Large-scale Optimization Problems Research Articles

An enhanced competitive swarm optimizer with strongly robust sparse operator for large-scale sparse multi-objective optimization problem

In the real world, the decision variables of large-scale sparse multi-objective problems are high-dimensional, and most Pareto optimal solutions are sparse. The balance of the algorithms is difficult to control, so it is challenging to deal with such problems in general. Therefore, An Enhanced Competitive Swarm Optimizer with Strongly Robust Sparse Operator (SR-ECSO) algorithm is proposed. Firstly, the strongly robust sparse functions which accelerate particles in the population better sparsity in decision space, are used in high-dimensional decision variables. Secondly, the diversity of sparse solutions is maintained, and the convergence balance of the algorithm is enhanced by the introduction of an adaptive random perturbation operator. Finally, the state of the particles is updated using a swarm optimizer to improve population competitiveness. To verify the proposed algorithm, we tested eight large-scale sparse benchmark problems, and the decision variables were set in three groups with 100, 500, and 1000 as examples. Experimental results show that the algorithm is promising for solving large-scale sparse optimization problems.

High-efficient sample point transform algorithm for large-scale complex optimization

Decomposition algorithms and surrogate model methods are frequently employed to address large-scale, intricate optimization challenges. However, the iterative resolution phase inherent to decomposition algorithms can potentially alter the background vector, leading to the repetitive evaluation of samples across disparate iteration cycles. This phenomenon significantly diminishes the computational efficiency of optimization. Accordingly, a novel approach, designated the Sample Point Transformation Algorithm (SPTA), is put forth in this paper as a means of enhancing efficiency through a process of mathematical deduction. The mathematical deduction reveals that the difference between sample points in each iteration loop is a simple function related to the inter-group dependent variables. Consequently, the SPTA method achieves the comprehensive transformation of the sample set by establishing a surrogate model of the difference between the sample sets of two cycles with a limited number of sample points, as opposed to conducting a substantial number of repeated samplings. This SPTA is employed to substitute the most time-consuming step of direct calculation in the classical optimization process. To validate the calculation efficiency, a series of numerical examples were conducted, demonstrating an improvement of approximately 75 % while maintaining optimal accuracy. This illustrates the advantage of the SPTA in addressing large-scale and complex optimization problems.

A population hierarchical-based evolutionary algorithm for large-scale many-objective optimization

In large-scale many-objective optimization problems (LMaOPs), the performance of algorithms faces significant challenges as the number of objective functions and decision variables increases. The main challenges in addressing this type of problem are as follows: the large number of decision variables creates an enormous decision space that needs to be explored, leading to slow convergence; and the high-dimensional objective space presents difficulties in selecting dominant individuals within the population. To address this issue, this paper introduces an evolutionary algorithm based on population hierarchy to address LMaOPs. The algorithm employs different strategies for offspring generation at various population levels. Initially, the population is categorized into three levels by fitness value: poorly performing solutions with higher fitness (Ph), better solutions with lower fitness (Pl), and excellent individuals stored in the archive set (Pa). Subsequently, a hierarchical knowledge integration strategy (HKI) guides the evolution of individuals at different levels. Individuals in Pl generate offspring by integrating differential knowledge from Pa and Ph, while individuals in Ph generate offspring by learning prior knowledge from Pa. Finally, using a cluster-based environment selection strategy balances population diversity and convergence. Extensive experiments on LMaOPs with up to 10 objectives and 5000 decision variables validate the algorithm’s effectiveness, demonstrating superior performance.

