Small Instances Research Articles

An exact algorithm for simultaneous pickup and delivery problem with split demand and time windows

This study introduces a new variant of the vehicle routing problem (VRP) called the simultaneous pickup and delivery problem with split demand and time windows (SPDP-SDTW). The motivation behind this study stems from real-life urban and rural delivery scenarios, encompassing features such as split demand, simultaneous pickup and delivery, many-to-many pickup and delivery, and time windows. The study thoroughly investigates the properties of the optimal solution for the SPDP-SDTW. Based on these properties, an arc flow model is developed for the SPDP-SDTW. Dantzig Wolfe (DW) decomposition techniques are employed to obtain the master problem and the pricing subproblem. In order to effectively address the SPDP-SDTW, an improved branch and price (I-BP) algorithm is proposed, incorporating a tailored column generation (CG) algorithm, branching strategies, and dual stabilization strategies. The proposed CG algorithm provides a framework that combines the improved adaptive degree heuristic (I-AGH) algorithm and the solver Gurobi. This integration substantially mitigates the computational burden involved in solving the subproblem. Extensive computational experiments conducted on datasets of varying sizes, including small, medium, and large instances, consistently demonstrate that the I-BP algorithm performs the best in both solution quality and computational efficiency when compared to existing exact and heuristic algorithms.

Multi-depot vehicle routing problem with roaming delivery locations considering hard time windows: Solved by a hybrid ELS-LNS algorithm

This paper investigates the multi-depot vehicle routing problem with roaming delivery locations considering hard time windows. In the mentioned problem, each customer can determine several locations with a distinct hard time windows and the service provider can choose between the proposed locations to visit the customer. Also, several depots are considered for the vehicles. A mathematical model is presented for the problem. The objective function of the model is minimizing the total travel time. This objective function is important in problems that include hard time windows; because in addition to the route navigation time, it considers the waiting time of the vehicles, which is one of the integral cost factors in hard time window problems. Considering the proposed problem is NP-hard, we proposed two heuristic algorithms. Also, a hybrid algorithm based on ELS is designed to solve the problem on large scales. The results show the appropriate efficiency of the algorithm for solving small and large instances. Overall, based on the results, the proposed algorithm improved the best-known solution of two instances in the multi depot vehicle routing problem with time windows benchmark datasets.

SAT-based Decision Tree Learning for Large Data Sets

Decision trees of low depth are beneficial for understanding and interpreting the data they represent. Unfortunately, finding a decision tree of lowest complexity (depth or size) that correctly represents given data is NP-hard. Hence known algorithms either (i) utilize heuristics that do not minimize the depth or (ii) are exact but scale only to small or medium-sized instances. We propose a new hybrid approach to decision tree learning, combining heuristic and exact methods in a novel way. More specifically, we employ SAT encodings repeatedly to local parts of a decision tree provided by a standard heuristic, leading to an overall reduction in complexity. This allows us to scale the power of exact SAT-based methods to comparatively very large data sets. We evaluate our new approach experimentally on a range of real-world instances that contain up to several thousand samples. In almost all cases, our method successfully decreases the complexity of the initial decision tree; often, the decrease is significant.

AILS-II: An Adaptive Iterated Local Search Heuristic for the Large-Scale Capacitated Vehicle Routing Problem

A recent study on the classical capacitated vehicle routing problem (CVRP) introduced an adaptive version of the widely used iterated local search paradigm, hybridized with a path-relinking (PR) strategy. The solution method, called adaptive iterated local search (AILS)-PR, outperformed existing meta-heuristics for the CVRP on benchmark instances. However, tests on large-scale instances suggest that PR is too slow, making AILS-PR less advantageous in this case. To overcome this challenge, this paper presents an AILS combined with mechanisms to handle large CVRP instances, called AILS-II. The computational cost of this implementation is reduced, whereas the algorithm also searches the solution space more efficiently. AILS-II is very competitive on smaller instances, outperforming the other methods from the literature with respect to the average gap to the best-known solutions. Moreover, AILS-II consistently outperforms the state of the art on larger instances with up to 30,000 vertices. History: Accepted by Ted Ralphs, Area Editor for Software Tools. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Software Tools for Vehicle Routing. Funding: This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 2013/07375-0, 2019/22067-6, and 2022/05803-3] and the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 309385/2021-0 and 403735/2021-1]. 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.2023.0106 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0106 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Tackling the crowdsourced shared-trip delivery problem at scale with a novel decomposition heuristic

