This paper introduces the Large Language Model-assisted Evolutionary Order Dispatching (LLMEOD) method, a novel approach designed to solve the complex and computationally intensive multi-agile Earth observation satellite scheduling problem (multi-AEOSSP). Our approach integrates three core components: 1) A LLM-assisted Evolutionary Framework: This framework efficiently generates order dispatching heuristics and employing customized prompt engineering to guide the LLM throughout the evolutionary operations. 2) An Iterative Dispatch-Scheduling Algorithm: Functioning as the fitness evaluator, this algorithm assesses the quality of candidate heuristics. It operates by assigning observation orders to individual satellites and then executing parallel scheduling simulations for each one. 3) Diversity-enhancing LLM agents: To ensure a broad exploration of the algorithm space, three specialized LLM agents systematically extract, refine, and generate new population. This process fosters the creation of a diverse set of dispatching heuristics within the evolutionary population. We evaluated the performance of LLMEOD through computational experiments across 15 distinct multi-AEOSSP scenarios. In 80% of these cases, our approach demonstrated superior performance in both solution quality and convergence speed when compared to existing heuristics. Additionally, ablation studies confirmed the critical contribution of the DELA, which enabled the discovery of more varied and high-performing heuristics than those produced by the standard evolutionary framework alone or by human-designed expert heuristics.

The Agile Earth Observation Satellite Scheduling Problem (AEOSSP) is a complex NP-hard challenge that involves selecting, sequencing, and timing observation tasks to maximize imaging profits while adhering to various constraints. In our study, we developed a mixed-integer programming model for AEOSSP, incorporating key constraints related to visible time windows and time dependencies. To tackle this, we propose an Evolutionary Adaptive Large Neighborhood Search Algorithm (evALNS) enhanced by Large Language Models (LLMs). Our work pioneers the application of LLMs to ALNS by being the first to automatically develop and evolve its critical destroy heuristics. However, a naive application of LLMs is insufficient for such a complex domain. We therefore introduce a novel Dual-Population Co-Evolutionary Computing Framework (DPEC) to bridge the LLM’s knowledge gap by synergizing LLM-generated heuristics with expert-designed ones. This co-evolution, guided by a Functional Natural Language Embedding (FNLE) strategy and customized prompts, significantly enhances the adaptability and efficiency of ALNS. Extensive numerical experiments demonstrated the superiority of the evALNS evolved under our framework, achieving an average profit improvement of 8.48% compared to the original ALNS with expert-designed destroy operators.

Due to the high-dimensional decision variables and the sparse nature of solutions in sparse large-scale multi-objective optimization problems (SLMOPs), traditional multi-objective evolutionary algorithms (MOEAs) encounter substantial challenges. Researchers have proposed various sparse evolutionary algorithms (SEAs) to address these challenges. However, most existing SEAs focus on accurately identifying non-zero variable positions while neglecting changes in objective function values during optimization. This paper introduces a Jaccard similarity coefficient-based evolutionary algorithm (JSCEA) designed to search for sparse distributions that optimize objective values rapidly and efficiently. Leveraging the Jaccard similarity coefficient (JSC) to identify critical sparse patterns among promising solutions and propagate them to subsequent generations enhances the algorithm’s computing efficiency, particularly under limited computational resources. Experimental results on three real-world problems and eight benchmark tests demonstrate that JSCEA performs competitively on problem sizes of up to 10,000 variables.

The Multi-Agile Earth Observation Satellite Scheduling Problem (MAEOSSP) is a complex NP-hard optimization problem, characterized by resource constraints and highly nonlinear, time-dependent constraints. To address this challenge, we propose a Lagrangian Relaxation-based Heuristic (LRD-H) algorithm, a hybrid approach that integrates mathematical decomposition with tailored heuristics. The framework first employs Lagrangian Relaxation to decompose the MAEOSSP into independent single-satellite subproblems, which are solved by an efficient heuristic. Subsequently, it leverages dual information to construct high-quality feasible solutions, which are then enhanced by an iterative improvement procedure. Additionally, we provide a theoretical analysis demonstrating that the expected quality of our algorithm’s solutions monotonically improves with the computational effort allocated to the subproblem solver. Finally, extensive computational experiments show that LRD-H provides strong dual values for quality estimation and achieves significantly better solution quality compared to state-of-the-art benchmarks, especially on large-scale scenarios. Detailed ablation study empirically validates the critical role of our dual-information-guided solution construction and priority-aware improvement heuristics.

