Matheuristic Approach Research Articles

Matheuristic approaches for multi-visit drone routing problem to prevent forest fires

Forest fires draw more attention as the impact of elements that threaten nature increases, such as the thinning of the ozone layer, and global warming. The prevention of forest fires is extremely important for the protection of natural life, and the provision of a healthy world to future generations. Some of the methods used for the prevention of forest fires are observation towers, unmanned aerial vehicles, images taken from satellites, and detectors. Noticing the fire as soon as it starts and intervening in the fire prevents the fire from spreading and causing major and negative consequences. The degree of fire sensitivity of forest areas may vary depending on factors such as the climate of the region, topographic structure, humidity ratio, vegetation, tree species, and density. Observing regions with high fire sensitivity more frequently than regions with low fire sensitivity will prevent the spread of fires faster by detecting them. Different from the literature, in this study, the degree of sensitivity of fire-sensitive areas are taken into account. Visit frequency is determined according to the degree of fire sensitivity. Due to the complexity of the constraints, the mathematical model can not reach the optimal solution in a short time. To solve larger problem decomposition based matheuristic approaches are proposed. Matheuristic algorithms are compared using different parameters for samples of different sizes.

The Hampered [formula omitted]-Median Problem with Neighbourhoods

This paper deals with facility location problems in a continuous space with neighbours and barriers. Each one of these two elements, neighbours and barriers, makes the problems harder than their standard counterparts. Combining all together results in a new challenging problem that, as far as we know, has not been addressed before, but has applications for inspection and surveillance activities and the delivery industry assuming uniformly distributed demand in some regions. Specifically, we analyse the k-Median problem with neighbours and polygonal barriers in two different situations. None of these problems can be seen as a simple incremental contribution since in both cases the tools required to analyse and solve them go beyond any standard overlapping of techniques used in the separated problems. As a first building block, we deal with the problem assuming that the neighbourhoods are not visible from one another and therefore there are no rectilinear paths that join two of them without crossing barriers. Under this hypothesis, we derive a valid mixed-integer linear formulation. Removing that hypothesis leads to a more general and realistic problem, but at the price of making it more challenging. Adapting the elements of the first formulation, we also develop another valid mixed-integer bilinear formulation. Both formulations rely on tools borrowed from computational geometry that allow to handle polygonal barriers and neighbours that are second-order cone (SOC) representable, which we preprocess and strengthen with valid inequalities. These mathematical programming formulations are also instrumental to derive an adapted matheuristic algorithm that provides good quality solutions for both problems in short computing time. The paper also reports extensive computational experience, counting 2400 experiments, showing that our exact and heuristic approaches are useful: the exact approach can solve optimally instances with up to 50 neighbourhoods and different number of barriers within one hour of CPU time, whereas the matheuristic approach always returns good feasible solutions in less than 300 s.

Exact and heuristic approaches for the Truck–Drone Team Logistics Problem

Truck-and-drone routing problems are a topic of increasing interest due to advancements in drone technology. Initially, drones were thought to serve only one customer per flight; however, recent improvements in drone technology have led to the definition of multi-visit truck-and-drone routing problems, where a drone can serve multiple customers in each flight. These routing problems, which require a careful synchronization between the truck and the drone, are challenging to solve, even with a small number of customers. In this work, we address a multi-visit, single-truck, single-drone routing problem also known in the literature as the Truck–Drone Team Logistics Problem (TDTLP). In particular, we study two versions of the TDTLP arising from the possibility for the drone to land or hover at the recollection points. Our study proposes a novel mixed-integer linear programming formulation for the TDTLP, solved by a Branch-and-Cut (B&C) algorithm. Then, we introduce a matheuristic approach that incorporates our B&C algorithm to solve medium- and large-size instances. Computational results on benchmark instances demonstrate the robustness and efficacy of the proposed methods.

Inventory reallocation in a fashion retail network: A matheuristic approach

We consider a fashion retail network consisting of a central warehouse, owned by a fashion firm, and a fairly large number of retail stores. Some stores are owned by the firm itself, whereas others are owned by franchisees. An initial inventory allocation decision is made at the beginning of the selling season and is periodically revised. Inventory reallocation comprises both direct shipments from the warehouse to stores and lateral shipments among the stores. Besides stock availability and shipping costs, a suitable reallocation policy must take into account the probability of selling each item, some operational constraints, as well as other preference factors that define the utility of shipping an item from a node of the network to another one. Since the problem does not lend itself to the application of typical tools from inventory theory, we propose an optimization model that complements such tools. The model, given the number of nodes and SKUs, may involve about one million binary variables, and just solving the LP relaxation may take hours using state-of-the-art software. Since typical metaheuristics for combinatorial optimization do not seem a viable alternative, we propose a matheuristic approach, in which a sequence of maximum-weight matching problems is solved in order to reduce the problem and restrict the set of potential shipping pairs, with a corresponding drop in the number of decision variables. Computational results obtained on a set of real-life problem instances are discussed, showing the viability of the proposed algorithm.

