Large Problem Instances Research Articles

Scaling adaptive quantum simulation algorithms via operator pool tiling

Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wave functions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) calculation on a smaller instance of the problem using a large, but computationally inefficient, operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems. Published by the American Physical Society 2024

Enhanced methods for the weight constrained shortest path problem

AbstractThe classic problem of constrained pathfinding is a well‐studied, yet challenging, network optimization problem with a broad range of applications in various areas such as communication and transportation. The weight constrained shortest path problem (WCSPP), the base form of constrained pathfinding with only one side constraint, aims to plan a cost‐optimum path with limited weight/resource usage. Given the bi‐criteria nature of the problem (i.e., dealing with the cost and weight of paths), methods addressing the WCSPP have some common properties with bi‐objective search. This article leverages the recent state‐of‐the‐art techniques in both constrained pathfinding and bi‐objective search and presents two new solution approaches to the WCSPP on the basis of A* search, both capable of solving hard WCSPP instances on very large graphs. We empirically evaluate the performance of our algorithms on a set of large and realistic problem instances and show their advantages over the state‐of‐the‐art algorithms in both time and space metrics. This article also investigates the importance of priority queues in constrained search with A*. We show with extensive experiments on both realistic and randomized graphs how bucket‐based queues without tie‐breaking can effectively improve the algorithmic performance of exhaustive A*‐based bi‐criteria searches.

Improved cooperative Ant Colony Optimization for the solution of binary combinatorial optimization applications

AbstractBinary combinatorial optimization plays a crucial role in various scientific and engineering fields. While deterministic approaches have traditionally been used to solve these problems, stochastic methods, particularly metaheuristics, have gained popularity in recent years for efficiently handling large problem instances. Ant Colony Optimization (ACO) is among the most successful metaheuristics and is frequently employed in non‐binary combinatorial problems due to its adaptability. Although for binary combinatorial problems ACO can suffer from issues such as rapid convergence to local minima, its eminently parallel structure means that it can be exploited to solve large and complex problems also in this field. In order to provide a versatile ACO implementation that achieves competitive results across a wide range of binary combinatorial optimization problems, we introduce a parallel multicolony strategy with an improved cooperation scheme to maintain search diversity. We evaluate our proposal (Binary Parallel Cooperative ACO, BiPCACO) using a comprehensive benchmark framework, showcasing its performance and, most importantly, its flexibility as a successful all‐purpose solver for binary combinatorial problems.

Synthetic aperture radar image segmentation with quantum annealing

AbstractIn image processing, image segmentation is the process of partitioning a digital image into multiple image segments. Among state‐of‐the‐art methods, Markov random fields can be used to model dependencies between pixels and achieve a segmentation by minimising an associated cost function. Currently, finding the optimal set of segments for a given image modelled as a Markov random fields appears to be NP‐hard. The authors aim to take advantage of the exponential scalability of quantum computing to speed up the segmentation of synthetic aperture radar images. For that purpose, the authors propose a hybrid quantum annealing classical optimisation expectation maximisation algorithm to obtain optimal sets of segments. After proposing suitable formulations, the authors discuss the performances and the scalability of authors’ approach on the D‐Wave quantum computer. The authors also propose a short study of optimal computation parameters to enlighten the limits and potential of the adiabatic quantum computation to solve large instances of combinatorial optimisation problems.

Learning Based 2D Irregular Shape Packing

2D irregular shape packing is a necessary step to arrange UV patches of a 3D model within a texture atlas for memory-efficient appearance rendering in computer graphics. Being a joint, combinatorial decision-making problem involving all patch positions and orientations, this problem has well-known NP-hard complexity. Prior solutions either assume a heuristic packing order or modify the upstream mesh cut and UV mapping to simplify the problem, which either limits the packing ratio or incurs robustness or generality issues. Instead, we introduce a learning-assisted 2D irregular shape packing method that achieves a high packing quality with minimal requirements from the input. Our method iteratively selects and groups subsets of UV patches into near-rectangular super patches, essentially reducing the problem to bin-packing, based on which a joint optimization is employed to further improve the packing ratio. In order to efficiently deal with large problem instances with hundreds of patches, we train deep neural policies to predict nearly rectangular patch subsets and determine their relative poses, leading to linear time scaling with the number of patches. We demonstrate the effectiveness of our method on three datasets for UV packing, where our method achieves a higher packing ratio over several widely used baselines with competitive computational speed.

