Optimization Problem Research Articles

ABSTRACT Large‐scale multi‐objective optimization problems (LSMOPs) are characterised by concurrent optimization of multiple conflicting objectives and no fewer than 100 decision variables. They widely exist in the fields of practical engineering and scientific research. Over the past decade, many large‐scale multi‐objective evolutionary algorithms (LSMOEAs) have emerged to address LSMOPs. This paper systematically reviews and comprehensively analyzes the ideas, advantages, disadvantages, and latest developments of these LSMOEAs. Firstly, it introduces the relevant concepts of LSMOEAs. Then classify them into four categories: decision variable grouping‐based LSMOEAs, non‐grouping dimensionality reduction‐based LSMOEAs, effective offspring generation‐based LSMOEAs, and learning models‐based LSMOEAs. It analyzes representative algorithms in each category, elaborating on their core strategies, advantages, and disadvantages. Finally, it explores the applications of LSMOEAs in computer vision, like tackling pixel‐level correlation, high‐resolution feature redundancy, dynamic target tracking, and complex visual modelling. This paper provides readers with a comprehensive and systematic overview of LSMOEAs, serving as a valuable reference for both researchers entering this field and practitioners seeking to select appropriate algorithms for practical problems.

Energy minimization in charged polymer-multi-biomolecule electrolyte solution systems faces major challenges, where the energy landscape is typically highly nonconvex, ill-conditioned, and dominated by long-range electrostatic interactions. In such settings, standard nonlinear conjugate gradient (NCG) methods often struggle to maintain sufficient descent directions due to unstable conjugate gradient parameters caused by poor curvature information and frequent oscillations in gradient directions. To address this, we develop an enhanced NCG algorithm, termed the ELS (short for Enlong Shang) method, which introduces a modified conjugate gradient coefficient βkELS with a tunable denominator parameter ω, enabling improved stability in regions with poor local curvature. In addition, existing studies have shown that the convergence analysis of current NCG methods usually relies on the pre-setting of the parameter σ, whose theoretical bounds are difficult to adapt to the complex demands of high-dimensional nonconvex optimization problems. Hence, a novel convergence proof technique is proposed to show that the ELS method satisfies the sufficient descent condition for a broad range of line search parameters σ ∈ (0, 1), while still ensuring global convergence under nonconvex objectives. For traditional unconstrained optimization problems, the numerical performance of the ELS method outperforms the existing representative NCG methods. We apply it to the energy minimization phase in complex biomolecular simulations. Compared to direct dynamics simulation without preprocessing, implementing this minimization saves about 60% of the total time required to reach dynamic equilibrium, even exceeding the mainstream staged minimization strategy in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Importantly, the final conformation closely matches that of the purely dynamics simulation thermodynamically and has an acceptable energy deviation.

Abstract Structural sparse representation (SSR) prior and quantization constraint (QC) prior have recently been successfully employed to overcome problems associated with block discrete cosine transform (BDCT) based image compression. By formulating the image de-blocking exercise as a maximum posteriori-based optimization problem, the image artifacts can be adequately reduced. However, the success of this approach depends on a Gaussian based quantization noise model which relies on empirically tuned parameters that may not be optimal for a wide variety of images and for images chosen from other genres e.g. medical images. The present work proposes to optimize the performance of SSR and QC prior based image de-blocking algorithm by utilizing metaheuristic optimization to optimize the quantization noise model. Grey wolf optimization (GWO) and improved Grey wolf optimization (IGWO) algorithms have been suitably utilized here to solve this new problem and extensive experiments carried out for medical images firmly establish the utility of our proposed algorithms over the state-of-the-art available.

Reconstructing a high-resolution image of observed radio sources from the incomplete visibilities poses a challenging, ill-posed, inverse problem. Although compressive sensing has demonstrated remarkable performance in radio interferometric imaging, traditional compressed sensing methods approximately replace the L_0-norm minimisation problem with the L_1-norm minimisation problem, which brings about a bias issue. To ameliorate the bias problem and efficiently obtain an accurate solution in radio interferometry, we propose a novel, non-convex sparse regularisation method based on smoothly clipped absolute deviation (SCAD) in this paper. The proposed method utilises the continuous SCAD penalty function to approximate the L_0 norm and efficiently solves the non-convex optimisation problem by using an improved proximal gradient algorithm. The improved proximal gradient algorithm introduces a restart strategy and an adaptive non-monotonic step-size strategy to improve the convergence speed of the algorithm. Moreover, the regularisation parameter was adaptively updated using the prior information of the image. Numerical simulation experiments are carried out on the Very Large Array (VLA) and Square Kilometre Array (SKA). We compare the proposed method with state-of-the-art imaging methods. The results show that it performs better in terms of reconstruction quality and computational efficiency.