A multi-period vaccines supply chain network design with capacity expansion and different replenishment cycles under uncertain demand

The World Health Organization (WHO) proposes guidelines for vaccine distribution networks that incorporate economic order quantity and risk pooling principles, specifically through implementing different replenishment cycles between different levels of the distribution network. The substantial impact of different replenishment cycles on inventory levels is demonstrated in the existing literature. However, current optimization network design research has paid limited attention to this aspect. This article aims to address this research gap by investigating a two-stage stochastic programming for a multi-period perishable vaccine network design problem, taking into account the different replenishment cycles characteristic and capacity expansion under uncertain demand conditions. Given the inherent difficulty of solving the proposed problem, a matheuristic approach based on Variable Neighborhood Search (VNS) is developed. To illustrate the practical application and analyze the impact of uncertain demand, we apply the proposed model and its solution method using the Indonesia dataset in the COVID-19 situation. The computational results indicate that lower replenishment cycles leads to higher inventory levels, total costs, and capacity requirements for the top-level distribution center. Optimum replenishment cycles and further managerial implications and future potential research are also presented.

Robust aircraft maintenance routing with Heterogeneous aircraft maintenance tasks

Robust aircraft maintenance routing problems (RAMRPs) have been extensively studied due to their significance on flight schedule reliability. In the current practice, the traditional huge A-check program is divided into multiple Heterogeneous small maintenance packages (with different maintenance durations and risk levels) and performed differently during the ground time between two connected flights. As the available maintenance time becomes relatively shorter, maintenance becomes a new source of disruption. Thus, the assignment of maintenance packages-to-ground times becomes more critical. Accordingly, this paper proposes a robust strategy to alleviate the disruption due to maintenance risk. The strategy is to provide each package the appropriate amount of buffer time based on the fuzzy risk assessment. Correspondingly, a robustness measure is developed to construct the RAMRP model. As its impact can be better illustrated in large scale problems, we adopt matheuristic approach. We examine 500 disruption scenarios, the results show that the proposed strategy can greatly reduce flight delays (i.e., an 82.7% reduction in the number of delayed flights) while maintaining an acceptable decrease in aircraft utilization (i.e., a 32.42% increase in average unused flying times) compared to those obtained from the traditional model. Additionally, the proposed model is further investigated from the perspectives of aircraft utilization constraints and the risk-averse attitude of airlines. Our study validates its cost-effectiveness for delay risks reduction and highlights the significance of being properly risk-averse in decision making.

Optimal operational planning of distribution systems: A neighborhood search-based matheuristic approach

This study proposes a strategy for short-term operational planning of active distribution systems to minimize operating costs and greenhouse gas (GHG) emissions. The strategy incorporates network reconfiguration, switchable capacitor bank operation, dispatch of fossil fuel-based and renewable distributed energy resources, energy storage devices, and a demand response program. Uncertain operational conditions, such as energy costs, power demand, and solar irradiation, are addressed using stochastic scenarios derived from historical data through a k-means technique. The mathematical formulation adopts a stochastic scenario-based mixed-integer second-order conic programming (MISOCP) model. To handle the computational complexity of the model, a neighborhood-based matheuristic approach (NMA) is introduced, employing reduced MISOCP models and a memory strategy to guide the optimization process. Results from 69 and 118-node distribution systems demonstrate reduced operational costs and GHG emissions. Moreover, the proposed NMA outperforms two commercial solvers. This work provides insights into optimizing the operation of distribution systems, yielding economic and environmental benefits.