Objective The Multi-Agile Earth Observation Satellite Mission Scheduling Problem(MAEOSMSP)is an NP-hard problem.Algorithm design for this problem has long been constrained by reliance on expert experience and limited adaptability across diverse scenarios.To address this limitation,an Adaptive Algorithm Design(AAD)framework is proposed.The framework integrates a Large Language Model(LLM)and Reinforcement Learning(RL)to enable automated generation and intelligent application of scheduling algorithms.It is built on a novel offline evolution-online decision-making architecture.The objective is to discover heuristic algorithms that outperform human-designed methods and to provide an efficient and adaptive solution methodology for the MAEOSMSP. Methods The AAD framework adopts a two-stage mechanism.In the offline evolution stage,LLM-driven evolutionary computation is used to automatically generate a diverse and high-quality library of task assignment algorithms,thereby alleviating the limitations of manual design.In the online decision-making stage,an RL agent is trained to dynamically select the most suitable algorithm from the library based on the real-time solving state(e.g.,solution improvement and stagnation).This process is formulated as a Markov decision process,which allows the agent to learn a policy that adapts to problem-solving dynamics. Results and Discussions The effectiveness of the AAD framework is evaluated through comprehensive experiments on 15 standard test scenarios.The framework is compared with several state-of-the-art methods,including expert-designed heuristics,an advanced deep learning approach,and ablation variants of the proposed framework.The results show that the dynamic strategies generated by AAD consistently outperform the baselines,with performance improvements of up to 9.8%in complex scenarios.Statistical analysis further indicates that AAD achieves superior solution quality and demonstrates strong robustness across different problem instances. Conclusions A novel AAD framework is presented to automate algorithm design for the MAEOSMSP by decoupling algorithm generation from algorithm application.The combination of LLM-based generation and RL-based decision making is validated empirically.Compared with traditional hyper-heuristics and existing LLM-based methods,the proposed architecture enables both the creation of new algorithms and their dynamic application.The framework provides a new paradigm for solving complex combinatorial optimization problems and shows potential for extension to other domains.

The Earth Observation Satellite Task Scheduling Problem (EOSTSP) is an NP-Hard challenge critical for space-based information acquisition. Conventional optimization methods are hampered by high development costs, limited adaptability to dynamic scenarios, and poor interpretability. We propose a training-free solution that leverages the reasoning capabilities of Large Language Models (LLMs) through a multiagent framework. Our approach introduces an order-driven scheduling strategy that fundamentally reconceptualizes the EOSTSP as a real-time order fulfillment process, drawing inspiration from dynamic resource allocation paradigms in complex service systems. This original methodology transforms the traditionally monolithic scheduling problem into a structured sequential decision flow, where each observation task is processed as an independent order through specialized decision phases. Implemented via the Tri-Stage LLM-Coordinated (TSLC) framework, this novel approach enables autonomous scheduling through coordinated multiagent reasoning while maintaining full operational feasibility via external validation. Empirical results demonstrate performance improvements of 4.58% and 13.38% over state-of-the-art algorithms in routine and emergency scenarios, respectively, while providing transparent interpretability through its structured decision-making process, effectively overcoming the opaque limitations of traditional optimization approaches.

