Gurobi Solver Research Articles

Location–allocation problem in the emergency logistics system considering lateral transshipment strategy

This paper explores the problem of designing an efficient emergency logistics system while considering lateral transshipment strategy. Firstly, a two-stage mixed-integer programming model is proposed to characterize the location–allocation problem in an emergency logistics system with the aim of minimizing the total cost. Secondly, we propose an improved Benders decomposition framework for solving the emergency logistics system model. The numerical results reveal that our algorithm can find the optimal solution efficiently for large-scale instances, outperforming the commercial programming solver Gurobi. Finally, using Poyang Lake in China as a case study, we demonstrate that the lateral transshipment strategy can reduce the total cost of the emergency logistics system by 8.3% through comparing with the one without considering the lateral transshipment strategy. At the same time, we argue that the equity factor prevents the affected people from being evacuated to more distant shelters. The contribution of our work can be summarized as follows: an improved Benders decomposition algorithm is developed to investigate the optimal design of location–allocation strategy in the three-level emergency logistics network, with the consideration of lateral transshipment strategy and equity factor.

High-speed train timetable optimization based on space–time network model and quantum simulator

Timetable scheduling is a combinatorial optimization problem that presents formidable challenges for classical computers. This paper introduces a pioneering methodology for addressing the high-speed train timetabling problem through quantum computing. Initially, a comprehensive binary integer programming model, grounded in the space–time network, is proposed (M1). To manage the intricacy of model M1, a knapsack problem reformulation is employed to establish a simplified binary integer programming model (M2). Both M1 and M2 are subsequently converted into quadratic unconstrained binary optimization (QUBO) models to harness the potential of quantum computing. Several techniques, including the Gurobi solver, simulated annealing, and the coherent Ising machine (CIM) quantum simulator, are deployed to solve the model across four distinct scenarios of varying complexity. The findings indicate that CIM quantum simulator outperforms the simulated annealing method in terms of solution quality for medium-scale problems.

Research on the scheduling method of ground resource under uncertain arrival time

We present a two-stage scheduling approach including proactive and reactive scheduling to solve the ground resource scheduling problem with uncertain arrival time. In the first stage, an integer programming model is constructed to minimize the delay and transfer costs. After solving this model, we obtain a baseline scheduling plan that considers the service arrival time uncertainty. In the second stage, the feasibility of the subsequent benchmark plan is evaluated based on the current state of the services and resources. The reactive scheduling model is enabled when trigger conditions are met. Moreover, an improved adaptive large neighborhood search is designed to solve the proactive scheduling model effectively. Real data from an international airport in South China is used as a test case to compare different scheduling strategies. The results show that it is difficult to handle the uncertainty of the problem with the benchmark plan that simply considered buffer time. Compared with rolling time-domain scheduling, the average transfer cost of the scheduling strategy proposed in this paper increased slightly, but the average service delay cost can be reduced significantly. Algorithm-wise, instances of different scales are designed to verify the effectiveness of the improved adaptive large neighborhood search algorithm. The efficiency of the algorithm scheme is better than that of the Gurobi solver scheme in medium to large-scale problems. Therefore, the forward and reactive strategies can better handle the uncertainty of airport ground protection services as they can simultaneously guide the allocation and utilization of airport ground protection resources.

Optimal scheduling of a microgrid with power quality constraints based on demand side management under grid-connected and islanding operations