Matheuristic fixed set search applied to the multidimensional knapsack problem and the knapsack problem with forfeit sets

In this paper, we present a solution method for the multidimensional knapsack problem (MKP) and the knapsack problem with forfeit sets (KPFS) using a population-based matheuristic approach. Specifically, the learning mechanism of the fixed set search (FSS) metaheuristic is combined with the use of integer programming for solving subproblems. This is achieved by introducing a new ground set of elements that can be used for both the MKP and the KPFS that aim to maximize the information provided by the fixed set. The method for creating fixed sets is also adjusted to enhance the diversity of generated solutions. Compared to state-of-the-art methods for the MKP and the KPFS, the proposed approach offers an implementation that can be easily extended to other variants of the knapsack problem. Computational experiments indicate that the matheuristic FSS is highly competitive to best-performing methods from the literature. The proposed approach is robust in the sense of having a good performance for a wide range of parameter values of the method.

A column-generation matheuristic approach for optimizing first-mile ridesharing services with publicly- and privately-owned autonomous vehicles

The burden of first-mile connection to public transit stations is a key barrier that discourages riders from taking public transportation. Public transit agencies typically operate a modest fleet of vehicles to provide first-mile services due to the high operating costs, thus failing to adequately meet the first-mile travel demands, especially during peak hours. At the same time, private cars are underutilized and have a lot of idle time. With the emergence of self-driving vehicles, new opportunities for addressing the current dilemma arise, such as integrating idle private self-driving vehicles to provide first-mile services, which is beneficial for public transportation agencies to provide high-quality services at low costs. This study investigates the first-mile ridesharing problem in which public transit agencies utilize idle privately-owned autonomous vehicles to dynamically inflate their fleet. This problem is more challenging in decision-making than conventional first-mile problems, as it involves decisions on heterogeneous fleet scheduling, vehicle routing, and time scheduling, all while taking into account the service quality for riders. To address this problem, an arc-based mixed-integer linear programming (MILP) model and a trip-based set-partitioning model are developed, both aiming to minimize total operational costs. To identify promising trips, we propose a tailored labeling algorithm with a novel dominance rule, along with a time window shift algorithm to determine the best schedule. To yield high-quality solutions in a short computation time, a tailored column-generation matheuristic algorithm is introduced. A branch-and-price exact algorithm and an adaptive large neighborhood search algorithm are developed to assess the matheuristic algorithm. Numerical experiments are conducted to demonstrate the effectiveness and applicability of the proposed models and algorithms. Experiments also show that this kind of ridesharing service can provide low-cost and high-quality services for the first-mile problem.

A Matheuristic Approach for the Multi-Depot Periodic Petrol Station Replenishment Problem

Planning petrol station replenishment is an important logistics activity for all the major oil companies. The studied Multi-Depot Periodic Petrol Station Replenishment problem derives from a real case in which the company must replenish a set of petrol stations from a set of depots, during a weekly planning horizon. The company must ensure refuelling according to available visiting patterns, which can be different from customer to customer. A visiting pattern predefines how many times (days) the replenishment occurs during a week and in which visiting days a certain amount of fuel must be delivered. To fulfill the weekly demand of each petrol station, one of the available replenishment plans must be selected among a given set of visiting patterns. The aim is to minimize the total distance travelled by the fleet of tank trucks during the entire planning horizon. A matheuristic approach is proposed, based on the cluster-first route-second paradigm, to solve it. The proposed approach is thoroughly tested on a set of realistic random instances. Finally, a weekly large real instance is considered with 194 petrol stations and two depots.

Matheuristic approach and a mixed-integer linear programming model for biomass supply chain optimization with demand selection

It is crucial to identify alternative energy sources owing to the ever-increasing demand for energy and the other environmental problems associated with using fossil fuels. Biomass as a source of bioenergy is considered a promising alternative to fossil fuels. This study aims to optimize the biomass supply chain by developing an integrated model incorporating typical tactical supply chain decisions based on market or demand selection decisions. To this end, a novel mixed-integer linear programming (MILP) model is proposed to maximize the profit of the corresponding biomass supply chain and to commercialize electricity production by selecting electricity demand and making supply chain decisions regarding power plant operations, biomass feedstock purchase and storage, and biomass transport trucks. Owing to the intricacy of the MILP model, a fix-and-optimize-based solution strategy is developed and validated by applying it to several instances of a real-world case study. The results demonstrate that the proposed strategy can significantly reduce computational time while preserving high solution quality. Additionally, it helps improve planning and decision-making as it reveals the effect of essential biomass logistics characteristics on routing outcomes.

