Discrete Optimization Research Articles

ROITP: Road Obstacle-Involved Trajectory Planner for Autonomous Trucks

Autonomous trucks have the potential to enhance both safety and convenience in intelligent transportation. However, their maximum speed and ability to navigate a variety of driving conditions, particularly uneven roads, are limited by a high center of gravity, which increases the risk of rollover. Road bulges, sinkholes, and unexpected debris all present additional challenges for autonomous trucks' operational design, which current perception and decision-making algorithms often overlook. To mitigate rollover risks and improve adaptability to damaged roads, this paper presents a novel Road Obstacle-Involved Trajectory Planner (ROITP). The planner categorizes road obstacles using a learning-based algorithm. A discrete optimization algorithm selects a multi-objective optimal trajectory while taking into account constraints and objective functions derived from truck dynamics. Validation across various scenarios on a hardware-in-loop platform demonstrates that the proposed planner is effective and feasible for real-time implementation.

Performance Improvement for Discretely Modulated Continuous-Variable Measurement-Device-Independent Quantum Key Distribution with Imbalanced Modulation

The modulation mode at the transmitters plays a crucial role in the continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol. However, in practical applications, differences in the modulation schemes between two transmitters can inevitably impact protocol performance, particularly when using discrete modulation with four-state or eight-state formats. This work primarily investigates the effect of imbalanced modulation at the transmitters on the security of the CV-MDI-QKD protocol under both symmetric and asymmetric distance scenarios. By employing imbalanced discrete modulation maps and numerical convex optimization techniques, the proposed CV-MDI-QKD protocol achieves a notably higher secret key rate and outperforms existing protocols in terms of maximum transmission distance. Specifically, simulation results demonstrate that the secret key rate and maximum transmission distance are boosted by approximately 77.77% and 24.3%, respectively, compared to the original protocol. This novel and simplified modulation method can be seamlessly implemented in existing experimental setups without requiring equipment modifications. Furthermore, it provides a practical approach to enhancing protocol performance and enabling cost-effective applications in secure quantum communication networks under real-world environments.

Solving combinatorial optimization problems through stochastic Landau-Lifshitz-Gilbert dynamical systems

We present a method to approximately solve general instances of combinatorial optimization problems using the physical dynamics of three-dimensional (3D) rotors obeying Landau-Lifshitz-Gilbert dynamics. Conventional techniques to solve discrete optimization problems that use simple continuous relaxation of the objective function followed by gradient-descent minimization are inherently unable to avoid local optima, thus producing poor-quality solutions. Our method considers the physical dynamics of macrospins capable of escaping from local minima, thus facilitating the discovery of high-quality, nearly optimal solutions, as supported by extensive numerical simulations on a prototypical quadratic unconstrained binary optimization (QUBO) problem. Our method produces solutions that compare favorably with those obtained using state-of-the-art minimization algorithms (such as simulated annealing) while offering the advantage of being physically realizable by means of arrays of stochastic magnetic tunnel-junction devices. Published by the American Physical Society 2025

ANALYSIS OF THE IMPACT OF TASK PRIORITIZATION LISTS ON THE POTENTIAL FOR AVOIDING ANOMALIES IN TASK SCHEDULING

This paper addresses relevant issues related to the anomalous deterioration in objective function values when attempting to improve the initial parameters in one of the discrete optimization problems. The primary focus is on investigating the conditions under which it is possible to prevent the occurrence of such anomalies. Contemporary scientific works devoted to schedule optimization and task prioritization management, particularly for location-allocation problems arising in the fields of computer science, engineering, and operations research, are reviewed. A priority dynamic redistribution algorithm is proposed, which al-lows minimizing delays and ensuring efficient resource utilization during parallel task execu-tion. An example of applying the algorithm is provided, and its effectiveness in preventing anomalies.

