Discrete Optimization Research Articles

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.

Portfolio Optimization with Translation of Representation for Transport Problems

Abstract The paper presents a hybridization of two ideas closely related to metaheuristic computing, namely Portfolio Optimization (researched by Xin Yao et al.) and Translation of Representation for different metaheuristics (researched by Byrski et al.). Thus, difficult problems (discrete optimization) are approached by a sequential run through a number of steps of different metaheuristics, providing the translation of representation (since the algorithms are completely different). Therefore, close cooperation of e.g. ACO, PSO, and GA is possible. The results refer to unaltered algorithms and show the superiority of the constructed hybrid.

Discrete optimization: A quantum revolution?

Discrete optimization: A quantum revolution?

A method to identify a representation of the set of non-dominated points for discrete tri-objective optimization problems

A method to identify a representation of the set of non-dominated points for discrete tri-objective optimization problems

Discrete Dynamic Berth Allocation Optimization in Container Terminal Based on Deep Q-Network

Discrete Dynamic Berth Allocation Optimization in Container Terminal Based on Deep Q-Network

Competitive Elimination Improved Differential Evolution for Wind Farm Layout Optimization Problems

The wind farm layout optimization problem (WFLOP) aims to maximize wind energy utilization efficiency under different wind conditions by optimizing the spatial layout of wind turbines to fully mitigate energy losses caused by wake effects. Some high-performance continuous optimization methods, such as differential evolution (DE) variants, exhibit limited performance when directly applied due to WFLOP’s discrete nature. Therefore, metaheuristic algorithms with inherent discrete characteristics like genetic algorithms (GAs) and particle swarm optimization (PSO) have been extensively developed into current state-of-the-art WFLOP optimizers. In this paper, we propose a novel DE optimizer based on a genetic learning-guided competitive elimination mechanism called CEDE. By designing specialized genetic learning and competitive elimination mechanisms, we effectively address the issue of DE variants failing in the WFLOP due to a lack of discrete optimization characteristics. This method retains the adaptive parameter adjustment capability of advanced DE variants and actively enhances population diversity during convergence through the proposed mechanism, preventing premature convergence caused by non-adaptiveness. Experimental results show that under 10 complex wind field conditions, CEDE significantly outperforms six state-of-the-art WFLOP optimizers, improving the upper limit of power generation efficiency while demonstrating robustness and effectiveness. Additionally, our experiments introduce more realistic wind condition data to enhance WFLOP modeling.

Research and Application of Characteristic Curve Correction Method for Cascade Hydropower Stations Considering Runoff Inconsistency

The situation wherein a hydrological series does satisfy the assumption of “independent and identically distributed” is called runoff inconsistency. “Flow Inversion Phenomenon” is also a kind of runoff inconsistency in space that reflects errors in the hydrological modeling process and can provide a basis for curve correction. In this paper, the causes of the flow inversion phenomenon are analyzed, and a characteristic curve correction method for hydropower stations based on runoff inconsistency is proposed. “Interval Fallacy Rate” is proposed to quantify the flow inversion phenomenon, and with the goal of minimizing the interval fallacy rate, several characteristic curve correction methods, such as single-point discrete optimization, multi-point discrete optimization, overall translation optimization and partial translation optimization, are constructed to correct the turbine characteristic curve, discharge curve, and capacity curve of a hydropower station. In the case study, we take a six-reservoir cascade reservoir system in China as an example. After curve correction, the interval fallacy rate of each interval is reduced to varying degrees. This study provides a new idea for the correction of hydropower stations’ characteristic curves in basins lacking measured flow data.