In pursuit of economic diversification and sustainable development, the Sultanate of Oman has strategically leveraged Mega Sporting Events (MSEs), guided by the national framework of Oman Vision 2040. However, the tangible sustainability outcomes of these events have been inconsistent. This study empirically analyzes the alignment of MSEs with Oman's tripartite sustainability goals—economic, social, and environmental—and proposes an optimized strategic framework. A descriptive-analytical methodology was employed, with data collected via a structured questionnaire (N=509) distributed in North Al Batinah Governorate. Regression analysis revealed a strong positive economic impact (β=0.72, R²=0.65) and a moderate social cohesion benefit (β=0.68, R²=0.59). Conversely, significant environmental shortcomings were identified, with only 42% of facilities meeting basic sustainability standards. The study conceptualizes the strategic hosting of MSEs as an optimization problem, aiming to balance economic efficiency with equitable social and environmental outcomes. We propose an integrated strategic model to maximize the sustainable developmental impact of future MSEs, offering practical insights for Omani policymakers and international sport event organizers.

The explosive growth of internet of everything (IoE) devices and the increasing demand for ultra-reliable, high-capacity wireless connectivity pose significant challenges to next-generation networks. Flying base stations (FBSs) make a significant contribution to the physical layer of vehicular communication by improving connectivity among different transportation systems. However, the mobility of FBSs and the IoE devices frequently disrupt communication links, impairing the performance of wireless communication. This issue can be addressed through strategic FBS positioning. In this paper, we propose a transmission structure based on multi-FBS with non-orthogonal multiple access (NOMA) in downlink 6G networks, where NOMA is employed at each FBS to provide services for IoE devices. Our objective is to maximize the total sum rate (TSR) by minimizing the inter/intra-cluster interference. To this end, the three-dimensional (3D) positions of the FBS are optimized in such a way that the FBS consistently remains at the center of the IoE devices' locations even when their locations change within the network. The optimization problem is non-convex optimization problem due to the optimization of FBSs' 3D positions. To address this issue, a genetic algorithm-based evolutionary algorithm is developed. Moreover, a perfect successive interference cancellation (SIC) strategy is introduced to address NOMA-SIC among IoE devices. The simulation results state that our proposed algorithm outperforms the other state-of-the-art in terms of TSR, achieving up to 21.03% higher TSR compared to Annealing, block coordinate descent, modified gray wolf optimization, and the center-of-cluster approach, thus demonstrating the advantages of optimizing the 3D positions of FBSs in this manner.

The Weibull distribution is widely used in reliability estimation across industries, but accurately identifying its parameters remains a challenging task. This research proposes an efficient method for estimating Weibull distribution parameters by combining the maximum likelihood method with optimization theory. First, the parameter estimation problem is formulated as an optimization problem. A constrained search space partitioning framework is introduced, leveraging parameter-specific minimum and maximum bounds for the shape, location, and scale parameters. By dividing the search space into smaller subspaces for each parameter, the method constrains the search direction, significantly reducing estimation time. To address the local optima problem common in heuristic algorithms, a randomness operator is integrated into the optimization process. The proposed constrained search space partitioning framework is implemented using a conventional g-best version of the particle swarm optimization algorithm with historical fault data. Experimental results demonstrate that the proposed scheme outperforms state-of-the-art methods and conventional optimization-based approaches in terms of estimation accuracy and computational efficiency.