Corrigendum to “A polyhedral study of lifted multicuts” [Discrete Optim. 47 (2023) 100757]

Corrigendum to “A polyhedral study of lifted multicuts” [Discrete Optim. 47 (2023) 100757]

Discrete optimization model for multi-product multi-supplier vehicle routing problem with relaxed time window

This study examines the complicated logistics optimization issue known as the vehicle routing problem for multi-product and multi-suppliers(VRP-MPMS), which deals with the effective routing of a fleet of vehicles to convey numerous items from multiple suppliers to a set of consumers. In this problem, products from various suppliers need to be delivered to different customers while considering vehicle capacity constraints, time windows, and minimizing transportation costs. We propose a hybrid approach that combines a generalized reduced gradient method to identify feasible regions with a feasible neighborhood search to achieve optimal or near-optimal solutions. The aim of the exact method is to get the region of feasible solution. Then we explore the region using feasible neighborhood search, to get an integer feasible optimal (suboptimal) solution. Computational experiments demonstrate that our model and method effectively reduce transportation costs while satisfying vehicle capacity constraints and relaxed time windows. Our findings provide a viable solution for improving logistics operations in real-world scenarios.

A new continuous optimization method of standardized cubic permanent magnets for stellarators

Abstract Stellarator configurations can be realized using permanent magnets in combination with tokamak-like planar coils. From the perspective of engineering feasibility and cost-effectiveness, using standardized cubic permanent magnets with a finite number of magnetization directions is particularly advantageous. However, optimizing the discrete magnetization directions of tens of thousands of cubic magnets poses a significant challenge. This paper introduces a novel method that converts the discrete optimization problem into a continuous nonlinear optimization problem, enabling the direct application of well-established nonlinear optimization algorithms. This approach leverages a specially tailored continuous function to represent the magnetization moment and incorporates a penalty term to ensure the direction vector converges to one of the discrete points. Subsequently, a discrete solution for the magnetization direction distribution is derived by truncating the continuous solution and eliminating adjacent magnets with opposing magnetization directions. The proposed optimization method is validated using the ESTELL stellarator configuration as a case study. The results demonstrate that the designed distribution of cubic permanent magnets can accurately reproduce the intended magnetic field configuration.

Design of polarization-maintaining fiber with uniform doping concentration supporting 14 weakly coupled modes based on discrete point configuration optimization

In this work, we propose a polarization-maintaining, weakly coupled few-mode fiber with a uniform doping concentration, designed via a particle swarm optimization algorithm and a discrete point configuration method. The design features a circular central air hole and an irregular doped boundary. Across the C+L band, all 14 modes exhibit an effective refractive index difference exceeding 1.43×10−4. Compared to conventional polarization-maintaining few-mode fibers, the proposed design offers enhanced flexibility, ensuring mode isolation with a very non-complicated process. This approach can be readily extended to other inhomogeneous optical waveguides, offering a valuable framework for intelligent design in non-uniform waveguide systems.

A State-of-the-Art Fractional Order-Driven Differential Evolution for Wind Farm Layout Optimization

The wind farm layout optimization problem (WFLOP) aims to maximize wind energy utilization efficiency and mitigate energy losses caused by wake effects by optimizing the spatial layout of wind turbines. Although Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO) have been widely used in WFLOP due to their discrete optimization characteristics, they still have limitations in global exploration capability and optimization depth. Meanwhile, the Differential Evolution algorithm (DE), known for its strong global optimization ability and excellent performance in handling complex nonlinear problems, is well recognized in continuous optimization issues. However, since DE was originally designed for continuous optimization scenarios, it shows insufficient adaptability under the discrete nature of WFLOP, limiting its potential advantages. In this paper, we propose a Fractional-Order Difference-driven DE Optimization Algorithm called FODE. By introducing the memory and non-local properties of fractional-order differences, FODE effectively overcomes the adaptability issues of advanced DE variants in WFLOP’s discreteness while organically applying their global optimization capabilities for complex nonlinear problems to WFLOP to achieve more efficient overall optimization performance. Experimental results show that under 10 complex wind farm conditions, FODE significantly outperforms various current state-of-the-art WFLOP algorithms including GA, PSO, and DE variants in terms of optimization performance, robustness, and applicability. Incorporating more realistic wind speed distribution and wind condition data into modeling and experiments, further enhancing the realism of WFLOP studies presented here, provides a new technical pathway for optimizing wind farm layouts.