Scheduling large-scale tasks within a multi-agile earth observation satellite system poses a formidable challenge. Given the complexity of this optimization problem, the responding solving strategy should exhibit both efficiency and effectiveness in terms of computational time and solution quality. The current strategies can broadly be categorized into all-in-one and two-stage methodologies. The latter, more conducive to real-world scenarios, owing to reducing the problem complexity and practical operational flexibility, dissects this challenge into task allocation and single-satellite scheduling. However, existing two-stage strategies still consider the objectives and constraints at the equivalent level and only adapt to specific algorithms. In this way, the pivotal issues concerning the solution complexity and strategy compatibility remain fundamentally unaddressed. To address this limitation, we proposed a generalized bilevel optimization model called Question-and-Answer model, which establishes two distinct optimization model with different contains and objectives. In this model, the upper questions are highly indispensable in the response from the lower level and constraints are considered separately at two stages. To ascertain the generalization of this framework, we conduct a comprehensive range of experiments employing various proposed strategies and algorithms in two stages. Diverse algorithms ranging from heuristic principles, and evolutionary strategies, to reinforcement learning can be seamlessly combined and integrated within this framework. The results demonstrate that the scale of scenarios does not affect the effectiveness of any amalgamated algorithms within this framework. Furthermore, the transition of upper questions according to the lower answers indeed improves the objectives but concurrently intensify the computational time.

To address the time-consuming and complex multiple agile Earth observation satellite scheduling problem (multi-AEOSSP), we propose a novel application of the LLMassisted evolutionary computation (LLM-EC) framework to design task dispatching heuristics with three key innovations: 1) Customized prompt strategies for initialization, crossover, and mutation tailored for efficient order-dispatching heuristics. 2) The evolved heuristics decompose multi-AEOSSP into parallel single-satellite subproblems, significantly reducing solution complexity. 3) Experiments conducted on realistic scenarios demonstrate that LLM-EC achieves a higher solution quality than expert-designed heuristics, with improvements of up to 6.8%.

With the increasing demand for large-scale Earth Observation Satellites (EOS), scheduling models are no longer sufficient to meet the requirements for flexibility and order-driven operations. To address this challenge, this paper proposes a Large Language Model (LLM)-based Bi-level Online Order Dispatching and Scheduling (LLM-BODS) algorithm. The proposed algorithm consists of three key components: a bi-level online optimization framework, an LLM-based order dispatching algorithm, and a metaheuristic algorithm for single-satellite order scheduling. Within the bi-level optimization framework, the upper level dynamically allocates orders to satellites based on real-time order demands and satellite resource states using the LLM-based order dispatching algorithm. The lower level employs an adaptive large neighborhood search (ALNS) metaheuristic to generate optimal task execution sequences for each satellite. Experimental results demonstrate that the proposed algorithm not only maintains scheduling quality but also enhances scheduling efficiency, effectively addressing the flexible scheduling needs of large-scale Earth Observation Satellites.

The linear complementary problem (LCP) is a unified formulation for linear and quadratic programming problems. Therefore, it has many applications in practical problems like bimatrix game. We prove that it makes sense to look for sparse LCP solutions. A l2−l1 regularization technique transforms the original sparse optimization problem into an unconstrained one. Thereafter, a linearized ADMM (for alternating direction method of multipliers) is designed to solve the regularization model. Then, using a penalty function approach, we propose an efficient sequential linearized ADMM to find the sparse LCP solutions. Finally, numerical experiments prove that the sparse solution of LCPs can be solved efficiently, and is competitive with other state-of-the-art algorithms. A practical application in bimatrix game is also reported.

Managing numerous observation requirements on a large-scale satellite constellation is arduous for satellite control departments. Concurrently, achieving fast and effective task scheduling necessitates autonomous observation task generation. To address this issue, we proposed a novel method combined with Observation Requirements Heat Grid Model (ORHGM) and a Grid Aggregation Algorithm Based on Field of View Exploration (GAAFVE). Firstly, we define a uniform description of the observation requirements for various target types by devising a heat grid model predicated on geographic grid segmentation. Experimental outcomes reveal that our uniform model saves up to 31.93% of the observation tasks for fulfilling identical requirements by independent task generation for various target types. Secondly, based on this model, an autonomous task generation is completed by GAAFVE. Under the constraints regarding satellite imaging width, our algorithm facilitates heat grid search for non-connected regions and demonstrates superiority in computing time compared to other clustering-based task algorithms. The proposed method can allow managing large-scale observation requirements to be completed relatively quickly for satellite control departments. This method can also be extended to task generation in other multi-agent systems beyond satellites, such as the automatic generation of multi-UAV disaster reconnaissance tasks. (c) 2024 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