Power quality (PQ) issues are direct consequences of integrating power electronics components and non-linear loads into microgrids. These issues can also be triggered by an unbalanced loading in the microgrid. Certainly, they affect the daily operation scheduling of the microgrid. This paper proposes an optimal harmonic power flow (OHPF) framework for the daily optimal scheduling of a grid-connected microgrid, which is constructed by combining the optimization formulation and harmonic power flow (HPF). Within the framework, PQ is evaluated by observing three indices including voltage magnitude, voltage total harmonic distortion (THDV), and voltage unbalance factor (VUF). A non-iterative mitigation scheme based on demand side management (DSM) is proposed to avoid PQ indices violations and is integrated into the optimization formulation part of the OHPF as a set of load constraints. The proposed constraints allow a flexible combination of different DSM actions including load shedding and interphase load transfer (ILT). Furthermore, the constraints to limit voltage magnitude, voltage THD, and VUF are integrated into the formulation in the form of penalty functions. The software implementation of the proposed OHPF involves Julia-based JuMP.jl and Gurobi solver for optimization part and OpenDSS for harmonic load flow part. The effectiveness of the proposed framework is tested using a modified IEEE 37-bus feeder for different load fluctuations, which allow different combinations of PQ indices violations. The assessment involves both normal and intentional islanding conditions. The results demonstrate that, under different random events, the proposed framework can avoid the violation of PQ indices limits in most cases without adding an excessive computational burden to the original optimization and harmonic load flow algorithms.

An adaptive large neighborhood search for the robust rig routing

In the oil and gas industry, there is a need for constructing auxiliary maintenance and storage buildings nearby exploration sites. As the initial stage for such constructing purposes, it is required to drill wells for construction piles. To this end, there is a fleet of mobile drilling rigs traveling from one exploration site to another, performing the work on drilling wells. For each site, we have a time window for completing all the work on drilling. To complete all the work among all the exploration sites in time, it may be necessary to allow several drilling rigs to perform work at the same site. Yet, in the real world, unforeseen circumstances can affect drilling time, and that, if disregarded, can lead to a disruption of the work plan. Thus, in this problem, we maximize possible deviations of drilling times from expected values when there is still a feasible solution to perform all well-drilling requests in time. At the same time, total traveling costs must be no more than a given threshold. It is a so-called threshold robustness approach. The described Drilling Rig Routing Problem (DRRP) differs from other well-studied variants of Vehicle Routing Problem (VRP) in that the work splitting affects the service time. There is a limited number of papers dealing with such problems and no papers about the robust formulation for them. This research proposes a mathematical model for the novel formulation of the DRRP with uncertainties and an Adaptive Large Neighborhood Search (ALNS) algorithm to solve it. The destruction operators work either at the route, customer, or visit level. The reconstruction operators take into account a possibility to change the work partition. Computational results for the algorithm and Gurobi solver show the dominance of the ALNS scheme for medium- and large-sized instances.

Integrated optimization of production scheduling and maintenance planning with dynamic job arrivals and mold constraints

Effective management of production often requires harmonizing maintenance and production activities. However, decsions on production scheduling and machine maintenance are usually made independently, leading to potential overlaps and inefficiencies. This paper joinly investigates the production scheduling and maintenance planning for a production machine subject to different types of jobs that arrive randomly. A unique emphasis is placed on the prerequisite of loading specific molds prior to job execution, an element often overlooked in previous studies. Maintenance considerations employ the reliability/availability framework. The overarching goal is the creation of an integrated schedule that minimizes the weighted sum of total costs and the machine's maximum unavailability. To address this intricate challenge, a novel hybrid differential evolution and genetic algorithm (DE-GA) is proposed, complemented by a solution refinement strategy. Performance evaluations indicate that DE-GA methodology consistently outperforms Gurobi solver and four other prevalent algorithms across different test instances.

Integrated Planning for Depot Location and Line Planning Problems in the Intercity Railway Network with Passenger Demand Uncertainty

In this study, we present a mathematical model and solution approach for addressing the robust integrated intercity railway depot location and line planning problem (RIDLLPP), which encompasses the initial two stages of the railway planning process. Our primary objective is to identify depot locations that exhibit robustness across a range of likely future scenarios, and this is achieved by incorporating line planning decisions. The model focuses on five critical strategic determinations, namely the depot location, depot storage capacity, line operation, passenger assignment, and fleet allocation. To tackle this complex problem, we propose an iterative solution framework that combines the Differential Evolution (DE) algorithm with improved rounding heuristics (DE-IRH). To evaluate the effectiveness of our framework, we conduct a comparative analysis with the Gurobi solver using multiple medium-sized artificial instances. The results demonstrate that our proposed framework achieves an optimality gap of 4.87% while requiring less computational time. Furthermore, we validate the robustness of the model’s location choices across various input scenarios, thereby providing valuable insights for transportation planning agencies and railway companies that can inform their decision-making processes.