Phase‐coded radar waveform design with quantum annealing

AbstractThe Integrated Side Lobe Ratio (ISLR) problem the authors consider here consists in finding optimal sequences of phase shifts in order to minimise the mean squared cross‐correlation side lobes of a transmitted radar signal and a mismatched replica. Currently, ISLR does not seem to be easier than the general polynomial unconstrained binary problem, which is NP‐hard. In their work, the authors aim to take advantage of the scalability of quantum computing to find new optima, by solving the ISLR problem on a quantum annealer. This quantum device is designed to solve quadratic optimisation problems with binary variables (QUBO). After proposing suitable formulation for different instances of the ISLR, the authors discuss the performances and the scalability of their approach on the D‐Wave quantum computer. More broadly, their work enlightens the limits and potential of the adiabatic quantum computation for the solving of large instances of combinatorial optimisation problems.

Maximizing truck platooning participation with preferences

Truck platooning refers to trucks traveling in convoy with longitudinal proximity. By reducing aerodynamic drag, platooning cuts truck energy use and operating cost along with other benefits to the freight transportation system. This research proposes a platform-based platooning system to maximize the participation of truck platooning considering stability of the formed platoons that arises from truck preferences of platooning partners. Preference-based platooning is of both scientific interest and practical importance to the trucking sector, which is highly fragmented especially in the US. The preferences depend on the benefits of fuel saving and schedule adjustment to coordinate the time for platoon formation. The formed platoons are stable in the sense that no two trucks in two platoons want to break away from their current platoons and platoon with each other. Tackling this operation planning problem, the proposed system involves a platform interacting with individual trucks in a way that reduces truck communication and computation burdens, mitigates truck privacy concerns, and overcomes trucks misreporting private information. The central methodological investigation of the interactive process is on how to solve the Maximum Stable Truck Platooning Participation (MS-TPP) problem, for which a two-phase algorithmic approach is proposed. The underlying idea of this approach is to progressively reduce the lengths of truck preference lists, by eliminating truck pairs that do not affect the MS-TPP solution presence and separating trucks in odd rotations – which are key constructs in this approach – from the rest of the truck population. Theoretical properties and computational complexity of this two-phase algorithmic approach are investigated, along with a comparison with an integer programming approach and extensive numerical experiments in the context of a northern Illinois road network in the US. We find that the proposed two-phase algorithmic approach is very efficient compared to the integer programming approach in forming a maximum number of truck platoons while ensuring stability. In addition, the percentage of trucks that end up platooning by solving MS-TPP is much greater than using a greedy approach. The algorithmic approach is computationally scalable for solving large problem instances. The advantages of MS-TPP, in terms of the percentage of trucks in platooning and the average utility gain, become even more prominent as we deal with a larger system with more trucks.

An adaptive greedy heuristic for large scale airline crew pairing problems

A crew pairing represents a sequence of flight legs that constitute a crew work allocation, starting and ending at the same crew base. A complete set of crew pairings covers all flight legs in the timetable of an airline for a given planning horizon. That determines the rosters for the crew and their quality, since those pairings would potentially include layovers, deadheads and connection times which are the key factors which directly contribute to the operational crew costs. Considering that crew costs form the second largest bit in the overall operational cost, generating optimized crew pairings is a vital process for the airline companies. In this study, a score-based adaptive greedy heuristic and a genetic algorithm are presented for solving large scale instances of airline crew pairing problems. Both solution methods are applied to a set of real-world problem instances from Turkish Airlines which is one of the largest carriers in the world. The empirical results show that the proposed approaches are indeed capable of generating high quality solutions for crew pairing, even for the large scale problem instances.

The multi-vehicle dial-a-ride problem with interchange and perceived passenger travel times

The Dial-a-Ride Problem (DARP) introduced in the early 1980s is the NP-Hard optimization problem of developing the most cost-efficient vehicle schedules for a number of available vehicles that have to start from a depot, pick up and deliver a set of passengers, and return back to the same depot. DARP has been used in many modern applications, including the scheduling of demand-responsive transit and car pooling. This study departs from the original definition of DARP and it extends it by considering an interchange point where vehicles can exchange their picked-up passengers with other vehicles in order to shorten their delivery routes and reduce their running times. In addition to that, this study introduces the concept of generalized passenger travel times in the DARP formulation which translates the increased in-vehicle crowdedness to increased perceived passenger travel times. This addresses a key issue because the perceived in-vehicle travel times of passengers might increase when the vehicle becomes more crowded (i.e., passengers might feel that their travel time is higher when they are not able to find a seat or they are too close to each other increasing the risk of virus transmission or accidents). Given these considerations, this study introduces the Dial-a-Ride Problem with interchange and perceived travel times (DARPi) and models it as a nonlinear programming problem. DARPi is then reformulated to a MILP with the use of linearizations and its search space is tightened with the addition of valid inequalities that are employed when solving the problem to global optimality with Branch-and-Cut. For large problem instances, this study introduces a tabu search-based metaheuristic and performs experiments in benchmark instances used in past literature demonstrating the computation times and solution stability of our approach. The effect of the perceived passenger travel times to the vehicle running costs is also explored in extensive numerical experiments.