Abstract In the class of hidden semi-Markov models with non-parametric sojourn-time distribution, we present a framework that penalises the latter with respect to its departure from a parametric base kernel. The penalised approach explicitly bridges parametric and non-parametric assumptions for the sojourn-time distributions, also in terms of the effective number of parameters. Inference is obtained via an expectation–maximisation algorithm. For Ridge-type penalties, we reduce the M step to a univariate optimisation problem, thereby greatly improving the computational burden. The penalty parameter is chosen using a computationally efficient Akaike-type information criterion. We illustrate our method with a simulation study, and a real data application to a large number of time series measuring traffic flow in several spots of five European cities. In the real data example, penalised hidden semi-Markov models are often preferred to hidden Markov models, and to hidden semi-Markov models with parametric and non-parametric sojourn-time specifications.

Excitation coefficients with a low dynamic range ratio (DRR) are advantageous in controlling mutual coupling between the elements of an antenna array. Their use also reduces the output power loss and simplifies the design of the feeding network. In this paper, a hybrid algorithm based on invasive weed optimization and convex optimization for the synthesis of distributed arrays with two subarrays is proposed. Arrays of this type are used in numerous applications, e.g. in aircraft. A constraint is added to the optimization problem to control the DRR of the array's excitation vector. Numerical results are presented for position-only, as well as for position and excitation control approaches. The trade-off between the peak sidelobe ratio and the obtained DRR is illustrated by numerical examples.

Abstract We introduce a novel construction procedure for one-dimensional function space summation-by-parts (FSBP) operators. Existing construction procedures for FSBP operators of the form $$D = P^{-1} Q$$ D = P - 1 Q proceed as follows: Given a boundary operator B , the norm matrix P is first determined and then in a second step the complementary matrix Q is calculated to finally get the FSBP operator D . In contrast, the approach proposed here determines the norm and complementary matrices, P and Q , simultaneously by solving an optimization problem. The proposed construction procedure applies to classical summation-by-parts (SBP) operators based on polynomial approximation and the broader class of FSBP operators. According to our experiments, the presented approach yields a numerically stable construction procedure and FSBP operators with higher accuracy for diagonal norm difference operators at the boundaries than the traditional approach. Through numerical simulations, we highlight the advantages of our proposed technique.

In the field of multi-objective evolutionary optimization, prior studies have largely concentrated on the scalability of objective functions, with relatively less emphasis on the scalability of decision variables. However, in practical applications, complex optimization problems often involve multiple objectives and large-scale decision variables. To address these challenges, this paper proposes an innovative large-scale multi-objective evolutionary optimization algorithm. The algorithm utilizes clustering techniques to categorize decision variables and introduces a novel dominance relation to enhance optimization efficiency and performance. By dividing decision variables into convergence-related and diversity-related groups and applying distinct optimization strategies to each, the algorithm achieves a better balance between convergence and diversity. Additionally, the algorithm incorporates a new angle-based dominance relationship to reduce dominance resistance during the optimization process. Experimental results on multiple mainstream multi-objective optimization test sets, such as standard DTLZ and UF problem sets, indicate that CLMOAS achieves smaller IGD values relative to mainstream algorithms such as MOEA/D and LMEA, thereby demonstrating that the proposed algorithm outperforms several existing multi-objective evolutionary algorithms and showcases its effectiveness in solving complex optimization problems with multiple objectives and large-scale decision variables.

Addressing irregular cutting and packing (C&P) optimization problems poses two distinct challenges: the geometric challenge of determining whether an item can be feasibly placed at a certain position and the optimization challenge of finding a good solution according to some objective function. Until now, those tackling such problems have had to address both challenges simultaneously, requiring two distinct sets of expertise and a lot of research and development effort. One way to lower this barrier is to decouple the two challenges. In this paper, we introduce a powerful collision detection engine (CDE) for two-dimensional (2D) irregular C&P problems, which assumes full responsibility for the geometric challenge. The CDE (i) allows users to focus with full confidence on their optimization challenge by abstracting geometry away, and (ii) enables independent advances to propagate to all optimization algorithms built atop it. We present a set of core principles and design philosophies to model a general and adaptable CDE focused on maximizing performance, accuracy, and robustness. These principles are accompanied by a concrete open-source implementation called jagua-rs. This paper, together with its implementation, serves as a catalyst for future advances in irregular C&P problems by providing a solid foundation that can either be used as it currently exists or further improved upon. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: This work was supported by Research Foundation – Flanders (FWO) [Grants 1S71222N and K804824N]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.1025 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.1025 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We present Noise-Directed Adaptive Remapping (NDAR), a heuristic algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that features a global attractor state. In a standard setting, such noise can be detrimental to the quantum optimization performance. Our algorithm bootstraps the noise attractor state by iteratively gauge-transforming the cost-function Hamiltonian in a way that transforms the noise attractor into higher-quality solutions. The transformation effectively changes the attractor into a higher-quality solution of the Hamiltonian based on the results of the previous step. The end result is that noise aids variational optimization, as opposed to hindering it. We present an improved Quantum Approximate Optimization Algorithm (QAOA) runs in experiments on Rigetti's quantum device. We report approximation ratios 0.9 - 0.96 for random, fully connected graphs on n = 82 qubits, using only depth p = 1 QAOA with NDAR. This compares to 0.34 - 0.51 for standard p = 1 QAOA with the same number of function calls.