This paper presents a set-partitioning formulation and a novel decomposition heuristic (D-H) solution algorithm to solve large-scale instances of the urban crowdsourced shared-trip delivery (CSD) problem. The CSD problem involves dedicated vehicles (DVs) and shared personal vehicles (SPVs) fulfilling delivery orders, wherein the SPVs have their own trip origins and destinations. The D-H begins by assigning as many package delivery orders (PDOs) to SPVs as possible, where the D-H enumerates the set of routes each SPV can feasibly traverse and then solves a PDO-SPV-route assignment problem. For PDO-DV assignment and DV routing, the D-H solves a multi-vehicle routing problem with time-window, tour duration, and capacity constraints using an insertion heuristic. Finally, the D-H seeks potential solution improvements by switching PDOs between SPV and DV routes through a simulated annealing (SA)-inspired procedure. The D-H outperforms a commercial solver in terms of computational efficiency while obtaining near-optimal solutions for small problem instances. The SA-inspired switching procedure outperforms a large neighborhood search algorithm regarding run time, and the two are comparable regarding solution quality. Finally, the paper uses the D-H to analyze the impact of several relevant factors on city-scale CSD system performance, namely the number of participating SPVs and the maximum willingness to detour of SPVs. Consistent with the existing literature, we find that CSD can substantially reduce delivery costs. However, we find that CSD can increase vehicle miles traveled. Our findings provide meaningful insights for logistics practitioners, while the algorithms illustrate promise for large real-world systems.

Packing spheres with quasi-containment conditions

A novel sphere packing problem is introduced. A maximum number of spheres of different radii should be placed such that the spheres do not overlap and their centers fulfill a quasi-containment condition. The latter allows the spheres to lie partially outside the given cuboidal container. Moreover, specified ratios between the placed spheres of different radii must be satisfied. A corresponding mixed-integer nonlinear programming model is formulated. It enables the exact solution of small instances. For larger instances, a heuristic strategy is proposed, which relies on techniques for the generation of feasible points and the decomposition of open dimension problems. Numerical results are presented to demonstrate the viability of the approach.

A configuration optimization approach for reconfigurable manufacturing system based on column-generation combined with graph neural network

Reconfigurable manufacturing systems (RMS) offer the potential to improve systemic responsiveness and flexibility to better cope with dynamic environments. However, the inherent modularity of RMS and dynamic environments pose challenges in optimising system configurations. To address this issue, a two-stage stochastic programming model is established to minimise configuration cost, reconfiguration cost, expected inventory and back-order cost. To efficiently handle a large number of variables, a set-covering model is obtained by using Danzig-Wolfe (DW) decomposition along with its corresponding pricing subproblem. This paper proposes a solution algorithm based on the column generation framework, which can quickly obtain a good feasible solution. To further improve the algorithm performance for larger instances, a column selection method is introduced to identify additional columns that have the potential to reduce the objective function value of the integer solution during the column generation iterations. These columns are then added to the set-covering model. The process of column selection is accelerated by employing the Graph Neural Network (GNN) algorithm. Furthermore, GNN trained on data from small instances can be directly applied to larger instances as well. The effectiveness of the proposed model and algorithm is verified by numerical experiments.

Railway line planning with passenger routing: Direct-service network representations and a two-phase solution approach

The railway line planning problem (LPP) plays a crucial role in determining the quality of services provided to passengers, as well as operation costs borne by railway companies. In periodic railway LPPs, it is common to consider passenger transfers between train lines to realize a general passenger travel cost setting in the railway system. While detecting passenger transfers requires incorporating passenger routing into mathematical formulations, thereby significantly complicating the problem. Studies on transfer-included LPPs are generally based on the Change&Go network that is constructed based on a pre-given line pool, which however is usually non-exhaustive due to computational intractability. To efficiently include passenger transfers in large-scale railway LPPs, this paper proposes a novel extended direct-service network representation of LPP, where lines are dynamically generated within the optimization process, and part of passenger transfers between lines can be precisely captured without the need for explicit modeling of passengers’ distribution on specific lines. A two-phase solution approach based on the representation is designed. The first phase formulates LPP with part of transfers as a path-based service network design model, solved using a branch-price-and-cut algorithm. The second phase conducts a neighborhood search around the first-phase solution to seek better ones when considering all passenger transfers. Numerical results showcase the good performance of the two-phase solution approach. It delivers optimal solutions in 18 out of 24 test instances for a small case and achieves optimality gaps within 2.85% across all small instances. The large case study of China’s Shandong high-speed railway network whose line pool size reaches millions demonstrates the scalability of the approach and its advantage over the traditional Change&Go method with partial line pools and an exact model developed in the paper.

