiple constraints: for each ton of iron output, the CO2 emissions are reduced by 85.7177 kg, accounting for about 9.97 % of the total emissions.