Robust analog circuit design is becoming increasingly challenging due to process, voltage, and temperature (PVT) variations at advanced technology nodes. In this paper, we formulate analog circuit synthesis as a robust optimization problem, and propose a Contextual Robust OptimiZAtion (CROZA) method for variation-aware analog circuit design. The proposed method uses Contextual Gaussian process to model both the design parameters and perturbation parameters, and a hybrid strategy of adversarially robust optimization and stochastically perturbed robust optimization to find robust solutions. Compared to state-of-the-art methods, our proposed approach achieves significant simulation and runtime speedups while delivering superior optimization results.

Metaheuristic algorithms are powerful tools for solving complex optimization problems where traditional methods fail. The Social Spider Optimization (SSO) algorithm, inspired by the cooperative foraging behavior of spiders, is a notable swarm intelligence technique. However, it can be prone to premature convergence. This paper presents an enhanced variant, the Elite Opposition-Based Social Spider Optimization (EOSSO) algorithm, which integrates an elite opposition-based learning (OBL) strategy and an elite selection mechanism into the standard SSO framework. This integration aims to improve population diversity, enhance global exploration, and accelerate convergence. The performance of EOSSO is rigorously evaluated on a comprehensive set of 23 benchmark functions, including unimodal, multimodal, and fixed-dimension multimodal problems. Experimental results demonstrate that EOSSO significantly outperforms the standard SSO and other well-known metaheuristics in terms of solution accuracy, convergence speed, and stability. The algorithm exhibits a remarkable ability to escape local optima and refine solutions efficiently, proving its robustness and effectiveness as a high-performance optimizer for complex landscapes.

This paper proposes a fuzzy copula-based optimization framework for modeling dependence structures and financial risk under parameter uncertainty. The parameters of selected copula families are represented as trapezoidal fuzzy numbers, and their α-cut intervals capture both the support and core ranges of plausible dependence values. This fuzzification transforms the estimation of copula parameters into a fuzzy optimization problem, enhancing robustness against sampling variability. The methodology is empirically applied to gold and oil futures (1 January 2015–1 January 2025), comparing symmetric copulas, i.e., Gaussian and Frank and asymmetric copulas, i.e., Clayton, Gumbel and Student-t. The results prove that the fuzzy copula framework provides richer insights than classical point estimation by explicitly expressing uncertainty in dependence measures (Kendall’s τ, Spearman’s ρ) and risk indicators (Value-at-Risk, Conditional Value-at-Risk). Rolling-window analyses reveal that fuzzy VaR and fuzzy CVaR effectively capture temporal dependence shifts and tail severity, with fuzzy CVaR consistently producing more conservative risk estimates. This study highlights the potential of fuzzy optimization and fuzzy dependence modeling as powerful tools for quantifying uncertainty and managing extreme co-movements in financial markets.

In inventory management, business organizations gradually face challenges due to the complexities of managing perishable goods whose value diminishes over time. In such circumstances, interval’s bounds estimated business policy can be adopted to study a non-deterministic inventory model incorporating decay, preservation technology, and financial incentives, viz. advanced payments and fixed discounts. This study explores an interval Economic Order Quantity (EOQ) model incorporating advanced payment with discount options under preservation technology framework in interval environment. In this model, the demand rate is expressed as a convex combination of linear and power patterns of the selling price. The present model is formulated mathematically using interval differential equations and interval mathematics. Then, the corresponding interval-valued average profit of the model is obtained. In order to optimize the corresponding interval optimization problem, C-U optimization technique is developed. Employing the C-U optimization technique, the said interval optimization problem is converted into crisp optimization problems. Then, these problems are solved numerically by Wolfrom MATHEMATICA-11.0 software and validated with the help of two numerical examples. Finally, sensitivity analyses have been performed to study the impact of known inventory parameters on optimal policy.