SLDPSO-TA: Track Assignment Algorithm Based on Social Learning Discrete Particle Swarm Optimization

In modern circuit design, the short-circuit problem is one of the key factors affecting routability. With the continuous reduction in feature sizes, the short-circuit problem grows significantly in detailed routing. Track assignment, as a crucial intermediary phase between global routing and detailed routing, plays a vital role in preprocessing the short-circuit problem. However, existing track assignment algorithms face the challenge of easily falling into local optimality. As a typical swarm intelligence technique, particle swarm optimization (PSO) is a powerful tool with excellent optimization ability to solve large-scale problems. To address the above issue, we propose an effective track assignment algorithm based on social learning discrete particle swarm optimization (SLDPSO-TA). First, an effective wire model that considers the local nets is proposed. By considering the pin distribution of local nets, this model extracts and allocates more segments to fully leverage the role of track assignment. Second, an integer encoding strategy is employed to ensure that particles within the encoding space range correspond one-to-one with the assignment scheme, effectively expanding the search space. Third, a social learning mode based on the example pool is introduced to PSO, which is composed of other particles that are superior to the current particle. By learning from various objects in the example pool, the diversity of the population is improved. Fourth, a negotiation-based refining strategy is utilized to further reduce overlap. This strategy intelligently transfers and redistributes wire segments in congested areas to reduce congestion across the entire routing panel. Experimental results on multiple benchmarks demonstrate that the proposed SLDPSO-TA can achieve the best overlap cost optimization among all the existing methods, effectively reducing congestion in critical routing areas.

Generating representative sets for multiobjective discrete optimization problems with specified coverage errors

Generating representative sets for multiobjective discrete optimization problems with specified coverage errors

Optimizing structure-property models of three general graphical indices for thermodynamic properties of benzenoid hydrocarbons

Cheminformatics is an interdisciplinary field that combines principles of chemistry, computer science, and information technology to process, store, analyze, and interpret chemical data. One area of cheminformatics is quantitative structure–property relationship (QSPR) modeling which is a computational approach that correlates the structural attributes of chemical compounds with their physical, chemical, or biological properties to predict the behavior and characteristics of new or untested compounds. Structure descriptors deliver contemporary mathematical tools required for QSPR modeling. One of a significant class of such descriptors is graph-based descriptors known as graphical descriptors. A degree-based graphical descriptor/invariant of a υ-vertex graph Ω=(VΩ,EΩ) has a general structure GDd=∑ij∈EΩπdegxi,degxj, where π is bivariate symmetric map, and degxi is the degree of vertex xi∈VΩ. For α∈R∖{0}, if π=(degxi×degxj)α (resp. π=(degxi+degxj)α, then GDd is called the general product-connectivity PCα (resp. sum-connectivity SCα) index of Ω. Moreover, the general Sombor index SOα has the structure π=(degxi2×degxj2)α. By choosing the heat capacity ΔH and the entropy E as representatives of thermodynamic properties, we in this paper find optimal value(s) of α which deliver the strongest potential of the predictors GDd∈{PCα,SCα,SOα} for predicting ΔH and E of benzenoid hydrocarbons. In order to achieve this, we employ tools such as discrete optimization and multivariate regression analysis. This, in turn, study completely solves two open problems proposed in the literature.

Machine learning-based multi-objective optimization of thermo-mechanical field of anisotropic plates

Designing plates is highly challenging due to the complex relationship between material layout and its properties. Traditional experimental, analytical, and computational methods suffer from problems such as long computation time and high cost, limiting their application in predicting and optimizing plates. In this paper, we propose an end-to-end prediction and multi-objective optimization framework integrating machine learning (ML) and non-dominated sorting genetic algorithm (NSGA-II). This framework can have high fidelity and simultaneously predict multiple thermo-mechanical fields of the anisotropic plate-heat source system. It can also perform multi-objective optimization for specific requirements by optimizing the distribution of materials and heat sources. To demonstrate the effectiveness of our approach, the maximum temperature and von Mises stress are considered as objectives, and the framework is applied to two different discrete multi-objective optimization problems, i.e., non-temperature constrained and temperature constrained optimization problem. By integrating ML and optimization algorithm, our framework offers a comprehensive solution for tackling complex optimization problems in the field of anisotropic plate-heat source system.