Multi-objective optimization of neural network with stochastic directed search

This work proposes a novel approach, the stochastic directed search, for optimizing deep neural networks framed as high-dimensional multi-objective problems which typically cannot be addressed with current methods. The proposed algorithm is based on the gradient-based predictor–corrector directed search method and it allows the efficient fine-tuning of a neural network (NN) without retraining the entire model. The contributions include the computation of the Jacobian using batches of data to account for GPU memory limitations, special routines for better approximating boundaries, and an early stopping criterion that limits the search space. Additionally, the proposed method scales well with the problem dimension given that it employs the Jacobian to steer the search in the objective space. The effectiveness of the algorithm is exemplified by fine-tuning a forecasting NN model, responsible for producing multi-horizon quantile forecasts of the S&P 500 Futures financial time series. The stochastic directed search optimizes the neural network in only 1.5% of the training time, i.e. 29.56 s, and the Pareto front obtained shows that variations of around 30% can be obtained for the objective with a degradation of only 5% in the loss function. When solving large problem instances with dimensions up to 240,000, the results show that it outperforms NSGA-II and NSGA-III by reducing function evaluations by a factor of 100, while increasing by more than 5% the hypervolume of Pareto fronts. Notably, this work showcases how a large NN model can be fine-tuned using a multi-objective framework.

Just-in-time scheduling problem with affine idleness cost

We study a single-machine scheduling problem which minimizes total earliness, tardiness and idleness costs. In this problem, n jobs with job-specific due dates and processing times need to be processed in a non-preemptive fashion. We assume that when the idle time between two jobs is strictly positive, an idleness cost will be generated which is affine in the idle time. A hybrid solution approach is designed by integrating a tailored dynamic programming (TDP) algorithm for the exact timing solution and a customized Genetic Algorithm with restarts and early discarding (GARED) as the sequencing heuristic. By bounding the number of segments of the optimal cost function, we show that the proposed TDP algorithm has a low time complexity of O(n2) despite the non-convexity of the idleness cost function. In GARED, we utilize the monotonicity in the optimal cost in TDP to design a fast-screening scheme called Early Discarding which identifies and abandons an unpromising sequencing solution by evaluating only a short starting sub-sequence. Restarts are allowed to make the algorithm more robust in the case of premature local convergence of one evolutionary trial. Experimental results show that GARED significantly outperforms the basic elitist GA with or without restarts under most problems tested. Our hybrid method also scales well to large problem instances with n=300 and achieves similar or better performance compared to an exact algorithm in the literature, but the latter only applies to problems with integer-valued time parameters and no idleness cost in between the jobs.

Route planning for last-mile deliveries using mobile parcel lockers: A hybrid q-learning network approach

Mobile parcel lockers (MPLs) have been recently proposed by logistics operators as a technology that could help reduce traffic congestion and operational costs in urban freight distribution. Given their ability to relocate throughout their area of deployment, they hold the potential to improve customer accessibility and convenience. In this study, we formulate the Mobile Parcel Locker Problem (MPLP), a special case of the Location-Routing Problem (LRP) which determines the optimal stopover location for MPLs throughout the day and plans corresponding delivery routes. A Hybrid Q-Learning-Network-based Method (HQM) is developed to resolve the computational complexity of the resulting large problem instances while escaping local optima. In addition, the HQM is integrated with global and local search mechanisms to resolve the dilemma of exploration and exploitation faced by classic reinforcement learning (RL) methods. We examine the performance of HQM under different problem sizes (up to 200 nodes) and benchmarked it against the exact approach and Genetic Algorithm (GA). Our results indicate that HQM achieves better optimisation performance with shorter computation time than the exact approach solved by the Gurobi solver in large problem instances. Additionally, the average reward obtained by HQM is 1.96 times greater than GA’s, which demonstrates that HQM has a better optimisation ability. Further, we identify critical factors that contribute to fleet size requirements, travel distances, and service delays. Our findings outline that the efficiency of MPLs is mainly contingent on the length of time windows and the deployment of MPL stopovers. Finally, we highlight managerial implications based on parametric analysis to provide guidance for logistics operators in the context of efficient last-mile distribution operations.

