Population-based Optimization Research Articles

Low-carbon diets across diverse dietary patterns: Addressing population heterogeneity under constrained optimization

Mathematical optimization is a useful tool for modeling diets that fulfill requirements for health and environmental sustainability, however, population-based optimization approaches fail to account for underlying dietary diversity in populations. This study proposes a methodological approach to consider diverse dietary intake patterns in mathematical optimization of nutritionally adequate low-carbon diets and investigates the differences between different population groups, along with trade-offs between greenhouse gas emission (GHGE) reduction and the inconvenience of dietary changes required to achieve optimized diets. A k-means clustering analysis was applied to individual dietary intake data from Denmark, which resulted in four clusters with different dietary patterns. This was followed by quadratic programming, wherein the total dietary changes required from the observed diet within each cluster were used as a proxy for consumer inconvenience (i.e., “inconvenience index”) and were minimized while fulfilling nutrient constraints and incrementally tightened GHGE constraints. Across clusters, a steep increase of the inconvenience index was observed at GHGE levels below approximately 3 kg CO2e/10 MJ, corresponding to GHGE reductions of 24–36 % in different clusters. In all clusters, the optimized diets with nutritional and GHGE constraints showed common traits of increased content of cereals and starches, eggs, and fish and decreased amounts of beef and lamb, cheese, animal-based fats, and alcoholic beverages, but differences across clusters were also observed, maintaining characteristics of the clusters' baselines. When additional health-based targets for food amounts were applied as constraints, the optimized diets converged towards the same type of diet. The total inconvenience of dietary changes required to fulfill constraints differed between clusters, indicating that specific sub-populations may be more effective targets for dietary transition. The method has potential for future integration of more sustainability aspects and different consumer preferences.

HAPI-DE: Differential evolution with hierarchical archive based mutation strategy and promising information

Differential Evolution (DE), as a population-based meta-heuristic global optimization technique, has shown excellent performance in handling optimization problems in continuous spaces. Despite its effectiveness, the DE algorithm suffers from shortcomings such as complexity of parameter selection and limitations of the mutation strategy. Therefore, this paper presents a new strategy for generating trial vectors based on a hierarchical archive, which integrates promising information during evolution with current populations to obtain a good perception of the objective landscape. Moreover, to mitigate mis-scaling by scale factor, an adaptive parameter generation mechanism with hierarchical selection (APSH) is proposed. Furthermore, a novel population diversity metric technique and a restart mechanism based on wavelet functions is introduced in this paper. Comparative experiments were conducted to evaluate the performance of the proposed algorithm using 100 benchmark functions from the CEC2013, CEC2014, CEC2017, and CEC2022 test suites. The results demonstrate that the HAPI-DE algorithm outperforms or is on par with 6 recent powerful DE variants. Additionally, HAPI-DE was utilized in parameter extraction for the photovoltaic model STP6-120/36. The findings suggest that our algorithm, HAPI-DE, demonstrates competitiveness when compared to the 6 other DE variants.

A population-based DNN-augmented optimization method for designing truss structures

Truss design problems have been extensively investigated for various purposes. How to efficiently optimize truss structures and obtain diverse optimized designs is still a challenging task. In this paper, a population-based DNN (deep neural network) -augmented method is proposed to address this issue. In the proposed method, truss design problems are firstly transformed into a DNN-based design loss minimization problem. The DNN model is gradually generated in an adaptive updating manner, and is used to indicate the truss design problem. In addition, the transformed minimization problem can be efficiently solved by DNN computation and a population of trusses can be optimized accordingly. Through the investigation of four truss design problems (two standard optimization problems and two optimization problems considering the design diversity), the effectiveness of the proposed method is validated. In addition, three aspects affecting the performance of the proposed method are also investigated, and the robustness and applicability of the proposed method are demonstrated.