Purpose This study aims to address the key challenges in multi-unmanned aerial vehicle (UAV) data sensing systems, where energy-constrained UAVs require real-time trajectory optimization to simultaneously maximize coverage efficiency and minimize energy consumption. Traditional centralized optimization approaches struggle with scalability and computational complexity due to the non-convexity and high dimensionality of the joint optimization problem. To overcome these limitations, the authors propose a distributed multi-agent deep reinforcement learning (MADRL) framework that leverages the autonomous decision-making capability of deep reinforcement learning to achieve distributed continuous action control of UAVs, thereby enabling efficient autonomous deployment. Design/methodology/approach This study proposes a multi-UAV energy-efficient data collection scheme (multi-UAV E2DC) based on an MADRL algorithm. The proposed approach enables UAVs to dynamically collect data from multiple ground sensors while accounting for practical constraints such as communication range, motion limits and energy consumption. To achieve this, the authors first construct a multi-objective optimization model by integrating an air-to-ground communication model with a UAV energy consumption model. Building on this foundation, the authors further develop an enhanced MADRL algorithm within a centralized training and decentralized execution (CTDE) actor-critic framework, which supports efficient continuous trajectory control and deployment of multi-UAV. Findings Extensive simulations demonstrate that the proposed approach achieves superior performance in multi-objective optimization compared to benchmark methods, including random policy, K-means clustering and multi-agent deep deterministic policy gradient. Specifically, the proposed method outperforms in terms of average coverage density, data volume and coverage energy efficiency index. Originality/value This study proposes an MADRL-based energy-efficient data collection framework for UAVs, which integrates air-to-ground communication and UAV energy consumption models to formulate a multi-objective optimization problem. By adopting a CTDE framework for continuous trajectory control, it effectively overcomes the computational challenges of traditional non-convex optimization methods in complex environments. The proposed approach offers a theoretically sound and practically applicable solution for distributed UAV sensing in extreme disaster scenarios.

With the rapid expansion of data scale, compute-intensive tasks will become a core application of 6G networks. As Unmanned Aerial Vehicle (UAV) technology advances, UAVs can assist in task offloading for mobile edge computing by collaborating to overcome individual UAV limitations in battery life and computational capacity. Hence, in this paper, we propose a task offloading algorithm for multiple UAVs based on a temporal graph. We first formulate an optimization problem to minimize the total completion time of UAV swarm task offloading by classifying tasks and determining task priorities and subtask dependencies. To solve this problem, we introduce a temporal graph to simulate service nodes and task sequences in computing networks. It can reveal task execution priorities by calculating proximity indices, which indicate the ratio of physical distance to the sum of task weights, and determining timestamp offsets. In the following, to reduce unnecessary waiting and computation resource allocation risks, we transform the optimization problem into a directed acyclic graph connectivity problem, which identifies the fastest temporal paths for each UAV, forming a dedicated service network. Finally, we propose a two-stage matching algorithm that achieves optimal matching based on service node locations, statuses, task types, and offloading demands. Simulation results demonstrate that the algorithm performs exceptionally well, reducing task completion times and significantly outperforming other algorithms in terms of task utility.

ABSTRACT This work presents a new inverse algorithm based on magnetic tomography (MT) for diagnosing fuel‐cell stacks (FC‐stacks). The objective is to determine the local internal resistivities of the stack from external magnetic measurements. The inverse problem is solved by minimizing the difference between the simulated magnetic induction and the measured magnetic induction using the gradient descent method. To limit the search space, a neighbor‐regularization is implemented as a penalty term, and the stack voltage is added as a constraint. To accelerate the solving process and improve the accuracy, we provide the derivatives of our optimization problem. This involves calculating the derivative of the employed finite element method (FEM) model, where sensitivities are determined using the adjoint‐state method. To validate our novel approach, the algorithm is applied to numerical data and subsequently tested it on measurements from a real FC‐stack, presenting the results in this article.