Large-scale Combinatorial Optimization Research Articles

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

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

Parametric Frequency Divider Based Ising Machines.

We report on a new class of Ising machines (IMs) that rely on coupled parametric frequency dividers (PFDs) as macroscopic artificial spins. Unlike the IM counterparts based on subharmonic-injection locking (SHIL), PFD IMs do not require strong injected continuous-wave signals or applied dc voltages. Therefore, they show a significantly lower power consumption per spin compared to SHIL-based IMs, making it feasible to accurately solve large-scale combinatorial optimization problems that are hard or even impossible to solve by using the current von Neumann computing architectures. Furthermore, using high quality factor resonators in the PFD design makes PFD IMs able to exhibit a nanowatt-level power per spin. Also, it remarkably allows a speedup of the phase synchronization among the PFDs, resulting in shorter time to solution and lower energy to solution despite the resonators' longer relaxation time. As a proof of concept, a 4-node PFD IM has been demonstrated. This IM correctly solves a set of Max-Cut problems while consuming just 600 nanowatts per spin. This power consumption is 2 orders of magnitude lower than the power per spin of state-of-the-art SHIL-based IMs operating at the same frequency.

Enhanced convergence in p-bit based simulated annealing with partial deactivation for large-scale combinatorial optimization problems

This article critically investigates the limitations of the simulated annealing algorithm using probabilistic bits (pSA) in solving large-scale combinatorial optimization problems. The study begins with an in-depth analysis of the pSA process, focusing on the issues resulting from unexpected oscillations among p-bits. These oscillations hinder the energy reduction of the Ising model and thus obstruct the successful execution of pSA in complex tasks. Through detailed simulations, we unravel the root cause of this energy stagnation, identifying the feedback mechanism inherent to the pSA operation as the primary contributor to these disruptive oscillations. To address this challenge, we propose two novel algorithms, time average pSA (TApSA) and stalled pSA (SpSA). These algorithms are designed based on partial deactivation of p-bits and are thoroughly tested using Python simulations on maximum cut benchmarks that are typical combinatorial optimization problems. On the 16 benchmarks from 800 to 5000 nodes, the proposed methods improve the normalized cut value from 0.8 to 98.4% on average in comparison with the conventional pSA.

Evolutionary Multitasking With Centralized Learning for Large-Scale Combinatorial Multi-Objective Optimization

Evolutionary Multitasking With Centralized Learning for Large-Scale Combinatorial Multi-Objective Optimization

Spatial layout and optimization of e-commerce logistics management based on combinatorial optimization algorithm

Abstract Warehousing space layout is crucial for e-commerce logistics. A refined and scientific approach to warehouse design enhances space utilization and operational efficiency. This minimizes unused space and idle time, lowers inventory costs, and strengthens the competitive edge of e-commerce logistics. In this study, we conceptualize the logistics space layout issue as a crate problem, harnessing the rapid optimization capabilities of genetic algorithms (GA) and simulated annealing (SA). We propose a hybrid algorithm where SA forms the core, using GA to generate initial solutions and new iterations. Design parameters for the combined operation process are systematically developed. This algorithm is evaluated using both datasets and real arithmetic cases, demonstrating superior performance in large-scale combinatorial optimization problems. It achieves a search accuracy of 0.5% to 3% higher than GA alone, converging more reliably to the global optimum, thus reducing search time and operational scope. This research offers vital theoretical insights for optimizing space layouts in e-commerce logistics management.