Skeleton-Driven Inbetweening of Bitmap Character Drawings

One of the primary reasons for the high cost of traditional animation is the inbetweening process, where artists manually draw each intermediate frame necessary for smooth motion. Making this process more efficient has been at the core of computer graphics research for years, yet the industry has adopted very few solutions. Most existing solutions either require vector input or resort to tight inbetweening; often, they attempt to fully automate the process. In industry, however, keyframes are often spaced far apart, drawn in raster format, and contain occlusions. Moreover, inbetweening is fundamentally an artistic process, so the artist should maintain high-level control over it. We address these issues by proposing a novel inbetweening system for bitmap character drawings, supporting both tight and far inbetweening. In our setup, the artist can control motion by animating a skeleton between the keyframe poses. Our system then performs skeleton-based deformation of the bitmap drawings into the same pose and employs discrete optimization and deep learning to blend the deformed images. Besides the skeleton and the two drawn bitmap keyframes, we require very little annotation. However, deforming drawings with occlusions is complex, as it requires a piecewise smooth deformation field. To address this, we observe that this deformation field is smooth when the drawing is lifted into 3D. Our system therefore optimizes topology of a 2.5D partially layered template that we use to lift the drawing into 3D and get the final piecewise-smooth deformaton, effectively resolving occlusions. We validate our system through a series of animations, qualitative and quantitative comparisons, and user studies, demonstrating that our approach consistently outperforms the state of the art and our results are consistent with the viewers' perception. Code and data for our paper are available at http://www-labs.iro.umontreal.ca/~bmpix/inbetweening/.

Discrete Optimization Algorithm Based on Probability Distribution with Transformation of Target Values

Discrete Optimization Algorithm Based on Probability Distribution with Transformation of Target Values

A New Multicommodity Network Flow Model and Branch and Cut for Optimal Quantum Boolean Circuit Synthesis

This study introduces a new optimization model and a branch-and-cut approach for synthesizing optimal quantum circuits for reversible Boolean functions, which are pivotal components in quantum algorithms. Although heuristic algorithms have been extensively explored for quantum circuit synthesis, research on exact counterparts remains relatively limited. However, the need to design quantum circuits with guaranteed optimality is increasing, especially for improving computational fidelity on noisy intermediate-scale quantum devices. This study presents mathematical optimization as a viable option for optimal synthesis, with the potential to accommodate practical considerations arising in fast-evolving quantum technologies. We set a demonstrative problem to implement reversible Boolean functions using high-level gates known as multiple control Toffoli gates while minimizing a technology-based proxy called quantum cost—the number of low-level gates used to realize each high-level gate. To address this problem, we propose a discrete optimization model based on a multicommodity network and discuss potential future variations at an abstract level to incorporate technical considerations. A customized branch and cut is then developed upon different aspects of our model, including polyhedron integrality, surrogate constraints, and variable prioritization. Our experiments demonstrate the robustness of the proposed approach in finding cost-optimal circuits for all benchmark instances within a two-hour time frame. Furthermore, we present interesting intuitions from these experiments and compare our computational results with relevant studies, highlighting newly discovered circuits with the lowest quantum costs reported in this paper. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Quantum Computing. Funding: This research was supported by the Ministry of Science and Information and Communication Technology, South Korea [Grants 2017R1E1A1A0307098814 and 2020R1A4A307986411]. 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.2024.0562 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0562 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

A Discrete Brain Storm Optimization Algorithm for Hybrid Flowshop Scheduling Problems with Batch Production at Last Stage in the Steelmaking-Refining-Continuous Casting Process.

The iron and steel industry is energy-intensive due to the large volume of steel produced and its high-temperature and high-weight characteristics, sensors such as high-temperature application sensors can be utilized to collect production data and support the process control and optimization. Steelmaking-refining-continuous casting (SRCC) is a bottleneck in the iron and steel production process. SRCC scheduling problems are worldwide problems and NP-hard. The problems are not only important for iron and steel enterprises to enhance production efficiency, but also play a significant role in saving energy and reducing resource consumption. SRCC scheduling problems can be modeled as hybrid flowshop scheduling problems with batch production at the last stage. In this paper, a Discrete Brain Storm Optimization (DBSO) algorithm is proposed to handle SRCC scheduling problems. In the proposed DBSO, population initialization and cluster center replacement are specially designed to enhance the intensification abilities. Moreover, a perturbation operator is devised to enhance its diversification abilities. Furthermore, a new individual generation operator is devised to improve the intensification and diversification abilities simultaneously. Experimental results have demonstrated that the proposed DBSO is an efficient method for solving SRCC scheduling problems.