A mixed-signal oscillatory neural network for scalable analog computations in phase domain

Digital electronics based on von Neumann’s architecture is reaching its limits to solve large-scale problems essentially due to the memory fetching. Instead, recent efforts to bring the memory near the computation have enabled highly parallel computations at low energy costs. Oscillatory neural network (ONN) is one example of in-memory analog computing paradigm consisting of coupled oscillating neurons. When implemented in hardware, ONNs naturally perform gradient descent of an energy landscape which makes them particularly suited for solving optimization problems. Although the ONN computational capability and its link with the Ising model are known for decades, implementing a large-scale ONN remains difficult. Beyond the oscillators’ variations, there are still design challenges such as having compact, programmable synapses and a modular architecture for solving large problem instances. In this paper, we propose a mixed-signal architecture named Saturated Kuramoto ONN (SKONN) that leverages both analog and digital domains for efficient ONN hardware implementation. SKONN computes in the analog phase domain while propagating the information digitally to facilitate scaling up the ONN size. SKONN’s separation between computation and propagation enhances the robustness and enables a feed-forward phase propagation that is showcased for the first time. Moreover, the SKONN architecture leads to unique binarizing dynamics that are particularly suitable for solving NP-hard combinatorial optimization problems such as finding the weighted Max-cut of a graph. We find that SKONN’s accuracy is as good as the Goemans–Williamson 0.878-approximation algorithm for Max-cut; whereas SKONN’s computation time only grows logarithmically. We report on Weighted Max-cut experiments using a 9-neuron SKONN proof-of-concept on a printed circuit board (PCB). Finally, we present a low-power 16-neuron SKONN integrated circuit and illustrate SKONN’s feed-forward ability while computing the XOR function.

Loads scheduling for demand response in energy communities

This paper focuses on optimizing the collective self-consumption rate in energy communities by scheduling members’ loads. The community remains connected to the public grid and comprises prosumers, traditional consumers, and distributed storage units. Prosumers can exchange their energy with the public grid or other members. The proposed strategy aims at implementing a Demand Side Management program taking advantage of controllable loads’ characteristics. A MILP formulation of the problem allows, on the one hand, to give the optimal planning for electrical devices’ operations. On the other hand, it provides optimal solutions for managing the storage units, peer-to-peer exchanges, and interactions with the public grid to minimize the energy flows from the public grid over time. However, this MILP only allows for solving small problem instances. Thus, we develop a column generation-based heuristic for large problem instances. Our numerical experiments based on real data collected in the south of France show that joining an energy community saves money on energy bills and reduces the total energy drawn from the primary grid by at least 15%.

Block-based state-expanded network models for multi-activity shift scheduling

This paper presents new mixed-integer linear programming formulations for multi-activity shift scheduling problems (MASSP). In these formulations, the rules governing shift feasibility are encoded in block-based state-expanded networks in which nodes are associated with states and arcs represent assignments of blocks of work or break periods inducing state transitions. A key advantage of these formulations is that for the anonymous MASSP in which all employees are considered as equal only a single network with integer flow variables is needed as long as the network encodes all shift composition rules. A challenging aspect is that the networks can become very large, yielding huge models that are hard to solve for large problem instances. To address this challenge, this paper proposes two exact modeling techniques that substantially reduce the size of the model instances: First, it introduces a set of aggregate side constraints enforcing that an integer flow solution can be decomposed into paths representing feasible shifts. Second, it proposes to decouple the shift composition from the assignment of concrete activities to blocks of work periods, thereby removing a large amount of symmetry from the original model. In a computational study with two MASSP instance sets from the literature dealing with shift scheduling problems, we demonstrate the effectiveness of these techniques for reducing the both size of the model instances and the solution time: We are able to solve all instances, including more than 70 previously open instances, to optimality–the vast majority of them in less than 30 min on a notebook computer.

Train stop scheduling problem: An exact approach using valid inequalities and polar duality

Consider the problem of minimizing the number of train stops on a particular rail line. The objective is to assign passengers of each origin-destination pair to different trains in such a way that train capacity and passenger demand constraints are satisfied with minimal stoppages. The literature refers to this problem as the train stop scheduling problem. The problem has been extensively studied for decades, yet an exact solution approach has not been proposed. This paper proposes several valid inequalities to strengthen the mixed-integer programming formulation and solve the problem exactly in a reasonable amount of CPU time. The concept of polar duality has been utilized to find more complex valid inequalities which may be hard to find otherwise. Despite the problem’s high practical relevance, valid inequalities for the problem have not yet been studied in the literature. An aggregation procedure has been proposed to solve large size problem instances exactly. Computational study demonstrate the efficacy of the proposed valid inequalities.