Hybrid Parallel Ant Colony Optimization for Application to Quantum Computing to Solve Large-Scale Combinatorial Optimization Problems

Quantum computing is a promising technology that may provide breakthrough solutions to today’s difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. An algorithm referred to as Quantum Approximate Optimization Algorithm (QAOA) has been recently proposed to approximately solve hard problems using a protocol know as bang–bang. The technique is based on unitary evolution using a Hamiltonian encoding of the objective function of the combinatorial optimization problem. The QAOA was explored in the context of several optimization problems such as the Max-Cut problem and the Traveling Salesman Problem (TSP). Due to the relatively small node-size solution capability of the available quantum computers and simulators, we developed a hybrid approach where sub-graphs of a TSP tour can be executed on a quantum computer, and the results from the quantum optimization are combined for a further optimization of the whole tour. Since the local optimization of a sub-graph is prone to becoming trapped in a local minimum, we overcame this problem by using a parallel Ant Colony Optimization (ACO) algorithm with periodic pheromone exchange between colonies. Our method exceeds existing approaches which have attempted partitioning a graph for small problems (less than 48 nodes) with sub-optimal results. We obtained optimum results for benchmarks with less than 150 nodes and results usually within 1% of the known optimal solution for benchmarks with around 2000 nodes.

Effective implementation of text{L}{0}-regularised compressed sensing with chaotic-amplitude-controlled coherent Ising machines

Coherent Ising machine (CIM) is a network of optical parametric oscillators that can solve large-scale combinatorial optimisation problems by finding the ground state of an Ising Hamiltonian. As a practical application of CIM, Aonishi et al., proposed a quantum-classical hybrid system to solve optimisation problems of l_0-regularisation-based compressed sensing. In the hybrid system, the CIM was an open-loop system without an amplitude control feedback loop. In this case, the hybrid system is enhanced by using a closed-loop CIM to achieve chaotic behaviour around the target amplitude, which would enable escaping from local minima in the energy landscape. Both artificial and magnetic resonance image data were used for the testing of our proposed closed-loop system. Compared with the open-loop system, the results of this study demonstrate an improved degree of accuracy and a wider range of effectiveness.

Research on Optimization Algorithm of Single-block Train Formation Plan of Technical Station

The optimization of train formation plan is a large-scale combinatorial optimization problem, which is difficult to solve. This paper mainly studies the optimization algorithm of the single-block train formation plan. The corresponding mathematical model is established by consulting relevant literature, and a positive feedback search algorithm based on absolute conditions is proposed. First of all, the wagon flow that meets the absolute conditions directly runs through train flow without making other choices. For the wagon flow that does not meet the absolute conditions, select the target station to reach directly according to the probability. The probability of wagon flow selecting a station is calculated according to the pheromone of the wagon flow at the station. At the same time, a pheromone update strategy with positive feedback mechanism is proposed to make the search process converge. Finally, the feasibility of the algorithm and the necessity of introducing absolute conditions into the algorithm are verified by taking eight technical stations in the linear direction of the road network as examples.

Low-Rank Combinatorial Optimization and Statistical Learning by Spatial Photonic Ising Machine.

The spatial photonic Ising machine (SPIM) [13D. Pierangeli et al., Large-Scale Photonic Ising Machine by Spatial Light Modulation, Phys. Rev. Lett. 122, 213902 (2019).PRLTAO0031-900710.1103/PhysRevLett.122.213902] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. The primitive version of the SPIM, however, can accommodate Ising problems with only rank-one interaction matrices. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, it acquires the learning ability of Boltzmann machines. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions. Thus, the proposed model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.

The applications of hybrid approach combining exact method and evolutionary algorithm in combinatorial optimization

Abstract Combinatorial optimization problems have very important applications in information technology, transportation, economics, management, network communication, and other fields. Since the problem size in real-scenario application is in large-scale, the demand for real-time and efficient solving approaches increases rapidly. The traditional exact methods guarantee the optimality of the final solution, but these methods can hardly solve the problem in acceptable time due to extremely high computational costs. Heuristic approaches can find feasible solutions in a limited time, while these approaches cannot meet the demand of solution quality. In recent years, hybrid algorithms based on exact methods and heuristic algorithms show outstanding performance in solving large-scale combinatorial optimization problems. The hybridization not only overcomes the shortcomings from single algorithm but also fully utilizes the search ability for population-based approaches as well as the interpretability in exact methods, which promotes the application of combinatorial optimization in real-world problems. This paper reviews existing studies on hybrid algorithms combining exact method and evolutionary computation, summarizes the characteristics of the existing algorithms, and directs the future research.