Solving the Travelling Salesman Problem Using the PSO Optimization

This article examines a potential solution to the well-known Travelling Salesman Problem (TSP), which is classified as an NP-hard problem. We also provide a theoretical synopsis of several approaches that have been employed to tackle this problem. A prominent example of a combinatorial problem is the traveling salesman problem (TSP). To address the fundamental PSO algorithm's premature convergence issue and stagnation behavior on TSP, a scout characteristic-based PSO algorithm is suggested.We address Particle Swarm Optimization (PSO), a member of the evolutionary methods class, and outline the methodology for applying PSO to the TSP. Among population-based metaheuristic optimization methods, Particle Swarm Optimization (PSO) is one of the most widely used. Scientific domains such as engineering, chemistry, medicine, advanced physics, and humanities have all effectively employed PSO. Numerous theoretical and empirical results on the convergence and parameterization of PSO versions have been produced as a result of the method's extensive investigation since its introduction in 1995. Hundreds of PSO versions have been developed. It is well recognized that population size has a significant impact on the effectiveness of metaheuristics; nevertheless, no comprehensive research has been done on the appropriate selection of PSO swarm size to date.Through the application of this approach, we examine the effects of various control settings. The ideal solution and the quality of the solution are contrasted.

A gazelle optimization expedition for key term separated fractional nonlinear systems with application to electrically stimulated muscle modeling

Various real-time processes are effectively represented with a fractional nonlinear autoregressive exogenous (F-NARX) model where estimation of model parameters is considered as an essential task. In this study, a population-based gazelle optimization algorithm (GOA) inspired by the evolutionary characteristics of gazelle's is exploited for the parameter estimation of the key term-separated F-NARX system. The Grünwald-Letnikov derivative, a fractional order calculus operator is integrated to develop the F-NARX system from a conventional non-linear autoregressive system. The mean square error-based merit function is developed and the effectiveness of the GOA for the F-NARX system is analyzed in terms of speedy convergence, estimation accuracy, complexity and robustness for different noise scenarios. The extendibility of the GOA is assessed through the estimation of stiff parameters of the electrically stimulated muscle model (ESMM) required for rehabilitation of paralyzed muscles. The efficacy of the GOA is endorsed through Wilcoxon signed rank statistical test in comparison with recent counterparts of Runge Kutta optimization algorithm, Whale optimization algorithm, and Harris Hawks optimization algorithm.

From Time-Series to Hybrid Models: Advancements in Short-Term Load Forecasting Embracing Smart Grid Paradigm

This review paper is a foundational resource for power distribution and management decisions, thoroughly examining short-term load forecasting (STLF) models within power systems. The study categorizes these models into three groups: statistical approaches, intelligent-computing-based methods, and hybrid models. Performance indicators are compared, revealing the superiority of heuristic search and population-based optimization learning algorithms integrated with artificial neural networks (ANNs) for STLF. However, challenges persist in ANN models, particularly in weight initialization and susceptibility to local minima. The investigation underscores the necessity for sophisticated predictive models to enhance forecasting accuracy, advocating for the efficacy of hybrid models incorporating multiple predictive approaches. Acknowledging the changing landscape, the focus shifts to STLF in smart grids, exploring the transformative potential of advanced power networks. Smart measurement devices and storage systems are pivotal in boosting STLF accuracy, enabling more efficient energy management and resource allocation in evolving smart grid technologies. In summary, this review provides a comprehensive analysis of contemporary predictive models and suggests that ANNs and hybrid models could be the most suitable methods to attain reliable and accurate STLF. However, further research is required, including considerations of network complexity, improved training techniques, convergence rates, and highly correlated inputs to enhance STLF model performance in modern power systems.

Simulation of monthly river flow using SVR neural network improved with population-based optimization algorithms

Simulation of monthly river flow using SVR neural network improved with population-based optimization algorithms

Performance improvement of PV systems during dynamic partial shading conditions using optimization algorithms