Joint scheduling of AGVs and parallel machines in an automated electrode foil production factory

In recent years, the automated guided vehicle (AGV) scheduling problem and parallel machine scheduling problem (PMSP) in workshops have become two hot topics in the field of operational research. In practical production, the two problems are closely related and coupled, and both play important roles in manufacturing systems. However, in the literature, the two problems are often addressed separately, which decreases the efficiency of manufacturing systems to a great degree. Therefore, this paper studies the joint scheduling problem of AGV and parallel machines in a production process of automatic electrode foil. Taking makespan as the optimization objective, a mixed-integer linear programming model is established and verified by the GUROBI solver. A discrete gray wolf optimization algorithm is proposed to solve the AGV-PMSP. An improved NEH heuristic is used to propose the quality of the initial solution. Six neighborhood operators are used to improve the exploration capabilities of the proposed algorithm. A theorem is proved to improve computational efficiency. The performance of the proposed algorithm is verified using comprehensive simulation experiments.

Piecewise Linear Approximation-Driven Primal SVM Approach for Improved Iris Classification Efficiency

Classification, a crucial aspect of machine learning, revolves around the meticulous analysis of data. However, the complexity of diverse life forms on Earth poses a challenge in distinguishing species that share similar attributes. The iris flower, with its subspecies exemplifies this challenge. The aim of the paper is to develop a methodology that not only enhances classification accuracy but also effectively addresses computational efficiency, facilitating faster and more practical categorization of iris patterns. This novel approach named Piecewise Linear Approximation based SVM (PLA-SVM) is applied to flower species classification and is benchmarked against alternative machine learning techniques. Implementation is carried out utilizing MATLAB – GUROBI interface of and GUROBI Solver. The performance metrics such as accuracy, precision, F1 score and ROC – AUC Curve are used to compare proposed algorithm performance. This comprehensive analysis enables a comparative study of diverse algorithms, ultimately validating the proposed PLA-SVM technique using the Iris dataset. The numerical implementation results shows that the PLASVM outperforms the existing standard classifiers in terms of different performance matrices.

Joint Optimal Train Rescheduling and Passenger Flow Control for Speed Limit and High-Demand Scenarios of Urban Rail Transits

In the operation of urban rail transits, train delays occur frequently, and emergency management is one of the key factors to ensure the service quality. For speed limit scenarios with high demand, this paper takes the train running in the restricted manual (RM) mode in the speed limit zone as an example and discusses a coping method by jointing train rescheduling and passenger flow control. With the goal of maximizing the number of passengers served and minimizing total train delay, a nonlinear optimization model is constructed by taking the train operation-related requirements and passenger flow control-related indicators as constraints, and the model is reformulated to a mixed-integer programming (MIP) model with quadratic constraints, which can be solved by the Gurobi solver. In order to obtain effective solutions faster, a two-stage approach is discussed, which first obtains a rescheduling timetable and then dynamically adjusts the requirement of boarding equalization to obtain the passenger flow control scheme. The validity of the model and the solution approach are discussed with the help of numerical experiments. The results suggest that the model and solution approach are feasible. When the number of trains is fixed, the reasonable implementation of passenger flow control will help to increase the number of passengers served, and the pursuit of a higher equalization of boarding is not conducive to the number of passengers served and the full utilization of transport capacity. The two-stage approach has certain advantages over the direct computing method. The methods in this paper have a guiding value for emergency decision-making in similar delay scenarios.