A new hybrid-heuristic for large-scale combinatorial optimization: A case of quadratic assignment problem

Real world combinatorial optimization problems arise in very-large-scale. Solving such problems to optimality is impractical. In the past several decades, different heuristics and meta-heuristics have been proposed as solution procedure. In particular, to tackle the large-scale real applications, researchers have intelligently combined key components of competing methodologies to create superior solution procedures. In this study, we design a hybrid-heuristic (HH) using high-level solution algorithm framework that blends key components of three well-known meta-heuristics, scatter search, critical even tabu search, and genetic algorithm random keys, and applies to large-scale quadratic assignment problem (QAP). The HH has the potential to go beyond the goals of usual hybrid-heuristics, it potentially provides a framework for a self-adapted heuristic that can be applied to a wide range of problems with minimal inclusion of problem specific information. Extensive computational experiments applied to large-scale QAP instances from database of benchmark problems e.g., QAPLIB and taixxeyy collections, show that the proposed hybrid-heuristic (HH) provides an efficient approach to the large-scale QAP. The algorithm provides new best solutions for 61 out of 70 taixxeyy instances of large-scale QAP and finds the same best known solutions for QAPLIB and the 9 remaining instances from taixxeyy collections.

QAOA-in-QAOA: Solving Large-Scale MaxCut Problems on Small Quantum Machines

The design of fast algorithms for combinatorial optimization greatly contributes to a plethora of domains such as logistics, finance, and chemistry. Quantum approximate optimization algorithms (QAOAs), which utilize the power of quantum machines and inherit the spirit of adiabatic evolution, are approaches to tackle combinatorial problems with potential runtime speedups. However, hurdled by the limited quantum resources nowadays, QAOAs are infeasible to manipulate large-scale problems. To address this issue, here we revisit the MaxCut problem via the divide-and-conquer heuristic: seek the solutions of subgraphs in parallel and then merge these solutions to obtain the global solution. Because of the ${\mathbb{Z}}_{2}$ symmetry in MaxCut, we prove that the merging process can be further cast into a new MaxCut problem and thus be addressed by QAOAs or other MaxCut solvers. In view of this, we propose QAOA-in-QAOA (${\mathrm{QAOA}}^{2}$) to solve arbitrary large-scale MaxCut problems using small quantum machines. We also prove that the performance of ${\mathrm{QAOA}}^{2}$ is lower bounded with respect to the divide-and-conquer process. Experiment results illustrate that, under different graph settings, ${\mathrm{QAOA}}^{2}$ attains a competitive or even better performance over classical algorithms when the node count is around $2000$. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale combinatorial optimization problems.

THD Reduction for Permanent Magnet Synchronous Motor Using Simulated Annealing

Any nonlinear behavior of the system is analyzed by a useful way of Total Harmonic Distortion (THD) technique. Reduced THD achieves lower peak current, higher efficiency and longer equipment life span. Simulated annealing (SA) is applied due to the effectiveness of locating solutions that are close to ideal and to challenge large-scale combinatorial optimization for Permanent Magnet Synchronous Machine (PMSM). The parameters of direct torque controllers (DTC) for the drive are automatically adjusted by the optimization algorithm. Advantages of the PI-Fuzzy-SA algorithm are retained when used together. It also improves the rate of system convergence. Speed response improvement and harmonic reduction is achieved with SA-based DTC for PMSM. This mechanism is known to be faster than other algorithms. Also, it is observed that as compared to other algorithms, the projected algorithm yields a reduced total harmonic distortion. As a result of the employment of Space Vector Modulation (SVM) technique, the system is resistant to changes in motor specifications and load torque. Through MATLAB & Simulink simulation, the experiment is done and the performance is calculated for the controller.