Hardware-efficient preparation of architecture-specific graph states on near-term quantum computers.

Highly entangled quantum states are an ingredient in numerous applications in quantum computing. However, preparing these highly entangled quantum states on currently available quantum computers at high fidelity is limited by ubiquitous errors. Besides improving the underlying technology of a quantum computer, the scale and fidelity of these entangled states in near-term quantum computers can be improved by specialized compilation methods. In this work, the compilation of quantum circuits for the preparation of highly entangled architecture-specific graph states is addressed by defining and solving a formal model, i.e., a form of discrete constraint optimization. Our model incorporates information about gate cancellations, gate commutations, and accurate gate timing to determine an optimized graph state preparation circuit. Up to now, these aspects have only been considered independently of each other, typically applied to arbitrary quantum circuits. We quantify the quality of a generated state by performing stabilizer measurements and determining its fidelity. We show that our new method reduces the error when preparing a seven-qubit graph state by 3.5x on average compared to the state-of-the-art Qiskit solution. For a linear eight-qubit graph state, the error is reduced by 6.4x on average. The presented results highlight the ability of our approach to prepare higher fidelity or larger-scale graph states on gate-based quantum computing hardware.

A Consensus Community-Based Spider Wasp Optimization for Dynamic Community Detection

There are many evolving dynamic networks in the real world, and community detection in dynamic networks is crucial in many complex network analysis applications. In this paper, a consensus community-based discrete spider wasp optimization (SWO) approach is proposed for the dynamic network community detection problem. First, the coding, initialization, and updating strategies of the spider wasp optimization algorithm are discretized to adapt to the community detection problem. Second, the concept of intra-population and inter-population consensus community is proposed. Consensus community is the knowledge formed by the swarm summarizing the current state as well as the past history. By maintaining certain inter-population consensus community during the evolutionary process, the population in the current time window can evolve in a similar direction to those in the previous time step. Experimental results on many artificial and real dynamic networks show that the proposed method produces more accurate and robust results than current methods.

Review of discrete variable topology optimization by sequential approximate integer programming

This article reviews the development of discrete-variable topology optimization using sequential approximate integer programming (SAIP). Beginning with an analysis of the limitations of traditional pixel-based material distribution topology optimization methods under continuous variables, a discussion is presented on discrete-variable approaches, which aim to resolve issues such as grey-scale solutions and ‘physical penalties’ of continuous variables. The theoretical foundations and algorithmic development of SAIP are detailed, highlighting that the key feature of SAIP is the use of classic sequential approximate programming while adhering to discrete variables. A major feature of SAIP, the discrete-variable sensitivity called topological derivative-based sensitivity analysis, is studied in depth. The construction of explicit separable integer programming subproblems and the canonical relaxation algorithm are discussed, emphasizing their scalability for large-scale problems. The trust-region approach for discrete variables that can ensure approximation is proposed. Numerical examples demonstrate the effectiveness of SAIP across various applications, topology-invariant control problems and multi-physical problems.

A novel gradient-based discrete time-delayed optimization algorithm for optimal control problems with Caputo–Fabrizio fractional derivative

A novel gradient-based discrete time-delayed optimization algorithm for optimal control problems with Caputo–Fabrizio fractional derivative

Ocotillo Optimization Algorithm (OcOA): A Desert-Inspired Metaheuristic for Adaptive Optimization