Optimization of distributed energy resources planning and battery energy storage management via large-scale multi-objective evolutionary algorithm

This paper investigates the synergistic integration of renewable energy sources and battery energy storage systems to enhance the sustainability, reliability, and flexibility of modern power systems. Addressing a critical gap in distribution networks, particularly regarding the variability of renewable energy, the study aims to minimize energy costs, emission rates, and reliability indices by optimizing the placement and sizing of wind and solar photovoltaic generators alongside battery energy storage systems. An improved large-scale multi-objective evolutionary algorithm with a bi-directional sampling strategy is employed.Two scenarios are considered. In the first scenario, six study cases are analyzed to determine the optimal number, location, and size of distributed generators at peak load demand. The proposed algorithm outperforms existing state-of-the-art methods for small-scale distributed resource allocation. In the second scenario, a multi-period load demand across various seasons is evaluated, introducing new opportunities for battery energy storage systems. The problem is modeled with intertemporal constraints, creating a large-scale optimization challenge. Results demonstrate significant improvements: cost savings of up to 51.67 %, power reductions of up to 76.78 %, and a 99.9 % improvement in voltage deviation. Emission rates decreased by 99.92 % in case 1, 95.19 % in case 2, and 97.38 % in case 3, compared to the base case. The proposed algorithm shows superior convergence and performance in solving both small- and large-scale optimization problems, outperforming recent multi-objective evolutionary algorithms.This study provides a robust framework for optimizing renewable energy integration and battery energy storage, offering a scalable solution to modern power system challenges.

A Quasi-Newton Subspace Trust Region Algorithm for Nonmonotone Variational Inequalities in Adversarial Learning over Box Constraints

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth equations. In this paper, we propose a quasi-Newton subspace trust region (QNSTR) algorithm for the least squares problems defined by the smoothing approximation of nonsmooth equations. Based on the structure of the nonmonotone VI, we use an adaptive quasi-Newton formula to approximate the Hessian matrix and solve a low-dimensional strongly convex quadratic program with ellipse constraints in a subspace at each step of the QNSTR algorithm efficiently. We prove the global convergence of the QNSTR algorithm to an ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon $$\\end{document}-first-order stationary point of the min-max optimization problem. Moreover, we present numerical results based on the QNSTR algorithm with different subspaces for a mixed generative adversarial networks in eye image segmentation using real data to show the efficiency and effectiveness of the QNSTR algorithm for solving large-scale min-max optimization problems.

A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems

Conjugate gradient methods are widely used and attractive for large-scale unconstrained smooth optimization problems, with simple computation, low memory requirements, and interesting theoretical information on the features of curvature. Based on the strongly convergent property of the Dai–Yuan method and attractive numerical performance of the Hestenes–Stiefel method, a new hybrid descent conjugate gradient method is proposed in this paper. The proposed method satisfies the sufficient descent property independent of the accuracy of the line search strategies. Under the standard conditions, the trust region property and the global convergence are established, respectively. Numerical results of 61 problems with 9 large-scale dimensions and 46 ill-conditioned matrix problems reveal that the proposed method is more effective, robust, and reliable than the other methods. Additionally, the hybrid method also demonstrates reliable results for some image restoration problems.

A one-time training machine learning method for general structural topology optimization

Machine learning (ML) methods have found some applications in structural topology optimization. In the existing methods, however, the ML models need to be retrained when the design domains and supporting conditions have been changed, posing a limitation to their wide applications. In this paper, we propose a one-time training ML (OTML) method for general topology optimization, where the self-attention convolutional long short-term memory (SaConvLSTM) model is introduced to update the design variables. An extension–division approach is used to enrich the training sets. By developing a splicing strategy, the training results of a small design space (i.e., a basic cell of either two- or three-dimensions) can be extended to tackling the optimization problem of a large design domain with arbitrary geometric shapes. Using the OTML method, the ML model needs to be trained for only one time, and the trained model can be used directly to solve various optimization problems with arbitrary shapes of design domains, loads, and boundary conditions. In the SaConvLSTM model, the material volume of the post-processed thresholded designs can be precisely controlled, though the control precision of the gray-scale designs might be slightly sacrificed. The effects of model parameters on the computational cost and the result quality are examined. Four examples are provided to demonstrate the high performance of this structural design method. For large-scale optimization problems, the present method can accelerate the structural form-finding process. This study holds a promise in the high-resolution structural form-finding and transdisciplinary computational morphogenesis.