A Large-Scale Combinatorial Many-Objective Evolutionary Algorithm for Intensity-Modulated Radiotherapy Planning

Intensity-modulated radiotherapy (IMRT) is one of the most popular techniques for cancer treatment. However, existing IMRT planning methods can only generate one solution at a time and, consequently, medical physicists should perform the planning process many times to obtain diverse solutions to meet the requirement of a clinical case. Meanwhile, multiobjective evolutionary algorithms (MOEAs) have not been fully exploited in IMRT planning since they are ineffective in optimizing the large number of discrete variables of IMRT. To bridge the gap, this article formulates IMRT planning into a large-scale combinatorial many-objective optimization problem and proposes a coevolutionary algorithm to solve it. In contrast to the existing MOEAs handling high-dimensional search spaces via variable grouping or dimensionality reduction, the proposed algorithm evolves one population with fine encoding for local exploitation and evolves another population with rough encoding for global exploration. Moreover, the convergence speed is further accelerated by two customized local search strategies. The experimental results verify that the proposed algorithm outperforms state-of-the-art MOEAs and IMRT planning methods on a variety of clinical cases.

ИНТЕЛЛЕКТУАЛЬНЫЙ АНАЛИЗ ДАННЫХ В УПРАВЛЕНИИ ПРЕДПРИЯТИЕМ НА ОСНОВЕ АЛГОРИТМА ИМИТАЦИИ ОТЖИГА

The article considers an analytical review of the annealing simulation algorithm for theproblem of efficient enterprise management. The optimization of the annealing simulation algorithmfor the problem of efficient enterprise management has been carried out. For the analysis ofcases, the optimization of the work schedule of workers in the organization was used. Establishedworker scheduling model with strong and weak constraints. The simulated annealing algorithm isused to optimize the strategy for solving the staff scheduling model. The simulated annealing algorithmis an algorithm suitable for solving large-scale combinatorial optimization problems. It alsoevaluates and obtains the optimal scheduling strategy. The simulated annealing algorithm has agood effect on the data mining of human resource management. Big data mining can help companiesconduct dynamic analysis in talent recruitment, and the talent recruitment plan is carried outin a quality and standard way to analyze the characteristics of various talents from many anglesand improve the level of human resource management. An algorithm has been developed that implementsthe operation of the annealing simulation algorithm. The simulated annealing algorithmmakes new decisions based on the Metropolis criterion, so in addition to making an optimizeddecision, it also makes a reduced decision in a limited range. The Metropolis algorithm is a samplingalgorithm mainly used for complex distribution functions. It is somewhat similar to the variancesampling algorithm, but here the auxiliary distribution function changes over time. Experimentalstudies have been carried out that show that a worker scheduling model based on strongand weak constraints is significantly better than a manual scheduling model, achieving an effectivebalance between controlling wage costs in an organization and increasing employee satisfaction.The successful application of a workforce scheduling model based on a simulated annealingalgorithm brings new insights and insights to solve large-scale worker scheduling problems.The results presented can serve as a starting point for studying personnel management systemsbased on data mining technology.

MEC-Based Dynamic Controller Placement in SD-IoV: A Deep Reinforcement Learning Approach

The flow fluctuations in the highly dynamic Internet of Vehicles (IoV) make the IoV difficult to provide reliable and scalable wireless network services for the emerging applications in the 5 G and beyond era. The software-defined networks (SDN) could feasibly manage and optimize the network according to the network load. Controller placement is a critical problem in SDN to achieve its robustness and flexibility with the changes of network status. Motivated by the advantages of SDN and Mobile-edge computing (MEC), this paper aims at enhancing the performance of IoV with the assistance of these two. Specifically, we consider a three-layer hierarchical SDN control plane for the IoV, where the SDN controllers are placed at the edge of networks. Under this framework, we investigate a multi-objective optimization problem on controller placement problem including delay, load balancing, and path reliability. To efficiently solve the formulated NP-hard problems, we develop an algorithm based on multi-agent deep Q-learning networks (MADQN) because of its advantages for large-scale combinatorial optimization. At last, we use multi-process technology to accelerate the operation of the algorithm, so as to complete the algorithm iteration faster. Numerical results show that the proposed methods achieve better performances than three baselines.