Shared travel demand forecasting and multi-phase vehicle relocation optimization for electric carsharing systems

ABSTRACT Electric shared mobility is flourishing in urban transportation. However, the problem of uneven vehicle distribution and untimely vehicle charging hampers user trip experience and system operation efficiency. To overcome these challenges, this study proposed a multi-phase vehicle relocation optimization approach for one-way station-based carsharing systems. In phase one, a micro-level shared travel demand forecasting model was developed to capture the number of orders in the short-term future. In phase two, stations were divided into different categories based on the results of user travel demand forecast. In phase three, the minimization of driving mileage and carbon emissions was taken as the optimization objective, and a solution method combining Gurobi solver and charging priority ranking was designed. Finally, the effectiveness and advantages of the proposed model and algorithm were comprehensively validated through a case study using real passenger orders and geographic data from the city of Shanghai, China.

A simulated annealing with variable neighborhood descent approach for the heterogeneous fleet vehicle routing problem with multiple forward/reverse cross-docks

With a greater awareness of the challenges regarding environmental, societal, political, and economic factors, where reverse logistics has become a significant part of supply chain networks, this paper presents an integrated forward and reverse logistics network, named the Heterogeneous Fleet Vehicle Routing Problem with Multiple Forward/Reverse Cross-Docks (HF-VRPMFRCD). We consider a heterogeneous fleet of vehicles with different loading capacities and transportation costs. We also consider multiple cross-docks with two different operations: forward and reverse processes. The former focuses on delivering the demand from suppliers to customers, while the latter aims at returning unsold products from customers to suppliers. We propose a Simulated Annealing with Variable Neighborhood Descent (SAVND) algorithm for solving HF-VRPMFRCD, where Variable Neighborhood Descent (VND) is a local search heuristic embedded in the framework of Simulated Annealing (SA). SAVND outperforms the state-of-the-art algorithm in solving the Heterogeneous Fleet Vehicle Routing Problem with Multiple Cross-Docks (HF-VRPMCD), where the VND heuristic significantly improves the quality of solutions. For HF-VRPMFRCD benchmark instances, SAVND provides optimal solutions for small-scale instances and better solutions than those of the GUROBI solver for remaining larger instances. Lastly, we present and discuss the benefits of integrating the forward and reverse processes.

Solving the incremental graph drawing problem by multiple neighborhood solution-based tabu search algorithm

With the advent of the era of big data, more and more complex networks and knowledge based systems require data visualization for analysis and presentation, where graphs have become a standard representation model. Graph drawing addresses the problems of constructing geometric representations of graphs to make them easy to analyze. In this paper we aim to reduce the edge crossing number in the context of the incremental graph drawing problem (IGDP), in which we want to preserve the layout of a graph over successive drawings to present complex networks or knowledge-based systems. Specifically, we propose a metaheuristic algorithm called multiple neighborhood solution-based tabu search (MNSB-TS) by combining a solution-based tabu strategy and a multiple neighborhood structure for solving the incremental graph drawing problem. Our MNSB-TS approach introduces four neighborhood operators to accompany the solution-based tabu strategy for determining the tabu status of each neighbor solution. Extensive computational experiments on public benchmark instances demonstrate that the proposed MNSB-TS is highly competitive in comparison with the state-of-the-art heuristics and the exact optimization solver Gurobi. Key components of the approach are analyzed to evaluate their impact on algorithm performance and learn which search mechanisms are better suited for incremental graph drawing.

Repositioning shared bikes under low-carbon policies

Low-carbon policies implemented by the Chinese government have a significant impact on third-party logistics, particularly for bike-sharing operators. This study investigated the static bike repositioning problem under low-carbon policies. Repositioning shared bikes under low-carbon policies such as emission cap, carbon trading, carbon offset, and carbon tax requires strict emission limitations and complicated routing plans. Therefore, a mixed-integer linear programming (MILP) model was formulated for the integrated planning of vehicle routes and bike allocation, aiming to minimize the repositioning cost and total imbalance penalty. An improved variable neighborhood search (IVNS) is proposed to solve this problem. The algorithm includes a route generation strategy heuristic and an improved neighborhood search operator for optimizing the route design, and a greedy heuristic for tackling loading and unloading instructions along the route. Numerical experiments show that (i) the proposed IVNS algorithm outperforms the GUROBI solver and existing method in striking a balance between solution quality and computational time; and (ii) the carbon trading policy is more flexible, not only effectively reducing emissions but also encouraging the further development of the bike-sharing industry.