Shakedown analysis of incompressible materials under cyclic loads: A locking-free CS-FEM-Q5 numerical approach

Volumetric locking may occur in plastic analysis of incompressible materials using low-order finite elements due to incompressibility constraints. This study presents a locking-free smoothed five-node quadrilateral element-based approach for plastic analysis in structural engineering. The proposed Q5-element employing four cell-based smoothing domains effectively alleviates the volumetric locking issues, here in the problems under plane strain conditions. The resulting large-scale optimization problem is formulated in a conic programming form, enabling efficient use of the interior-point optimizer. Numerical investigations demonstrate the method’s effectiveness in alleviating volumetric locking, accurately predicting collapse and shakedown limits, and generating interaction diagrams for load-carrying capacity and structural collapse mechanisms.

Reducing Overall Active Power Loss by Placing Solar and Wind Generators in a Distribution Power System using Wild Horse Optimizer Algorithm

This study optimized the locations and sizes of wind-based distributed generators (WDGs) and solar photovoltaic-based distributed generators (PVDGs) to reduce the overall active power loss (OAPL) of an IEEE 85-bus distribution power system (DPS). Three meta-heuristic algorithms, including the Wild Horse Optimizer Algorithm (WHOA), the Archimedes Optimization Algorithm (AOA), and the Transient Search Optimization (TSO) algorithm, were applied and compared to each other to identify the most effective method for finding the best value of OAPL. Based on the analysis, WHOA outperformed the other methods in achieving the best value of OAPL according to different criteria. Additionally, the effectiveness of WHOA was compared with previous studies, while WHOA also proved its strength in reducing overall losses, decreasing grid power, and improving voltage profiles. Moreover, the effectiveness of WHOA was tested for a 24-hour period with varying loads and the addition of PVDGs and WDGs. The results indicated that WHOA could successfully determine the optimal positions of both PVDGs and WDGs in Case 3, Case 4.1, and Case 4.2, achieving the optimal value of OAPL in the selected DPS, decreasing grid power utilization, and improving the voltage profile. In conclusion, WHOA proved itself to be an effective optimization tool for dealing with large-scale optimization problems

Competitive swarm optimizer with dynamic multi-competitions and convergence accelerator for large-scale optimization problems

Large-scale optimizations (LSOPs) with high dimensional decision variables have become one of the most challenging problems in engineering optimization. High dimensional information causes serious interference to the algorithm optimization performance. The optimization performance of the algorithms will be seriously degraded. Competitive swarm optimizer (CSO) is a robust algorithm to tackle LSOPs. However, CSO randomly selects two particles to compare, then generates the winner and the loser. Although this search mechanism can enhance the diversity of the swarm, a single comparison is difficult to guarantee the quality of winners and losers. Therefore, there exists a risk of producing unqualified solutions. In order to enhance the quality of solution, a novel CSO with dynamic multi-competitions and convergence accelerator, namely DMCACSO, is designed in this paper. In the DMCACSO, a dynamic multi-competitions based evolutionary information is designed to pick out the losers more efficiently and improve the quality of winners. In addition, a convergence accelerator with hybrid evolutionary strategy is developed to speed up the particle search when the algorithm is a state of stagnation. The experiment results in solving large-scale benchmark functions from CEC2010 and CEC2013 indicate that the DMCACSO has competitive optimization performance by comparing with some state-of-the-art algorithms. Finally, the DMCACSO is effective in terms of quality in solving an actual feature selection problem.