PV power plants encounter varying levels of irradiance, temperature fluctuations, and partial shading because of the differences in sunlight conditions. Partial shading can cause an increase in the power loss, leading to a reduction in efficiency. Maximum Power Point Tracking (MPPT) is of utmost importance in the functioning of photovoltaic (PV) systems for electricity generation because it is indispensable for maximizing power extraction from PV modules, thereby increasing the overall power output. In situations where partial shading is present, the utilization of MPPT algorithms to achieve maximum power output becomes complex because of the existence of multiple distinct peak power points, each having a unique local optimum. To overcome this issue, a method is proposed that uses Darts Game Optimization (DGO), a game-based optimization process, to efficiently determine and extract the maximum power from various local optimal peaks. A population-based optimization method known as the Darts Game Optimization algorithm exists. In this approach, the optimization process begins by creating a population of random players. Then, the algorithm iteratively updates and improves the population to search for the best player or solution. In this study, the DGO algorithm was applied to the MPPT process for voltage optimization in the PV procedure. The DC-DC converter is utilized to capture the maximum available power, and the findings demonstrate that the DGO algorithm efficiently identifies the global maximum, resulting in accelerated convergence, reduced settling time, and minimized power oscillation. Through simulations, the feasibility and effectiveness of the DGO centered MPPT approach was confirmed and compared with MPPT algorithms relying on perturb and observe (P&O) and Particle Swarm Optimization (PSO). The simulation results offer compelling evidence that the DGO algorithm, as proposed in this study, proficiently traces the global maximum, thereby substantiating its practicality and efficiency.

General Multi-Objective Performance Expression for Population-Based Search and Optimization

General Multi-Objective Performance Expression for Population-Based Search and Optimization

SWOAM: Swarm optimized agents for energy management in grid-interactive connected buildings

With increasing complexity of smart city energy systems and rising energy demand, effective energy management solutions are crucial. Buildings now incorporate renewable energy sources and battery storage for efficient energy utilization, making optimal control strategies important. Compared to rule-based controllers and model-based methods, swarm and evolutionary algorithms have the advantages of providing cost-effective, stable, and scalable alternatives. However, their potential in data-rich environments and multi-building energy systems remains underexplored. This research bridges this gap by demonstrating the cooperative capabilities of population-based optimization agents for efficient energy management. Specifically, novel algorithm and framework, named Swarm Optimized Agents for Sequential Decision Making (SWOAM) is proposed. It combines an online k-means classifier and a swarm optimizer for optimal control of multi-building energy systems. By designing an online K-means learning strategy and an agent-based sequential episodic sampling approach, it is feasible to train a swarm of agents find an optimal energy management policy for buildings in a district. For training and evaluation, we use the standardized CityLearn building energy management environment. The agents are evaluated on three key metrics: electricity cost, carbon dioxide emissions and grid ramping. SWOAM delivers state-of-the-art performance and outperforms modern reinforcement learning and rule-based controllers.

Dynamic Demand Modeling Incorporating Renewable Energy Sources Using a Population-Based Optimization Method

Due to the inclusion of distributed generation (DG) in microgrids (MGs), the accelerated growth in demand, and environmental concerns, suitable management and operational strategies are imperative. The utilization of wind and solar energy has rapidly increased in MGs. However, due to the uncertainties these systems present, accurately predicting energy generation remains challenging. This necessitates modeling the system’s random variables (such as renewable resource output and possibly load demand) using appropriate and feasible methods. The primary objective of this article is to determine the optimal setpoints for renewable energy sources (RES) and all elements involved in the MG, minimizing the total operation cost. The system comprises wind turbines (WT), photovoltaic panels (PV), energy storage systems (ESS), and electric vehicles (EVs). Weibull distribution and the Hottel and Liu Jordan equations are employed to determine the potential available capacity of wind and solar energy generation, respectively. ESS is utilized to enhance MG performance. For optimal management, a comprehensive mathematical model with practical constraints for each MG element is extracted. An efficient Population-Based Incremental Learning (PBIL) metaheuristic method is proposed to solve the optimization objective in an MG, demonstrating that this energy management system optimizes and effectively coordinates DG and ESS energy generation considering economic considerations. Finally, PBIL is compared with a commonly used model, Particle Swarm Optimization (PSO), across various scenarios, analyzing and evaluating their outcomes, showcasing a reduction in operation costs.