A hybrid matheuristic approach for the integrated location routing problem of the pineapple supply chain

This paper proposes a matheuristic approach for the location-routing of industrial platforms of the pineapple supply chain problem. We have proposed a three-phase methodology to solve the considered problem. The first phase consists of obtaining the potential supply in terms of suitability and productivity, the potential location of platforms, and the times of the value chain echelons. In the second phase, a mathematical optimization model for the location problem of platforms considering the coverage in terms of timing is proposed. Finally, the final phase proposes a cluster-routing and a granular reactive tabu search approach for the routing phase. The proposed methodology uses official information on production times, speed, and capacity and georeferenced aptitude, spatial, economic, and land yield information for the first time. The proposed approach has been validated through scenarios, particularly pineapple exports for the Colombian country. The obtained results show the efficiency of the proposed approach.

A Matheuristic Approach for Delivery Planning and Dynamic Vehicle Routing in Logistics 4.0

A Matheuristic Approach for Delivery Planning and Dynamic Vehicle Routing in Logistics 4.0

A memetic based algorithm for simultaneous preventive maintenance scheduling and spare-parts inventory management for manufacturing systems

To increase machine availability, it may be necessary to halt them to replace components before failures occur. Therefore, optimizing spare parts inventory management is a key factor in improving maintenance activities. Spare part costs are a significant contributor to total maintenance costs, including holding and ordering costs, and are often dependent on the maintenance schedule. Hence, it is important to optimize preventive maintenance scheduling and spare parts inventory management together. The first attempt to introduce a new Mixed-Integer Linear Programming (MILP) model that integrates both decisions was by Mjirda et al. (2016). Our paper is the first to extend their work in order to come up with an efficient aided decision making framework based on a mat-heuristic approach that delivers a good trade-off between computational time and solution quality. Indeed, this paper introduces a novel Hybrid Memetic Algorithm (HMA) that synergistically combines Memetic Algorithm (MA) with MILP to solve this NP-hard problem. The paper aims to provide a unified and efficient mat-heuristic based aided decision making framework that optimizes the sum of maintenance, operating, holding, and ordering costs by synchronizing preventive maintenance schedules and spare parts inventory for a set of independent machines. Its efficiency is illustrated through an extensive computational study. The HMA outperforms standalone MILP solvers, solving 36% of instances to optimality within a computational time of less than 141 s, and achieving a maximum gap of 5% for 46% of instances within less than 200 s. Our findings highlight the computational efficiency and solution quality offered by the HMA, thereby advancing the state-of-the-art in integrated spare parts inventory management and preventive maintenance scheduling.

A fix-and-optimize heuristic for the Unrelated Parallel Machine Scheduling Problem

This paper proposes and evaluates a matheuristic approach for the Unrelated Parallel Machine Scheduling Problem (UPMSP). The UPMSP consists of assigning jobs to unrelated parallel machines considering different processing times for the same job in different machines. Additionally, a setup time is considered between the execution of jobs in the same machine. The problem is addressed by a fix-and-optimize matheuristic that iteratively selects a subset of variables to be fixed to their current values so that the remaining variables will compose a subproblem to be optimized by a mathematical programming solver. In the proposed approach, each subproblem consists of a subset of jobs that are assigned to a subset of machines in the incumbent solution. The subproblems are solved by the state-of-the-art exact algorithm for the UPMSP. In the experiments conducted on benchmark instances, the proposed fix-and-optimize algorithm achieved remarkable results. It outperformed the standalone exact algorithm by a large margin and resulted in competitive solutions when compared to the literature’s best-performing heuristic method for the problem. The proposed algorithm obtained the best solution for 669 out of the 1000 instances addressed in this work. Among them, 338 are new best-known solutions. In general, the proposed approach excels at solving instances with a high number of jobs per machine — it resulted in the best solution for 89% of the instances with a ratio of 10 or more jobs per machine in total.

A matheuristic for aircraft maintenance routing problem incorporating cruise speed control

Aircraft maintenance routing problem incorporating cruise speed control (AMRP-CSC) is an extension of the well-known aircraft maintenance routing problem (AMRP) where the flexible cruise times of flights are considered in route construction. Changing cruise times in AMRP can transform the infeasible flight connections into feasible ones, resulting in a larger solution space and further opportunities for efficiently routing. This may open up the possibility for a substantial improvement in aircraft utilization, but also increases resolution complexity. In this study, a new solution methodology, namely a matheuristic approach, is proposed for this problem. It is composed of three main components: an improved ant colony optimization (IACO) algorithm, a set partitioning (SP) procedure, and a neighborhoods search (NS) procedure. The IACO algorithm serves as a route generator, populating a pool of routes with promising feasible aircraft maintenance routes. Then, a SP model, which features the high-quality columns corresponding to the routes in the pool, is solved to produce a possible better solution. Finally, this solution is further improved by a NS procedure that iteratively solves the reduced AMRP-CSC instances to optimality. This matheuristic approach is analyzed and tested using the data extracting from the Bureau of Transportation Statistics (BTS), and then its accuracy and the efficiency have been demonstrated by experiment analyses.