Convex relaxation for optimal fixture layout design

This article proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem; we relax it to a convex Semi-Definite Programming (SDP) problem by adopting sparse learning and SDP relaxation techniques. It can be solved efficiently by existing convex optimization algorithms and thus generates a near-optimal fixture layout. A real case study in the half-to-half fuselage assembly process indicates the superiority of our proposed algorithm compared to the current industry practice and state-of-art methods.

The incremental online k-means clustering algorithm and its application to color quantization

Color quantization is a common image processing operation with various applications in computer graphics, image processing, and computer vision. Color quantization is essentially a large-scale combinatorial optimization problem. Many clustering algorithms, both of hierarchical and partitional types, have been applied to this problem since the 1980s. In general, hierarchical color quantization algorithms are faster, whereas partitional ones produce better results provided that they are initialized properly. In this paper, we propose a novel partitional color quantization algorithm based on a binary splitting formulation of MacQueen’s online k-means algorithm. Unlike MacQueen’s original algorithm, the proposed algorithm is both deterministic and free of initialization. Experiments on a diverse set of public test images demonstrate that the proposed algorithm is significantly faster than two popular batch k-means algorithms while yielding nearly identical results. In other words, unlike previously proposed k-means variants, our algorithm addresses both the initialization and acceleration issues of k-means without sacrificing the simplicity of the algorithm. The presented algorithm may be of independent interest as a general-purpose clustering algorithm.

Optimizing Transport Logistics under Uncertainty with Simheuristics: Concepts, Review and Trends

Background: Uncertainty conditions have been increasingly considered in optimization problems arising in real-life transportation and logistics activities. Generally, the analysis of complex systems in these non-deterministic environments is approached with simulation techniques. However, simulation is not an optimization tool. Hence, it must be combined with optimization methods when our goal is to: (i) minimize operating costs while guaranteeing a given quality of service; or (ii) maximize system performance using limited resources. When solving NP-hard optimization problems, the use of metaheuristics allows us to deal with large-scale instances in reasonable computation times. By adding a simulation layer to the metaheuristics, the methodology becomes a simheuristic, which allows the optimization element to solve scenarios under uncertainty. Methods: This paper reviews the indexed documents in Elsevier Scopus database of both initial as well as recent applications of simheuristics in the logistics and transportation field. The paper also discusses open research lines in this knowledge area. Results: The simheuristics approaches to solving NP-hard and large-scale combinatorial optimization problems under uncertainty scenarios are discussed, as they frequently appear in real-life applications in logistics and transportation activities. Conclusions: The way in which the different simheuristic components interact puts a special emphasis in the different stages that can contribute to make the approach more efficient from a computational perspective. There are several lines of research that are still open in the field of simheuristics.

Solution of Multi-Crew Depots Railway Crew Scheduling Problems: The Chinese High-Speed Railway Case

This paper presents a novel mathematical formulation in crew scheduling, considering real challenges most railway companies face such as roundtrip policy for crew members joining from different crew depots and stricter working time standards under a sustainable development strategy. In China, the crew scheduling is manually compiled by railway companies respectively, and the plan quality varies from person to person. An improved genetic algorithm is proposed to solve this large-scale combinatorial optimization problem. It repairs the infeasible gene fragments to optimize the search scope of the solution space and enhance the efficiency of GA. To investigate the algorithm’s efficiency, a real case study was employed. Results show that the proposed model and algorithm lead to considerable improvement compared to the original planning: (i) Compared with the classical metaheuristic algorithms (GA, PSO, TS), the improved genetic algorithm can reduce the objective value by 4.47%; and (ii) the optimized crew scheduling plan reduces three crew units and increases the average utilization of crew unit working time by 6.20% compared with the original plan.