Auto-tuning data-driven model for biogas yield prediction from anaerobic digestion of sewage sludge at the south-tehran wastewater treatment plant: Feature selection and hyperparameter population-based optimization

In this study, two data-driven models, artificial neural networks and support vector regression (SVR), have been trained and optimized to predict the biogas yield from anaerobic digesters at the South-Tehran municipal wastewater treatment plant. The auto-tuning approach, including feature selection and hyperparameter population-based optimization, was applied through the genetic algorithm (GA) and particle swarm optimization to improve the training models' performance and help them obtain the best input parameters. The Shapley Additive Explanations (SHAP) analysis was also done to interpret models effectively and assign credit for a model's prediction to each feature. The findings demonstrated that biogas prediction using SVR-GA achieved the highest accuracy, with R2 values of 0.725 and 0.773, and RMSE values (regarding normalized datasets) of 0.477 and 0.492 for the train and test, respectively, while requiring the least computational time compared to other models. The auto-tuning technique, by removing the less important inputs, was able to show that temperature, pH, effluent and influent dry solids, effluent volatile solids (VS), and influent VS of waste sludge were the best input parameters for optimal biogas production modeling. The SHAP analysis revealed that VSeff and temperature were two of the most important features affecting biogas production, exhibiting an inverse impact.

Chaotic opposition Golden Sinus Algorithm for global optimization problems

Optimization techniques are required to find the best solutions to challenging problems in many engineering disciplines. Metaheuristic algorithms that effectively increase search performance using various evolutionary strategies have become increasingly popular in recent years. The Golden Sinus Algorithm (GoldSa) is a population-based optimization algorithm that uses the sine function and the golden ratio. In this study, a chaotically enhanced opposition-based Golden Sinus Algorithm (Co-GoldSa) has been proposed to improve the efficiency of the exploitation and exploration ability of the GoldSa method. While designing this approach, it is first necessary to analyze the chaotic behavior of the GoldSa parameters. For this purpose, three chaotic GoldSa methods have been developed using eight chaotic maps to determine the effect of the chaotic maps on the parameters with different behaviors. Secondly, the opposition-based learning strategy is adjusted to the cGoldSa to enhance the searching ability. To investigate the proficiency of the proposed Co-GoldSa method, it has been examined with well-known and newly introduced metaheuristic approaches on benchmark functions and classical engineering design problems. Besides, an efficient framework of the multilevel thresholding image segmentation has been presented based on the Co-GoldSa method since the efficient processing of pathological images is quite important in medical diagnostics. The experimental outcomes reveal the superiority of the proposed method in solving global optimization problems, image segmentation, and engineering problems. Thus, the outcomes of the benchmark functions, image segmentation, and classical engineering problems support that the proposed Co-GoldSa approach can be considered a promising method for resolving challenging optimization problems.

An efficient improved exponential distribution optimizer: application to the global, engineering and combinatorial optimization problems

Population-based meta-heuristic optimization algorithms play a vital role in addressing optimization problems. Nowadays, exponential distribution optimizer (EDO) can be considered to be one of the most recent among these algorithms. Although it has achieved many promising results, it has a set of shortcomings, for example, the decelerated convergence, and provides local optima solution as it cannot escape from local regions in addition to imbalance between diversification and intensification. Therefore, in this study, an enhanced variant of EDO called mEDO was proposed to address these shortcomings by combining two efficient search mechanisms named orthogonal learning (OL) and local escaping operator (LEO). In mEDO, the LEO has been exploited to escape local optima and improve the convergence behavior of the EDO by employing random operators to maximize the search process and to effectively discover the globally optima solution. Then the OL has been combined to keep the two phases (i.e., exploration and exploitation) balanced. To validate the effectiveness and performance of the mEDO algorithm, the proposed method has been evaluated over ten functions of the IEEE CEC’2020 test suite as well as eight real-world applications (engineering design optimization problems), Furthermore we test the applicability of the proposed algorithm by tackling 21 instance of the quadratic assignment problem (QAP). The experimental and statistical results of the proposed algorithm have been compared against seven other common metaheuristic algorithms (MAs), including the basic EDO. The results show the supremacy of the mEDO algorithm over the other algorithms and reveal the applicability and effectiveness of the mEDO algorithm compared to well-established metaheuristic algorithms. The experimental results and different statistical measures revealed the reliability and applicability of the mEDO method in solving the global, engineering design, and combinatorial optimization problems by achieving a reasonable solution in terms of scoring a global optima solutions and avoiding premature convergence by increasing the population’s diversity.