Bilevel large neighborhood search for the electric autonomous dial-a-ride problem

The electric autonomous dial-a-ride problem (E-ADARP) represents a challenging and practically relevant extension of the dial-a-ride problem, which takes electric vehicle charging into account. It introduces battery constraints and the option to recharge vehicles at different charging stations. The present paper proposes a bilevel large neighborhood search approach (BI-LNS) for the E-ADARP. In the outer level of the proposed approach, charging sessions are inserted in the routes of vehicles and in the inner level, the pick-up and drop-off locations of the requests are inserted. In numerical experiments, it is shown that BI-LNS is able to outperform existing approaches on a number of common E-ADARP benchmark instances. Furthermore, the scalability of BI-LNS is evaluated on a set of large problem instances. The results show that the proposed approach is able to find feasible solutions within five minutes for problem instances with up to a few thousand transportation requests.

A heuristic approach to the stochastic capacitated single allocation hub location problem with Bernoulli demands

Hubs are critical components of transportation and distribution systems, and hub networks play a special role in freight and passenger transportation services worldwide. This paper studies a capacitated single allocation hub location problem with Bernoulli demands. Since the origin-destination (OD) demands are stochastic in nature, and the nodes are allocated to hubs before knowing their realized values, the actual total demand allocated to each hub is uncertain. Therefore, demand can exceed the capacity of hubs, rendering a need for outsourcing. The problem is studied under two distinct outsourcing policies, namely the facility and customer outsourcing. Mathematical models are developed for each case as two-stage stochastic programs. Deterministic equivalent formulations are obtained for problems, assuming a homogeneous demand distribution for all OD pairs. A Tabu Search-based algorithm is presented as a solution approach to deal with large problem instances. Extensive computational tests demonstrate the outstanding performance of the developed models and the metaheuristic procedure in terms of solution quality and computational time. The relevance of using stochastic programming approach for the problems is demonstrated via computational results. This study also reports solutions for problems with 200 nodes for the first time.

Rolling Horizon Based Temporal Decomposition for the Offline Pickup and Delivery Problem with Time Windows

The offline pickup and delivery problem with time windows (PDPTW) is a classical combinatorial optimization problem in the transportation community, which has proven to be very challenging computationally. Due to the complexity of the problem, practical problem instances can be solved only via heuristics, which trade-off solution quality for computational tractability. Among the various heuristics, a common strategy is problem decomposition, that is, the reduction of a large-scale problem into a collection of smaller sub-problems, with spatial and temporal decompositions being two natural approaches. While spatial decomposition has been successful in certain settings, effective temporal decomposition has been challenging due to the difficulty of stitching together the sub-problem solutions across the decomposition boundaries. In this work, we introduce a novel temporal decomposition scheme for solving a class of PDPTWs that have narrow time windows, for which it is able to provide both fast and high-quality solutions. We utilize techniques that have been popularized recently in the context of online dial-a-ride problems along with the general idea of rolling horizon optimization. To the best of our knowledge, this is the first attempt to solve offline PDPTWs using such an approach. To show the performance and scalability of our framework, we use the optimization of paratransit services as a motivating example. Due to the lack of benchmark solvers similar to ours (i.e., temporal decomposition with an online solver), we compare our results with an offline heuristic algorithm using Google OR-Tools. In smaller problem instances (with an average of 129 requests per instance), the baseline approach is as competitive as our framework. However, in larger problem instances (approximately 2,500 requests per instance), our framework is more scalable and can provide good solutions to problem instances of varying degrees of difficulty, while the baseline algorithm often fails to find a feasible solution within comparable compute times.

Proactive project scheduling using GPU-accelerated simulations under uncertainty environment

ABSTRACT Numerous scheduling generation and revision methods have been developed for project scheduling under uncertain environments in previous research. However, most of these methods have yet to address a practical project with more than a hundred activities involving multiple decisions in scheduling generation and execution phases. This study proposes a local search-based scheduling method that comprehensively evaluates a baseline schedule considering decision-making in both the planning and execution phases. The proposed method performs simulations to evaluate schedule robustness accurately using GPU to find a locally optimal solution for large problem instances in a reasonable time. A series of numerical experiments demonstrate that the proposed method can generate a robust schedule for large-scale project instances. These results conclude that the proposed method utilizing the simulation-based evaluation and the GPU acceleration is effective and provide insight into developing a scheduling method for practical projects.