Optimal Pole-Swapping in Bipolar DC Networks With Multiple CPLs Using an MIQP Model

This express brief presents a mixed-integer quadratic programming (MIQP) model to address the problem of optimal pole-swapping in asymmetric bipolar DC networks. The exact mixed-integer nonlinear programming model is convexified by using two stages. Using Taylor’s series expansion, the first stage corresponds to linearizing the hyperbolic relationship between voltage and powers in the constant power loads. The second stage applies the concept of the big-M number in order to obtain a linear equivalent for the product between binary and continuous variables. The proposed MIQP model is solved using the MATLAB programming environment, with the convex disciplined tool known as CVX and the Gurobi solver. Numerical results in the 21-and 85-bus grids demonstrate the effectiveness of the proposed MIQP formulation when compared to combinatorial optimization methods. The MIQP model ensures reductions of about 3.7609 and 49.7928kW in the total grid power losses for the 21-and 85-bus grids, respectively, when the neutral wire is assumed to be floating in all the nodes of the network except for the substation bus.

Multi-objective solution and decision-making framework for coordinating the short-term hydropeaking-navigation-production conflict of cascade hydropower reservoirs

The transformation of energy structure motivates hydropower to participate in peak shaving operations for grid stability, which conflicts with the multiple uses of cascade hydropower reservoirs. To coordinate the principal contradictory tasks of peak shaving, ship navigation, and power generation in day-ahead scheduling, a mixed integer linear programming model for the short-term multi-objective optimal scheduling is constructed. Specifically, a novel power release-based indicator is adopted to describe the navigation objective, while the minimization of the peak-valley difference of the residual load and the total water released are taken as the other two objective functions. Constraint aggregation and rectangular meshing methods are employed to handle the challenging nonlinear and nonconvex constraints. Subsequently, the Normalized Normal Constraint method, integrated with the mathematical optimization solver Gurobi, generates a set of well-distributed Pareto solutions, each representing a scheduling scheme. Finally, the Combined Weighting - Technique for Order Preference by Similarity to Ideal Solution is utilized as a decision-maker to trade off and determine a compromise solution for final implementation. Case studies on the cascade hydropower reservoirs of the Wujiang River in China demonstrate that the proposed model can adequately characterize the demands of various stakeholders, and the suggested framework can obtain an even and extensive Pareto front, mediate conflicts, and make reasonable decisions. Compared to the original peak-shaving scheme, the finalized compromise scheme reduces the peak-shaving effect by just 27.82% but offers simultaneous boosts of 96.54% in navigation benefits and 10.88% in power generation benefits. Consequently, the presented framework can be a promising alternative for conflict resolution of cascade hydropower reservoirs.

Waste Collection Optimisation: A Path to a Green and Sustainable City of Makkah

Background: Saudi Arabia is a leading country endorsing a sustainable future, from policymaking and investment to infrastructure development. One of the rising concerns in Saudi Arabia's Vision 2030 is solid waste management, especially in Makkah. The Solid Waste Collection Problem (SWCP) refers to the route optimisation of waste collection trucks visiting containers across various locations. Manually generated routes might contain some mistakes, and constructing and revising designed solutions can take a long time. Thus, there is a need to find optimal and fast solutions to this problem. Solving this problem demands tackling numerous routing constraints while aiming to minimise the operational cost. Since solid waste has a significant impact on the environment, reducing fuel consumption must be an objective. Methods: Thus, a mixed-integer programming model is proposed in this paper while using the time-oriented nearest neighbour heuristic. The goal is to investigate their performance on nine existing instances of SWCP in the city of Makkah. The proposed model is implemented in the Gurobi solver. The time-oriented nearest neighbour heuristic constructs the initial solution and is then re-optimised using Google OR-tools. Results: Using the greedy method to construct a solution for this problem generated better solutions when compared to the results obtained without the greedy method. Computational times are also improved by 55.7% on the problem instances. Conclusions: The findings confirm the competitive performance of the proposed method in terms of computational times and solution quality.