Multi-objective optimization driven by preponderant individuals and symmetric sampling for operational parameter design in aluminum electrolysis process

Developing advanced population-based multi-objective optimization algorithms to explore optimal operating parameters is a crucial means of achieving energy saving and consumption reduction in aluminum electrolysis process (AEP). Many techniques, such as NSGA-II/NSGA-III, rely on dominance relationships among population members to prioritize evolving individuals. However, this mechanism assumes equal relationships among selected candidates, overlooking the potential of preponderant individuals to guide rapid population evolution. To tackle this issue, we propose a multi-objective optimization algorithm driven by preponderant individuals and symmetric sampling (MOPISS). This algorithm first establishes an individual selection strategy driven by preponderant individuals to expedite population evolution. Subsequently, it employs the count of preponderant individuals to calculate the interaction learning probability (ILP) for adaptively adjusting the genetic intensity of population. ILP is then integrated into the evolutionary process to create a novel genetic mechanism based on symmetric sampling, thereby enhancing the randomness of the solution space and genetic efficacy. Finally, MOPISS is validated across 17 benchmark functions and operational parameter optimization cases of AEP. The results indicate that the proposed method exhibits a significant competitive advantage over other mainstream approaches in terms of evolutionary speed and optimization performance. Specifically, it can increase current efficiency by approximately 3% and reduce energy consumption by 276 kW⋅h/t-Al for AEP.

Particle swarm intelligence promotes cooperation by adapting interaction radii in co-evolutionary games

Particle swarm optimization (PSO), a population-based optimization algorithm inspired by swarm behaviors, has been applied extensively to simulate social behaviors such as migration, urban planning, or resource utilization. It capitalizes on the inherent principles of social cooperation, adaptability and learning from peers to help individuals in a population search for optima. In this work, we propose a novel co-evolutionary game model in which individuals adapt their interaction radii by applying the PSO algorithm and study how the learning factor ω in the algorithm shapes the cooperation dynamics. We find that the adaptive interaction radii based on PSO could significantly enhance cooperation, especially in the scenario with strong social dilemma. By studying the snapshots of strategy pattern and the distributions of interaction radii in the population, we further reveal that the PSO-based adapting mechanism can protect cooperators by shrinking the interaction radii in a severe environment with an appropriate ω. Nevertheless, when cooperation is favorable, the adaptation leads to a relatively wide distribution of interaction radii to facilitate the spread of cooperation. The results of this work highlight the potential of the PSO algorithm to resolve social dilemmas when combined with the evolutionary dynamics.

Design of Runge-Kutta optimization for fractional input nonlinear autoregressive exogenous system identification with key-term separation

Population-based metaheuristic algorithms have gained significant attention in research community due to its effectiveness in solving complex optimization problems in diverse fields. In this study, knacks of population-based Runge-Kutta optimizer (RUN) are exploited for the identification of fractional input non-linear exogenous auto-regressive (FINARX) system with key term separation. The fractional order calculus operator of the Grünwald-Letnikov derivative is exploited to develop FINARX from a conventional non-linear auto-regressive exogenous system. The identification scheme for FINARX model is implemented through a mean-square-error-based fitness function. RUN utilizes the slope variations calculated by the well-known Runge-Kutta method for an effective search mechanism in the exploration and exploitation phases. Moreover, an enhanced solution quality mechanism is employed for speedy convergence and keeping the movement toward the best solution by escaping the local optima. The robustness of the algorithm is analyzed by multiple variations of non-linearity as well as different noise scenarios. The performance of the RUN to identify the FINARX system is validated in terms of convergence rate, fitness value, robustness, and accuracy in weight estimation. The effectiveness of the RUN is further assessed through exhaustive simulations with their statistics as well as comparison with the standard recent counterparts, including the Whale optimization algorithm, Reptile Search algorithm, and Aquila optimizer on different performance indices for the FINARX system.