Large-scale 3D multiphysics topology optimization of flow–heat–structural models including an islands constraint

This article demonstrates a large-scale 3D topology optimization problem formulation for components in need of internal cooling owing to surrounding hot gas flow. A conjugate heat transfer model is used and the goal of the optimization problem is to maximize the thermal performance subject to a coolant consumption limit. As a model problem, the interior design of a gas turbine guide-vane-like geometry is considered. High-quality finite element meshes are generated automatically by means of a voxelization method. A structural compliance constraint for thermo-mechanical loads, and a constraint for the suppression of free-floating structural parts, are included in the problem formulation. For the latter, an analytical expression for the constraint limit is derived. Several numerical examples indicate that the proposed problem formulation is able to generate interesting conceptual designs for interior-vane-cooling solutions.

Optimal Deployment of Container Weighing Equipment: Models and Properties

Container weighing is crucial to the safety of the shipping system and has garnered significant attention in the maritime industry. This research develops a container weighing optimization model and validates several propositions derived from this model. Then, a case study is conducted on ports along the Yangtze River, and the sensitivity analysis of the model is provided. We report the following findings. First, the model can be solved efficiently for large-scale optimization problems. Second, as the number of weighing machines increases, the container weighing mode changes—from selectively weighing containers at their origin ports, then weighing containers at their transshipment ports or destination ports, to all of the containers weighed at their origin ports. Third, in order to improve the safety benefits of weighing containers, port authorities can increase the weighing capacity of weighing machines. The research provides theoretical guidance for shipping system managers to design container weighing plans that enhance maritime safety.

Optimal Launch Manifesting for Space Freight Forwarders

This paper proposes a novel framework to optimize a launch vehicle manifesting plan for small satellites from the perspective of a space freight forwarder. The forwarder in space logistics coordinates individual shipment orders from the launch customers and launch service providers like a freight forwarder in ground logistics does. An optimal launch manifesting problem is formulated as a variant of the vehicle routing problem involving the decisions on carriers, launch strategies (dedicated or multi-payload), launch dates, and satellite deployment sequences. A solution procedure based on the column generation method is proposed to address the challenges associated with the large-scale combinatorial optimization problem. A case study demonstrates the effectiveness of the proposed framework and solution procedure.

Energy management in a grid-connected microgrid using hybrid Golden Jackal optimization and gradient descent optimization and the concept of loadability

Golden Jackal optimization (GJO) maintains diversity and can simultaneously explore multiple regions of the search space since it operates on a population of solutions. However, the GJO has the demerit of deprived exploitation capability and it struck in local optima easily. For enhanced optimization efficacy, the suggested approach integrates a hybrid optimization algorithm that combines gradient descent and the GJO algorithm. The goal of this hybrid strategy is to influence the complimentary advantages of both algorithms: the local exploitation potential of gradient descent and the global exploration capabilities of GJO. The suggested hybrid method uses GJO to initialize a population of possible results. Then, iteratively exploring the search space, it notifies solutions based on GJO's mechanisms for exploration and exploitation. Furthermore, a portion of the population undergoes refinement using gradient descent in order to effectively converge towards local minima by utilizing local knowledge. The hybrid algorithm demonstrates improved convergence speed, robustness to diverse search space characteristics, and effectiveness in handling large-scale optimization problems compared to various optimization techniques including particle swarm optimization, pelican optimization, artificial bee colony, whale optimization algorithm and grey wolf optimization, standalone GJO and gradient descent algorithms. The total cost of the MG with the proposed methodology has reduced to 12017 rupees from 12350 by gradient descent and 12332 using GJO. Detailed comparison of various optimization techniques has been presented in the results section. Further, this paper also addressed the concept of loadability, which refers to the MG's ability to meet electricity demand under varying conditions, relying solely on its internal resources. Achieving optimal loadability in isolated MGs involves diversifying generation sources, leveraging energy storage systems, implementing demand-side management measures, utilizing predictive analytics, and designing resilient grid infrastructure. By implementing Bayesian sparse polynomial chaos expansion, the concept of loadability has been assessed. Due to which the MG operators can enhance energy management capabilities and maximize loadability, ensuring reliable and sustainable electricity supply to connected loads.