Optimisation of process plan generation for reconfigurable manufacturing systems: efficient heuristics and lower bounds

ABSTRACT We address the process plan generation problem in a reconfigurable manufacturing environment. The objective is to minimise the total production time of a given part which includes the processing times of operations, as well as the changeover times for machines, configurations, and tools. A new efficient 0–1 mathematical programming formulation is proposed, together with a heuristic and two lower bounds. The formulation is based on one main decision variable (1MDV). It outperforms a well known two-main decision variable formulation (2MDV) from the literature. Using a commercial solver, the 1MDV formulation is on average almost five times faster than the 2MDV formulation across all instances where optimality was achieved. The proposed heuristic is a decomposition mathematical programming-based heuristic. For small benchmark instances solved to optimality using 1MDV formulation, the heuristic obtains solutions at less than 1% distance on average from optimum in few seconds. The best of the two proposed lower bounds, LB2, is obtained in less than 0.56 seconds, across all tested instances, while the 1MDV model needs about 30 seconds on average to reach the same result. These lower bounds are used to measure the performance of the heuristics on large size instances

A novel solid waste instance creation for an optimized capacitated vehicle routing model using discrete smell agent optimization algorithm

This paper presents an optimal vehicle routing model for an efficient waste collection process using the Ogun State Waste Management Agency (OGWAMA) as a case study. Just like in many cases, the current manual predetermined routing method used by OGWAMA is inefficient and contributes to excessive fuel usage. These challenges, in addition to the small instances reported in most literature, inspire this research to propose an improved routing scheme that takes into account real-time costs and eventually develops a novel instance based on OGWAMA's operation mode. The developed model was optimized using a new discrete smell agent optimization (SAO) algorithm and compared to firefly algorithm (FA) and particle swarm optimization (PSO). The SAO outperformed FA and PSO, achieving 3.92 % and 19.38 % improvements in service cost (SC) and 2.65 % and 14.96 % improvements in total travel distance (TTD), respectively. The convergence rates of the algorithms were also compared; using the Optimized Depot (OD) techniques and results shows the acceptability of the proposed approaches.

Optimal Preventive Maintenance Policy for Equipment Rented under Free Leasing as a Contributor to Sustainable Development

Leasing has proven to be a business model that is perfectly suited to the circular economy. It significantly contributes to sustainable development by enabling the reuse of machinery and equipment after each lease period and by including preventive maintenance and overhauls within and between lease terms. This helps to extend the life cycle of equipment, promote value recovery, and reduce waste. This paper examines an imperfect preventive maintenance (PM) strategy applied to equipment rented under the terms of “free leasing”. In free leasing, the lessor makes the equipment available to the customer for a specified period of time without charging rent. In return, the customer is required to purchase the equipment’s consumables exclusively from the lessor. The lessor is also responsible for the maintenance of the equipment at the customer’s premises. The greater the quantity of consumables used by the customer, the more the equipment will deteriorate. Consequently, the lessor must be able to determine the most effective approach to preventive maintenance, ensuring that it aligns with the customer’s planned usage rate while maximizing profit. This work proposes a PM strategy to be adopted by the lessor during the free lease period. This strategy involves the performance of imperfect PM actions just before the start of the lease period and then periodically. Different packages of preventive actions can be applied each time, with each package having a different cost depending on the level of effectiveness in terms of rejuvenating the equipment. Minimal repairs are performed in the event of equipment failure. The decision variables are the PM period to be adopted and the maintenance efficiency level to be chosen for each preventive intervention. The objective is to determine, for a given customer with an estimated consumption rate profile of consumables, the optimal values of these decision variables so that the lessor maximizes their profit. A mathematical model is developed to express the lessor’s average profit over each lease period. A solution procedure is developed for small instances of the problem, and an Artificial Bee Colony algorithm is implemented for larger instances. A numerical example and a sensitivity analysis are presented.

Engineering holography with stabilizer graph codes

The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the experimental realization of such holographic codes now within reach. Formulating the hyperbolic pentagon code in terms of a stabilizer graph code, we give gate sequences that are tailored to systems with long-range interactions. We show how to obtain encoding and decoding circuits for the hyperbolic pentagon code, before focusing on a small instance of the holographic code on twelve qubits. Our approach allows to verify holographic properties by partial decoding operations, recovering bulk degrees of freedom from their nearby boundary.