Improving transonic performance with adjoint-based NACA 0012 airfoil design optimization

This study delves into the discrete adjoint method, a powerful tool in high-fidelity aerodynamic shape optimization that efficiently computes derivatives of a target function for different design variables. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables. It is implemented to a NACA0012 airfoil at a transonic speed. This designated test case is qualitatively evaluated, considering specified Mach number and Reynolds number values of 0.7 and 15.96 million, respectively. The standard Spalart-Allmaras turbulence model is adapted to improve computational cost efficiency. The results validate the efficiency of Discrete Adjoint with OpenFOAM, showcasing its capability to generate optimal configurations. The achieved optimized performance is evidenced by minimizing the drag coefficient value (Cd) to an impressive value of 0.00871, 62.2 % lower than the previous studies, thus securing a novelty. While this research does not consider the post-processing of sensitivity calculations, it enables the potential for future research. The primary target of this paper is to assess the educational and training needs of researchers, engineers, and graduate students, offering a comprehensive introduction to discrete adjoint aerodynamic design optimization, presenting a novel methodology, and contributing to future advancements in the design optimization field.

An Efficient Algorithm for Exact Segmentation of Large Compositional and Categorical Time Series

ABSTRACTChange‐point detection, also known as signal segmentation, is an essential preprocessing step in many applications, ranging from industrial monitoring to bioinformatics. In short, it consists in finding the temporal boundaries of homogeneous regimes in long and non‐stationary time series. While this area of research is active, most existing methods are designed for Euclidean data. However, in many practical scenarios, the collected time series are compositional, meaning that each observation belongs to the probability simplex (the set of non‐negative vectors whose components sum to one). In this work, we propose an algorithm detecting change‐points in large compositional signals with an underlying piecewise stationary model. We cast the change‐point detection task as a discrete optimization problem, whose solution is shown to converge to the true change‐points. We introduce a new and time‐efficient dynamic programming algorithm that solves exactly this problem. To limit the number of operations, we describe a novel pruning rule that allows us to reduce the set of candidate change‐point indices. Our method is tested on a thorough simulation study, which confirms its efficiency. Additionally, we apply our method to a human activity segmentation task, highlighting the necessity for such novel techniques compared to standard algorithms.

PTE: Prompt tuning with ensemble verbalizers

Prompt tuning has achieved remarkable success in facilitating the performance of Pre-trained Language Models (PLMs) across various downstream NLP tasks, particularly in scenarios with limited downstream data. Reframing tasks as fill-in-the-blank questions represents an effective approach within prompt tuning. However, this approach necessitates the mapping of labels through a verbalizer consisting of one or more label tokens, constrained by manually crafted prompts. Furthermore, most existing automatic crafting methods either introduce external resources or rely solely on discrete or continuous optimization strategies. To address this issue, we have proposed a methodology for optimizing discrete verbalizers based on gradient descent, which we refer to this approach as PTE. This method integrates discrete tokens into verbalizers that can be continuously optimized, combining the distinct advantages of both discrete and continuous optimization strategies. In contrast to prior approaches, ours eschews reliance on prompts generated by other models or prior knowledge, merely augmenting a matrix. This approach boasts remarkable simplicity and flexibility, enabling prompt optimization while preserving the interpretability of output label tokens without constraints imposed by discrete vocabularies. Finally, employing this method in text classification tasks, we observe that PTE achieves results comparable to, if not surpassing, previous methods even under extreme conciseness. This furnishes a simple, intuitive, and efficient solution for automatically constructing verbalizers. Moreover, through quantitative analysis of optimized verbalizers, we uncover that language models likely rely not only on semantic information but also on other features for text classification. This revelation unveils new avenues for future research and model enhancements.