Data-driven robust optimisation of hydrogen infrastructure planning under demand uncertainty using a hybrid decomposition method

In the race towards “Net-zero”, hydrogen has emerged as one of the key alternatives to carbon-based fossil fuels for a sustainable decarbonisation. This work studies the spatially explicit multi-period hydrogen infrastructure planning under demand uncertainty that contributes to the heat decarbonisation in Great Britain. Demand uncertainty surrounding future hydrogen supply chains poses challenges to cost optimisation and system security, so uncertainty-resilient policies are required to ensure robust operations. In this work, we employ data-driven robust optimisation to develop a framework for uncertainty-aware representative days explicitly characterised by polyhedral uncertainty sets. The proposed framework is applied on a multi-period mixed-integer linear model with dual temporal resolution which aims to determine the optimal yearly investment decisions and hourly operational decisions for the hydrogen infrastructure planning under demand uncertainty. To efficiently solve the large-scale two-stage adaptive robust optimisation problem, a hybrid decomposition algorithm is developed based on a two-step hierarchical procedure and the column-and-constraint generation method, which can significantly reduce the computational complexity. The optimisation results highlight how uncertainty can result in the total cost increase, and verify the advantages on controlling solution conservatism in the adaptive robust optimisation compared to the static robust optimisation.

EvolutionViT: Multi-objective evolutionary vision transformer pruning under resource constraints

Vision Transformer (ViT) has emerged as a pivotal model for a variety of visual tasks, surpassing convolutional neural networks by a substantial margin. However, the performance of ViT is seriously impaired by intensive computational and storage costs requirements, posing significant barriers for real-world applications or deployment on resource-constrained edge devices. To address this limitation, compressing the ViT to accelerate its inference at no appreciable degradation of vision performance has attracted widespread attention. Although there are some studies on accelerating ViT, they seldom consider resource constraints and multi-criteria decision making in the process. This article formulates ViT pruning as a large-scale constrained multi-objective optimization problem, and proposes a patch pruning framework for accelerating ViT, called EvolutionViT, based on the developed multi-objective optimization model. EvolutionViT can effectively tradeoff between computational cost and performance under resource constraints, automatically searching for solutions while optimizing two conflicting objectives. In particular, exploiting the knee solution and boundary solutions to directly guide the entire evolutionary process, EvolutionViT can efficiently identify a knee solution that satisfies the resource constraints, which in turn avoids the manual search for a good trade-off. To verify and evaluate our proposed method, we compare EvolutionViT with a number of representative ViT models on the ImageNet dataset. The comprehensive simulation results show that the proposed EvolutionViT demonstrates a competitive advantage compared to peers, with significantly reduced computational expense at the cost of slightly degraded performance.

Development and Sensitivity Analysis of an Improved Harmony Search Algorithm with a Multiple Memory Structure for Large-Scale Optimization Problems in Water Distribution Networks

The continuous supply of drinking water for human life is essential to ensure the sustainability of cities, society, and the environment. At a time when water scarcity is worsening due to climate change, the construction of an optimized water supply infrastructure is necessary. In this study, an improved version of the Harmony Search Algorithm (HSA), named the Maisonette-type Harmony Search Algorithm (MTHSA), was developed. Unlike the HSA, the MTHSA has a two-floor structure, which increases the optimizing efficiency by employing multiple explorations on the first floor and additional exploitations of excellent solutions. Parallel explorations enhance the ability in terms of exploration (global search), which is the tendency to uniformly explore the entire search space. Additional exploitations among excellent solutions also enhance the ability of local searches (effective exploitation), which is the intensive exploration of solutions that seem to have high possibilities. Following the development of the improved algorithm, it was applied to water distribution networks in order to verify its efficiency, and the numerical results were analyzed. Through the considered applications, the improved algorithm is shown to be highly efficient when applied to large-scale optimization problems with large numbers of decision variables, as shown in comparison with the considered optimizers.