In this paper, we propose the Ocotillo Optimization Algorithm (OcOA), a novel desert-inspired metaheuristic designed to solve complex optimization problems. Inspired by the adaptive strategies of desert plants, OcOA aims to achieve a balance between exploration and exploitation in high-dimensional and multimodal search spaces. The algorithm dynamically adjusts its behavior based on feedback from prior iterations, optimizing both search breadth and solution refinement. To evaluate its effectiveness, OcOA was tested against several well-known algorithms on a range of benchmark functions, including unimodal and multimodal functions from the CEC 2005 suite such as Sphere, Rosenbrock, Ackley, and Rastrigin. The results demonstrate that OcOA outperforms competing approaches in terms of accuracy, convergence speed, and computational efficiency. Additionally, its adaptability was validated through feature selection tasks, highlighting its robustness in handling both continuous and discrete optimization challenges. This study positions OcOA as a competitive optimization tool for various real-world applications

An outclassing Multi-objective Hybrid Genetic-based Discrete PSO for Solving the PECT Problem

The Post Enrolment based Course Timetabling (PECT) Problem belongs to, one of the classical problems, the timetabling problems, and it is a part of the most real-life problems that come with multiple constraints of nature. Such a problem is investigated together with both hard and soft constraints, and the solution is an optimal timetable satisfying both constraints as far as possible which reflects the quality of the solution. As a result, there are many approaches to solving the PECT Problem. However most approaches rely upon both the determination of parameters or understanding of domain knowledge. In this research, the Genetic-based Discrete Particle Swarm Optimization (PSO) has been developed with two different local search approaches: Local Search and Tabu Search to solve multi-objective functions and get good solutions by improving the performance of searching solution, which has few parameters to be tuned, and it can outperform all related algorithms from the published work.

Dynamic mathematical model for resource management and scheduling in cloud computing environments

The object of the research is resource management and scheduling in Kubernetes clusters, in particular, data centers. It was determined that in many publications dedicated to optimization models of scheduling for Kubernetes, mathematical models either do not include constraints at all, or only have the constraints determined on the high level only. The purpose of the research is the creation of a dynamic low-level mathematical optimization model for resource management and scheduling in cloud computing environments that utilize Kubernetes. Examples of such environments include the data centers where the customers can rent both dedicated servers and resources of shared hosting servers that are allocated on demand. The suggested model was created using the principles of creation of mathematical models of discrete (combinatorial) optimization, and was given the name “dynamic” because it takes the time parameter into account. The model receives data about individual servers in the cluster and individual pods that should be launched as an input. The model aims to regulate not only individual assignments of pods to nodes, but also turning on and off the servers. The model has objectives of: minimization of the average number of shared hosting servers running; maximization of the average resource utilization coefficient on such servers; minimization of the number of occasions when the servers are turned on and off; minimization of resource utilization by the pods that are running on shared hosting servers but created by the customers renting the dedicated servers. The model considers resource constraints, among other limitations.

Solving Multi-Objective Satellite Data Transmission Scheduling Problems via a Minimum Angle Particle Swarm Optimization

With the increasing number of satellites and rising user demands, the volume of satellite data transmissions is growing significantly. Existing scheduling systems suffer from unequal resource allocation and low transmission efficiency. Therefore, effectively addressing the large-scale multi-objective satellite data transmission scheduling problem (SDTSP) within a limited timeframe is crucial. Typically, swarm intelligence algorithms are used to address the SDTSP. While these methods perform well in simple task scenarios, they tend to become stuck in local optima when dealing with complex situations, failing to meet mission requirements. In this context, we propose an improved method based on the minimum angle particle swarm optimization (MAPSO) algorithm. The MAPSO algorithm is encoded as a discrete optimizer to solve discrete scheduling problems. The calculation equation of the sine function is improved according to the problem’s characteristics to deal with complex multi-objective problems. This algorithm employs a minimum angle strategy to select local and global optimal particles, enhancing solution efficiency and avoiding local optima. Additionally, the objective space and solution space exhibit symmetry, where the search within the solution space continuously improves the distribution of fitness values in the objective space. The evaluation of the objective space can guide the search within the solution space. This method can solve multi-objective SDTSPs, meeting the demands of complex scenarios, which our method significantly improves compared to the seven algorithms. Experimental results demonstrate that this algorithm effectively improves the allocation efficiency of satellite and ground station resources and shortens the transmission time of satellite data transmission tasks.