The Linear Complementarity Problem (LCP) offers a comprehensive modeling framework for addressing a wide range of optimization problems. In many real-world applications, finding an LCP solution with a sparse structure is often necessary. To address this problem, we introduce an innovative global optimization framework named the Particle Dynamical System Algorithm (PDSA), which consists of two components. The first component is a dynamical system (DS) inspired by the Absolute Value Equation (AVE), proven to have equilibria corresponding to LCP solutions, with additional relaxing regulators that enhance coverage rate and stability. The second component is an Adaptive Oscillated Particle Swarm Optimization (AOPSO) designed to globally enhance sparsity in LCP solutions, addressing the complexities posed by non-convex and non-smooth regulation models. Within this framework, the DS achieves optimality, while the AOPSO promotes solution sparsity. We compared our proposed DS with relaxing regulators to two classic efficient DSs, fully validating the effectiveness of our approach and underscoring the significant role of the introduced relaxing regulators in improving the convergence rate. Our newly developed variant of PSO, AOPSO, was compared with three classic and state-of-the-art variants on fourteen benchmark functions, demonstrating its competitive performance. Finally, we performed experiments on seven test examples and an application in portfolio selection, showing that the proposed PDSA algorithm surpasses other competitors in finding sparse LCP solutions.

The linear complementary problem (LCP) is a unified formulation for linear and quadratic programming problems. Therefore, it has many applications in practical problems like bimatrix game. We prove that it makes sense to look for sparse LCP solutions. A l 2 − l 1 regularization technique transforms the original sparse optimization problem into an unconstrained one. Thereafter, a linearized ADMM (for alternating direction method of multipliers) is designed to solve the regularization model. Then, using a penalty function approach, we propose an efficient sequential linearized ADMM to find the sparse LCP solutions. Finally, numerical experiments prove that the sparse solution of LCPs can be solved efficiently, and is competitive with other state-of-the-art algorithms. A practical application in bimatrix game is also reported.

The ongoing global coronavirus pandemic (COVID-19) has significantly increased urban medical waste. Such waste often contains pathogenic microorganisms, harmful chemicals, and even radioactive and defective sub-stances, hence imposing disease transmission and public health risks. Nevertheless, due to multiple factors, the amount of medical waste produced in medical institutions is stochastic. This paper proposed an optimization model for a waste recycling network consideration of loading reliability to minimize the collective cost of location, vehicle usage, and transportation. A modified ant colony algorithm combined with the K-means clus-tering method based on a genetic algorithm is then proposed (MACO-GKA) to solve the optimal location problem and the vehicle routing problem (LP-VRP). The numerical examples are then conducted in Xuzhou City, China to evaluate the performance of the proposed model. Taking the loading reliability level & theta; = 0.9 as an example, the results show that the total cost will reach $100546.53 when collection points are not set, but decrease to $86,907.11 when they are set. In the latter case, the total cost was reduced by 13.57%. The detailed results indicate that the selection and establishment of medical waste collection points are essential factors in designing an urban medical waste recycling network. The proposed MACO-GKA algorithm also outperforms the CPLEX solver.

Traffic assignment model (TAM) is an important research issue of urban traffic design and planning. Most of the existing studies are conducted under deterministic conditions. In reality, the link travel time and waiting time at signalized intersections are stochastic due to many uncertain factors in transportation networks. Under this circumstance, this paper proposes a new travel time reliability-based user equilibrium (TRUE) traffic assignment model with consideration of link travel time correlations and waiting time at signalized intersections in stochastic traffic networks. Under the assumption that link travel times and waiting times at signalized intersections follow normal distributions, the proposed model is transformed into a variational inequality (VI) model. It is rigorously proven that there is at least one solution for the VI problem, and the method of successive average (MSA) is employed to solve the proposed model. The numerical experiments are used to illustrate the applications and effectiveness of the proposed model.