Random Contrastive Interaction for Particle Swarm Optimization in High-Dimensional Environment

In high dimensional environment, the interaction among particles significantly affects their movements in searching the vast solution space and thus plays a vital role in assisting particle swarm optimization (PSO) to attain good performance. To this end, this paper designs a random contrastive interaction (RCI) strategy for PSO, resulting in RCI-PSO, to tackle large-scale optimization problems (LSOPs) effectively and efficiently. Unlike existing interaction mechanisms for low-dimensional problems, RCI randomly chooses several different peers from the current swarm to construct a random interaction topology for each particle. Then, it lets the particle interact with the selected peers based on their current evolutionary information instead of their historical evolutionary information. Within the topology, RCI only propagates the evolutionary information of two contrastive dominators with the largest difference in fitness to direct the evolution of the particle. Therefore, particles with no more than two dominators in their topologies are not updated. Furthermore, a dynamic topology size adjustment scheme is devised to gradually enlarge the interaction topology. In this way, the swarm gradually switches from exploring the immense search space dispersedly to exploiting the found optimal regions intensively as the evolution continues. With these two strategies, RCI-PSO expectedly compromises search diversity and search convergence well at the swarm level and the particle level. At last, extensive experiments executed on two public LSOP suites verify that RCI-PSO performs competitively with or even much better than totally 40 state-of-theart large-scale approaches and preserves a good capability and scalability in tackling complex LSOPs.

Distributed sparsity constrained optimization over the Stiefel manifold

Distributed optimization aims to effectively complete specified tasks through cooperation among multi-agent systems, which has achieved great success in large-scale optimization problems. However, it remains a challenging task to develop an effective distributed algorithm with theoretical guarantees, especially when dealing with nonconvex constraints. More importantly, high-dimensional data often exhibits inherent structures such as sparsity, which if exploited accurately, can significantly enhance the capture of its intrinsic characteristics. In this paper, we introduce a novel distributed sparsity constrained optimization framework over the Stiefel manifold, abbreviated as DREAM. DREAM innovatively integrates the ℓ2,0-norm constraint and Stiefel manifold constraint within a distributed optimization setting, which has not been investigated in existing literature. Unlike the existing distributed methods, the proposed DREAM not only can extract the similarity information among samples, but also more flexibly determine the number of features to be extracted. Then, we develop an efficient Newton augmented Lagrangian-based algorithm. In theory, we delve into the relationship between the minimizer, the Karush–Kuhn–Tucker point, and the stationary point, and rigorously demonstrate that the sequence generated by our algorithm converges to a stationary point. Extensive numerical experiments verify its superiority over state-of-the-art distributed methods.

A fluid–particle decomposition approach to matching market design for crowdsourced delivery systems

This paper considers a crowdsourced delivery (CSD) system that effectively utilizes the existing trips to fulfill parcel delivery as a matching problem between CSD drivers and delivery tasks. This matching problem has two major challenges. First, it is a large-scale combinatorial optimization problem that is hard to solve in a reasonable computational time. Second, the evaluation of the objective function for socially optimal matching contains the utility of drivers for performing the tasks, which is generally unobservable private information. To address these challenges, this paper proposes a hierarchical distribution mechanism of CSD tasks that decomposes the matching problem into the task partition (master problem) and individual task-driver matching within smaller groups of drivers (sub-problems). We incorporate an auction mechanism with truth-telling and efficiency into the sub-problems so that the drivers’ perceived utilities are revealed through their bids. Furthermore, we formulate the master problem as a fluid model based on continuously approximated decision variables. By exploiting the random utility framework, we analytically represent the objective function of the problem using continuous variables, without explicitly knowing the drivers’ utilities. The numerical experiment shows that the proposed approach solved large-scale matching problems at least 100 times faster than a naive LP solver and approximated the original objective value with errors of less than 1%. The code of this work is available at https://github.com/yuki-oyama/fluid-particle-csd.