Overlapping Channel Allocation Method for Wireless Communication Network Based on Discrete Particle Swarm Optimization Algorithm

To address the challenges of interference between network channels and low-frequency resource utilization efficiency, and to improve the overall performance and resource allocation fairness of the network, this study proposes a wireless communication network overlapping channel allocation strategy based on a discrete particle swarm optimization algorithm. First, the overlapping channel allocation problem in wireless networks is abstracted as a linear programming model with specific constraints, with the core objective of minimizing weighted interference between links. To solve this model, a discrete particle swarm optimization algorithm is introduced. In this algorithm, each particle’s position corresponds to a feasible overlapping channel allocation scheme, which is the potential solution to the optimization problem; The velocity of particles reflects the process of transitioning from the current channel configuration to the target channel configuration. Subsequently, based on the characteristics of discrete variables, corresponding operation rules and particle motion equations were defined. In addition, when particle swarm aggregation occurs, an optimal asymptotic mutation operator is introduced, which not only enhances the local search ability of the algorithm but also strengthens its global search ability. During algorithm execution, this mutation operator is applied based on a certain probability of mutation. The experimental results show that when using this strategy for overlapping channel allocation in wireless communication networks, even with an increase in the number of traffic flows, the average network throughput can remain stable, demonstrating a high network carrying capacity. Meanwhile, wireless networks exhibit a higher fairness factor, indicating a more balanced allocation of network resources among different users. In the process of optimal channel allocation, the packet loss rate reaches the lowest level, ensuring the reliability of data transmission.

Least angle sparse principal component analysis for ultrahigh dimensional data

AbstractPrincipal component analysis (PCA) has been a widely used technique for dimension reduction while retaining essential information. However, the ordinary PCA lacks interpretability, especially when dealing with large scale data. To address this limitation, sparse PCA (SPCA) has emerged as an interpretable variant of ordinary PCA. However, the ordinary SPCA relies on solving a challenging non-convex discrete optimization problem, which maximizes explained variance while constraining the number of non-zero elements in each principal component. In this paper, we propose an innovative least angle SPCA technique to address the computational complexity associated with SPCA, particularly in ultrahigh dimensional data, by sequentially identifying sparse principal components with minimal angles to their corresponding components extracted through ordinary PCA. This sequential identification enables solving the optimization problem in polynomial time, significantly reducing computational challenges. Despite its efficiency gains, our proposed method also preserves the main attributes of SPCA. Through comprehensive experimental results, we demonstrate advantages of our approach as a viable alternative for dealing with the computational difficulties inherent in ordinary SPCA. Notably, our method emerges as an efficient and effective solution for conducting ultrahigh dimensional data analysis, enabling researchers to extract meaningful insights and streamline data interpretation.

A Global Coverage Path Planning Method for Multi-UAV Maritime Surveillance in Complex Obstacle Environments

The study of unmanned aerial vehicle (UAV) coverage path planning is of great significance for ensuring maritime situational awareness and monitoring. In response to the problem of maritime multi-region coverage surveillance in complex obstacle environments, this paper proposes a global path planning method capable of simultaneously addressing the multiple traveling salesman problem, coverage path planning problem, and obstacle avoidance problem. Firstly, a multiple traveling salesmen problem–coverage path planning (MTSP-CPP) model with the objective of minimizing the maximum task completion time is constructed. Secondly, a method for calculating obstacle-avoidance path costs based on the Voronoi diagram is proposed, laying the foundation for obtaining the optimal access order. Thirdly, an improved discrete grey wolf optimizer (IDGWO) algorithm integrated with variable neighborhood search (VNS) operations is proposed to perform task assignment for multiple UAVs and achieve workload balancing. Finally, based on dynamic programming, the coverage path points of the area are solved precisely to generate the globally coverage path. Through simulation experiments with scenarios of varying scales, the effectiveness and superiority of the proposed method are validated. The experimental results demonstrate that this method can effectively solve MTSP-CPP in complex obstacle environments.