Upward scalable vehicle routing problem of automobile inbound logistics with pickup flexibility

Motivated by the inbound logistics of a famous automobile manufacturing company, we introduce the upward scalable vehicle routing problem (for order pickup) with time windows (USVRPTW), where the pickup from each supplier can be adjusted upward by a certain degree (pickup flexibility) based on the order volume, thus increasing the vehicle utilization and reducing logistics cost. We solve the USVRPTW exactly by a branch-and-price algorithm, where the flexibility affects the pricing problem, leading to the elementary shortest path problem having to consider resource allocation except the resource constraints. The consideration of resource allocation adds many new properties to the shortest path problem, based on which we design a tree search algorithm. We develop a heuristic algorithm based on the bipartite graph to generate initial columns for the column generation (CG) process. The algorithm can also be adopted as an efficient method for solving large-scale problems due to its ability to find near-optimal solutions quickly. We also propose the penalty stabilization method and the drill-down strategy to accelerate CG. Numerical experiments show that our designed branch-and-price algorithm outperforms the commercial solver Gurobi. The efficiency of the tree search algorithm, the heuristic algorithm, and the CG acceleration methods is also verified. Real-data experiments illustrate that the low increase in driving cost can significantly improve vehicle utilization, proving the significance of flexibility. We then provide management insights to reveal that adopting the proposed flexibility mechanism can reduce logistics cost.

The Electric Vehicle Routing Problem with Time Windows, Partial Recharges, and Parcel Lockers

This paper presents an extension of the Electric Vehicle Routing Problem with Time Windows and Partial Recharges (EVRPTW-PR), which incorporates the use of parcel lockers as a delivery method (i.e., self-pickup method). This variant, named the electric vehicle routing problem with time windows, partial recharges, and parcel lockers (EVRPTW-PR-PL), focuses on minimizing delivery costs by employing a homogeneous fleet of electric vehicles (EVs) and providing two delivery methods for serving customers: home delivery and self-pickup methods. We derive a mathematical formulation and propose an adaptive large neighborhood search (ALNS) algorithm to address EVRPTW-PR-PL. Moreover, in ALNS, the solution representation is constructed to handle the assignment of delivery methods. The performance of our proposed ALNS algorithm is evaluated by solving EVRPTW-PR benchmark instances. Finally, the results of EVRPTW-PR-PL obtained by using the GUROBI solver and our ALNS algorithm are provided, accompanied by managerial insights on the implementation of parcel lockers.

Optimizing the Production of Test Vehicles Using Hybrid Constrained Quantum Annealing

Optimization of pre-production vehicle configurations is one of the challenges in the automotive industry. Given a list of tests requiring cars with certain features, it is desirable to find the minimum number of cars that cover the tests and obey the configuration rules. In this paper, we model the problem in the framework of satisfiability and solve it utilizing the newly introduced hybrid constrained quadratic model (CQM) solver provided by D-Wave. The problem definition is based on the “Optimizing the Production of Test Vehicles” use-case given in the BMW quantum computing challenge. We formulate a constrained quadratic model for the problem and use a greedy algorithm to configure the cars. We benchmark the results obtained from the CQM solver with the results from the classical solvers like coin-or branch and cut and Gurobi solver. We conclude that the performance of the CQM solver is comparable to the classical solvers in optimizing the number of test vehicles, given the noise-prone quantum hardware. However, the CQM solver takes much more time, which prohibits obtaining useful quantum advantages. As an extension to the problem, we describe how the scheduling of the tests can be incorporated into the model.