A matheuristic approach for the multi-level capacitated lot-sizing problem with substitution and backorder

The lot-sizing problem aims at determining the products to be produced and their quantities for each time period, which is a difficult problem in production planning. This problem becomes even more complicated when practical aspects such as limited production capacity, bill of materials, and item substitution are considered. In this paper, we study a new variant of the lot-sizing problem, called the multi-level capacitated lot-sizing problem with substitution and backorder. Unlike previous studies, this variant considers substitutions at both the product and component levels, which is based on the real needs of manufacturers to increase planning flexibility. Backorders are allowed, but should be delivered within a certain time limitation. We formulate this problem using a mathematical programming model. A matheuristic approach is proposed to solve the problem. This first generates an initial feasible solution using a relax-and-fix algorithm, and then improves it using a hybrid fix-and-optimise algorithm. The proposed algorithm is calibrated with a full factorial design of experiments, and its efficiency is well validated. Finally, through extensive numerical experiments, we analyse the properties of this new lot-sizing problem, such as the effect of substitution options, and the influence of backorder time limitation, and provide several useful managerial insights for manufacturing companies to save costs in production planning.

Matheuristic approaches to the green sequencing and routing problem

The paper addresses the green sequencing and routing problem, which consists in determining the best sequence of locations to visit within a warehouse for storing and/or retrieval operations, using a fleet composed of both electric vehicles, e.g., equipped with a lithium-ion battery, and conventional vehicles, i.e., with an internal combustion engine. We present a Mixed-Integer Linear Programming formulation to the problem and propose two matheuristics based on suitable decompositions of the mathematical formulation. The two matheuristics have been tested on a pool of small-medium size instances and their performance has been compared to the one of a third matheuristic, previously proposed for the case of conventional vehicles only and here suitable extended to deal with the green aspects of the problem. The performed analysis allowed one to identify the most promising matheuristic in terms of some standard computational indicators, i.e., computing time and percentage optimality gap, as well as in terms of some qualitative aspects of the solutions agreed with a reference company. Such a most promising algorithm has then been further tested to gather some technical insights on what makes the problem hard to solve, as well as to outline some managerial insights. Moreover, its performance has been tested on a pool of real instances comprising ordinary days (with a usual amount of operations to perform) and extremely busy days, showing its efficacy and efficiency also in the considered real application context.

A matheuristic approach for the family traveling salesman problem

In the family traveling salesman problem (FTSP), there is a set of cities which are divided into a number of clusters called families. The salesman has to find a shortest possible tour visiting a specific number of cities from each of the families without any restriction of visiting one family before starting the visit of another one. In this work, the general concept of the Partial OPtimization Metaheuristic Under Special Intensification Conditions is linked with the exact optimization by a classical solver using a mathematical programming formulation for the FTSP to develop a matheuristic. Moreover, a genetic and a simulated annealing algorithm are used as metaheuristics embedded in the approach. The method is examined on a set of benchmark instances and its performance is favorably compared with a state-of-the-art approach from literature. Moreover, a careful analysis of the specific components of the approach is undertaken to provide insights into the impact of their interplay.

A Two-Step Matheuristics for Order-Picking Process Problems with One-Directional Material Flow and Buffers

The necessity for undertaking this research is driven by the prevailing challenges encountered in logistic centers. This study addresses a logistic order-picking issue involving unidirectional conveyors and buffers, which are assigned to racks and pickers with the objective of minimizing the makespan. Subsequently, two variations of a two-step matheuristic approach are proposed as solution methodologies. These matheuristics entail decomposing the primary order-picking problem into two subproblems. In the initial step, the problem of minimizing the free time for pickers/buffers is solved, followed by an investigation into minimizing order picking makespan. An experimentation phase is carried out across three versions of a distribution center layout, wherein one or more pickers are allocated to one or more buffers, spanning 120 test instances. The research findings indicate that employing a mathematical programming-based technique holds promise for yielding solutions within reasonable computational timeframes, particularly when distributing products to consumers with limited product variety within the order. Furthermore, the proposed technique offers the advantages of expediency and simplicity, rendering it suitable for adoption in the process of designing and selecting order-picking systems.