Research on airport apron planning strategy in emergency situations

In events of local war or highly infectious epidemics, airports face the problem of how to park numerous non-missioned aircraft on aprons. In this study, the apron planning problem in emergency situations (APPES) was considered to replan existing parking stands and taxiways, thus determining the numbers and locations of different aircraft types. A mixed-integer programming formulation for the APPES was developed to maximise the total revenue for the apron, where the aircraft was planned to be parked based on factors such as the safety distance and aircraft taxiing method. A two-stage approach based on the discrete particle swarm optimisation algorithm and bottom-left algorithm was designed to solve the APPES. Random instances of different sizes were generated, and the experimental results demonstrated the effectiveness of the proposed approach. The two-stage approach could find optimal solutions to the APPES for 19 of the 20 small instances and could well approximate optimal solutions for the medium and large instances within a reasonable timeframe. Parking priority factor and aircraft taxiing methods sensitivity analyses were also designed to develop a strategy that can adhere to the preferences of decision makers or increase the total revenue.

Optimal decision-making of post-disaster emergency material scheduling based on helicopter–truck–drone collaboration

In the last decades, natural disasters, such as earthquakes and landslides, have occurred frequently, seriously threatening the safety of people’s lives and property. How emergency material is scheduled and delivered efficiently to the affected sites after a disaster has become a critical issue in emergency management. Current studies on emergency material scheduling mainly focus on truck or helicopter transport. Inspired by the success of employing drones in commercial logistics, this work investigates the emergency material scheduling issue based on the cooperative transport of drones, helicopters, and trucks. Specifically, this paper considers the limited transport capacity, road conditions in the early stage of the disaster rescue, and affected sites restricted by road conditions that can only be served by helicopters or drones. The studied problem is formulated as a mixed integer programming model, and a two-stage heuristic algorithm is developed to solve the model. For the proposed model, instances of different sizes are generated, and extensive experiments are performed to test the efficiency of the proposed algorithm. The comparison between the solutions obtained by the two-stage algorithm and Gurobi Solver for the small instances validates the effectiveness of the proposed heuristic algorithm. Experimental results for the larger instances show that the proposed two-stage algorithm can effectively solve the problem of emergency material scheduling. Sensitivity analysis of ten typical instances is performed to provide managerial insights. Finally, a case study of the Sichuan earthquake and the visualization of transport routes are presented. The model and solving approach proposed in this work can provide essential decision references for emergency management decision-making.

Comparison of MOEAs in an Optimization-Decision Methodology for a Joint Order Batching and Picking System

This paper investigates the performance of a two-stage multi-criteria decision-making procedure for order scheduling problems. These problems are represented by a novel nonlinear mixed integer program. Hybridizations of three Multi-Objective Evolutionary Algorithms (MOEAs) based on dominance relations are studied and compared to solve small, medium, and large instances of the joint order batching and picking problem in storage systems with multiple blocks of two and three dimensions. The performance of these methods is compared using a set of well-known metrics and running an extensive battery of simulations based on a methodology widely used in the literature. The main contributions of this paper are (1) the hybridization of MOEAs to deal efficiently with the combination of orders in one or several picking tours, scheduling them for each picker, and (2) a multi-criteria approach to scheduling multiple picking teams for each wave of orders. Based on the experimental results obtained, it can be stated that, in environments with a large number of different items and orders with high variability in volume, the proposed approach can significantly reduce operating costs while allowing the decision-maker to anticipate the positioning of orders in the dispatch area.

Management of a post-disaster emergency scenario through unmanned aerial vehicles: Multi-Depot Multi-Trip Vehicle Routing with Total Completion Time Minimization

One of the most valuable and promising applications for Unmanned aerial vehicles (UAVs) is in natural disaster management, where these aircraft can operate autonomously without any need for human intervention during their flights.In this paper, we foster the interface of Operational Research with computer science in general and sensor networking in particular by focusing on managing a post-disaster emergency scenario where the use of a fleet of UAVs helps rescue teams identify people needing help inside an affected area. We model this situation as an original graph theoretical problem called Multi-Depot Multi-Trip Vehicle Routing Problem with Total Completion Time minimization (MDMT-VRP-TCT). The main novelty of the MDMT-VRP-TCT is the combination of the following three features: multi-depot, multi-trip, and completion time minimization.We propose a mixed-integer linear programming (MILP) formulation, develop a matheuristic framework to address large instances, and present an extended set of experiments to test the performance of the proposed matheuristic: first, we compare the matheuristic with the MILP formulation on a set of small instances (up to 30 nodes); then, we compare our matheuristic with two heuristics from networking literature, showing that it outperforms the existing algorithms.