Consideration of the travel time variation for rescue vehicles is significant in the field of emergency management research. Because of uncertain factors, such as the weather or OD (origin-destination) variations caused by traffic accidents, travel time is a random variable. In emergency situations, it is particularly necessary to determine the optimal reliable route of rescue vehicles from the perspective of uncertainty. This paper first proposes an optimal reliable path finding (ORPF) model for rescue vehicles, which considers the uncertainties of travel time, and link correlations. On this basis, it investigates how to optimize rescue vehicle allocation to minimize rescue time, taking into account travel time reliability under uncertain conditions. Because of the non-additive property of the objective function, this paper adopts a heuristic algorithm based on the K-shortest path algorithm, and inequality techniques to tackle the proposed modified integer programming model. Finally, the numerical experiments are presented to verify the accuracy and effectiveness of the proposed model and algorithm. The results show that ignoring travel time reliability may lead to an over- or under-estimation of the effective travel time of rescue vehicles on a particular path, and thereby an incorrect allocation scheme.

Solving the absolute value equation (AVE) is a nondifferentiable NP-hard and continuous optimization problem with a wide range of applications. Because its solutions have different forms, it is challenging to design the most efficient algorithm that can solve different AVEs without using overcomplicated technical improvement and problem-dependent objectives. Hence, this paper proposed an improved glowworm swarm optimization (GSO) algorithm with an adaptive step size strategy based on the sigmoid function (SIGGSO) that solves the AVEs. Seven test AVEs, including multisolution and high-dimensional AVEs, are selected for testing and compared with seven metaheuristic algorithms. The experimental results show that the proposed SIGGSO algorithm has higher solution accuracy and stability when seeking multiple solution of AVEs compared to the basic GSO. Moreover, it obtains competitive advantages on multisolution and high-dimensional AVEs compared with other metaheuristic algorithms and provides an effective method for engineering and scientific calculations.

Electric vehicles are an important part of urban green transportation network, and their popularization and application are of great significance to the sustainable development of cities. In recent years, electric vehicles continue to make up greater portions of the vehicle fleet, yet are restricted by battery capacity and shortages of charging stations. Reasonable path planning for electric vehicles is not only conducive to improving the utilization rate of road resources, easing traffic congestion, but also of great significance to the energy utilization rate of vehicles and reducing greenhouse gas emissions. This paper deals with a reliable energy consumption path-finding (RECPF) algorithm for signalized traffic networks with electric vehicles in the presence of uncertainty. The RECPF problem is formulated as the probability of completing a trip without exhausting a given battery energy budget. We extend RECPF models accounting for the link travel speed correlations and delays at signalized intersections. Addressing the nonadditivity and nonlinearity of the suggested optimization model, a modified heuristic algorithm based on the Dijkstra and k shortest path algorithms is proposed to tackle the RECPF problems. The grid-based road network of Hong Kong is employed to demonstrate efficacy and usefulness of the established algorithm. The obtained results reveal that incorporating link travel speed correlations and delays at signalized intersections bring about more accurate prediction of electric vehicle energy consumption, producing more efficient optimal reliable path recommendations.

广义绝对值方程式是一个不可微的方程,解决绝对值方程的算法有很多,但这些方法基本上属于传统的迭代法,由于它们的计算时间极大地依赖于问题的规模、维数以及所使用的算法,因此很难满足实时并行的要求.论文通过两种光滑近似方法,将广义绝对值方程转化为一个可微的无约束优化问题,建立起最速下降神经网络模型对其进行求解并证明了神经网络的稳定性以及神经网络的平衡态是绝对值方程的解.论文最后比较采用不同光滑函数去近似绝对值方程时,用最速下降神经网络求解广义绝对值方程的时间、迭代步数以及解的误差.最后用试验证明该方法的正确性及有效性.