SHuffled Ant Lion Optimization approach with an exponentially weighted random walk strategy

Ant Lion Optimization (ALO) method is one of the population-based nature-inspired optimization algorithms which mimics the hunting strategy of antlions. ALO is successfully employed for solving many complicated optimization problems. However, it is reported in the literature that the original ALO has some limitations such as the requirement of high number of iterations and possibility of trapping to local optimum solutions, especially for complex or large-scale problems. For this purpose, the SHuffled Ant Lion Optimization (SHALO) approach is proposed by conducting two improvements in the original ALO. Performance of the proposed SHALO approach is evaluated by solving some unconstrained and constrained problems for different conditions. Furthermore, the identified results are statistically compared with the ones obtained by using the original ALO, two improved ALOs which are the self-adaptive ALO (saALO) and the exponentially weighted ALO (EALO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) approaches. Identified results indicated that the proposed SHALO approach significantly improves the solution accuracy with a mean success rate of 76% in terms of finding the global or near-global optimum solutions and provides better results than ALO (22%), saALO (25%), EALO (14%), GA (28%), and PSO (49%) approaches for the same conditions.

High Aspect Ratio Composite Wings: Geometrically Nonlinear Aeroelasticity, Multi-Disciplinary Design Optimization, Manufacturing, and Experimental Testing

In the field of aerospace engineering, the design and manufacturing of high aspect ratio composite wings has become a focal point of innovation and efficiency. These long, slender wings, constructed with advanced materials such as carbon fiber and employing efficient manufacturing methods such as vacuum bagging, hold the promise of significantly lighter aircraft, reduced fuel consumption, and enhanced overall performance. However, to fully realize these benefits, it is imperative to address a multitude of structural and aeroelastic constraints. This research presents a novel aeroelastically tailored Multi-objective, Multi-disciplinary Design Optimization (MMDO) approach that seamlessly integrates numerical optimization techniques to minimize weight and ensure structural integrity. The optimized wing configuration is then manufactured, and a Ground Vibration Test (GVT) and static deflection analysis using the Digital Image Correlation (DIC) system are used to validate and correlate with the numerical model. Within the fully automated in-house Nonlinear Aeroelastic Simulation Software (NAS2) package (version v1.0), the integration of analytical tools offers a robust numerical approach for enhancing aeroelastic and structural performance in the design of composite wings. Nonlinear aeroelastic analyses and tailoring are included, and a population-based stochastic optimization is used to determine the optimum design within NAS2. These analytical tools contribute to a comprehensive and efficient methodology for designing composite wings with improved aeroelastic and structural characteristics. This comprehensive methodology aims to produce composite wings that not only meet rigorous safety and performance standards but also drive cost-efficiency in the aerospace industry. Through this multidisciplinary approach, the authors seek to underscore the pivotal role of tailoring aeroelastic solutions in the advanced design and manufacturing of high aspect ratio composite wings, thereby contributing to the continued evolution of aerospace technology.

Structural damage identification with output-only strain measurements and swarm intelligence algorithms: a comparative study

The identification of structural damage with the unavailability of input excitations is highly desired but challenging since structural dynamic responses are affected by the coupling effect of structural parameters and external excitations. To deal with this issue, in this paper, an output-only damage identification strategy based on swarm intelligence algorithms and correlation functions of strain responses is proposed to identify structures subjected to single or multiple unknown white noise excitations. In the proposed strategy, four different population-based optimization algorithms—particle swarm optimization, the butterfly optimization algorithm, the tree seed algorithm, and a micro search Jaya (MS-Jaya)—are employed and compared. The micro search mechanism is integrated into a basic Jaya algorithm to improve its computational efficiency and accuracy by eliminating some damage variables with small values for the identified best solution after several iterations. The objective function is established based on the proposed auto/cross-correlation function of strain responses and a penalty function. The effectiveness of the proposed method is verified with numerical studies on a simply supported beam structure and a steel grid benchmark structure under ambient excitation. In addition, the effect of the reference point, number of sensors, and arrangement of strain gauges on the performance of the proposed method are discussed in detail. The investigated results demonstrate that the proposed approach can accurately detect, locate, and quantify structural damage with limited sensors and 20% noise-polluted strain responses. In particular, the proposed MS-Jaya algorithm presents a more superior capacity in solving the optimization-based damage identification problem than the other three algorithms.