An efficient multi-objective adaptive large neighborhood search algorithm for solving a disassembly line balancing model considering idle rate, smoothness, labor cost, and energy consumption

The concept of green manufacturing emphasizes the importance of product disassembly in achieving energy-efficient recycling and remanufacturing operations. Disassembly line balancing (DLB) is a critical component of the product disassembly process, wherein a set of tasks must be allocated to workstations for disassembly. This study proposes a multi-objective DLB model that aims to minimize multiple conflicting objectives simultaneously including idle rate, smoothness, labor cost, and energy consumption. A key innovation of this study involves the creation of a tailored adaptive large neighborhood search (ALNS) algorithm which is one of the first studies in the literature on product disassembly algorithms. The developed ALNS employs efficient construction and destruction heuristics to solve the proposed multi-objective DLB problem. The ALNS algorithm aims to destroy and repair solutions effectively, while a local search procedure helps it escape from local optimum solutions. The provided DLB model is effectively solved by applying the proposed ALNS algorithm to the disassembly process of a turbine reducer. The obtained results from this application serve as a compelling demonstration of the efficiency and effectiveness of the proposed approach. Furthermore, comparisons conducted with various state-of-the-art algorithms using small and large instance sets consistently highlight the superiority of the proposed ALNS approach.

An Observation on the Repetitive Nearest Neighbour Heuristic for the Travelling Salesman Problem

The travelling salesman problem is a well-known optimisation problem, with a large scope of application and high theoretical significance. The problem may be stated as this. A travelling salesman has to visit some cities. He starts from one city, visits every other city exactly once, going from one city to another, and comes back to the city from where he started. The cost of visiting a city from another city is given. The total cost of the visits is to be minimised. The repetitive nearest neighbour (RNN) heuristic method is a heuristic method to solve the problem. We describe a property of the RNN heuristic method of the travelling salesman problem. A general, simple and elementary example is constructed to show the property of the heuristic method. It is shown that the RNN heuristic method, too, can have efficiency that is arbitrarily bad, without any bound. This may happen even for small instances of the problem.

Fuzzy Optimization Model for Decision-Making in Single Machine Construction Project Planning

Scheduling for a construction project with a limited number of machines is a critical and well-studied problem. Most studies assume that task processing times are exact; in practice, delays frequently occur, rendering the initial work plan invalid. Therefore, adaptability is crucial to the success of a project. This work introduces a fuzzy optimization model for the planning of construction projects executed simultaneously and having only one backhoe. The model assumes imprecise task processing times, represented by triangular fuzzy sets, that accept delays up to a permitted degree of tolerance. The model solution obtains a fuzzy work plan. This is a robust plan that supports incidents (delays). A method to apply the model was created. The fuzzy model can help construction companies reduce delays in the delivery of their projects and avoid excessive penalties. The model was implemented in the CPLEX solver, which can quickly obtain an optimal solution for small and medium instances. For large instances, the model must be solved with metaheuristics. This scientific contribution is important for future work since it consists of the application of fuzzy optimization in a specific area of civil engineering.

A reinforcement learning-based hyper-heuristic for AGV task assignment and route planning in parts-to-picker warehouses

Globally, e-commerce warehouses have begun implementing robotic mobile fulfillment systems (RMFS), which can improve order-picking efficiency by using automated guided vehicles (AGVs) to realize operations from parts to pickers. AGVs depart from their initial points, move to a target rack position, and subsequently transport racks to picking stations. The AGVs return the racks to their original positions after the workers pick them up. When all tasks are completed, the AGVs return to their starting point. In this context, the main challenge is the task assignment and route planning of multiple AGVs to minimize travel times. We formulate a mixed-integer linear programming (MILP) model with valid inequalities to solve small problem instances optimally. We introduce a reinforcement learning (RL)-based hyper-heuristic (HH) framework to solve large instances to near-optimality. A typical HH framework comprises two levels: high-level heuristics (HLH) and low-level heuristics (LLH). The framework starts from an initial solution and improves iteratively through LLHs, while the HLH invokes a selection strategy and an acceptance criterion to generate a new solution. We propose a novel selection strategy based on the improved Multi-Armed Bandits algorithm called Co-SLMAB and Exponential Monte Carlo with counters (EMCQ) as the acceptance criterion. The corresponding collision avoidance rules are then formulated for different conflicts to construct a conflict-free traveling route for AGVs. Besides testing the proposed framework’s effectiveness in real-life warehouse layouts, we perform extensive computational experiments and a thorough sensitivity analysis. The results show that (i) the proposed valid inequalities aid in obtaining better lower bounds and significantly speed up the solution process; (ii) the Co-SLMAB-HH framework is quite competitive compared to CPLEX, outperforming the other tested hyper-heuristics and the problem-specific heuristic regarding convergence and computation time; and (iii) a pool of LLHs consisting of a wide range of different operators is advantageous over a limited set of simple operators while solving problems using hyper-heuristics.