Insertion Heuristics Research Articles

Optimizing Vendor-Managed Inventory in Multi-Tier Distribution Systems

This paper addresses the concept of the vendor-managed inventory (VMI) problem, focusing on the replenishment policy and the vehicle routing problem (VRP) model. These components are integrated to tackle a three-echelon distribution issue comprising a single plant, multiple depots, and multiple retailers, with the primary objective of minimizing transportation and inventory costs within this complex distribution network. A three-phase methodology is proposed to optimize the entire supply chain, from the plant to the final retailer, and its performance is evaluated through computational experiments. This research is motivated by a real-life supply network, highlighting its practical relevance and applicability. To extend the capabilities of existing methods for solving the combined inventory and routing problem, an insertion heuristic is incorporated to enhance vehicle utilization, thereby reducing total costs. Computational results demonstrate the effectiveness of the improved algorithm, indicating that it is sufficiently robust for practical application. Significant cost savings can be achieved with the proposed approach, making it a valuable contribution to the field of supply chain optimization.

Offline planning and online operation of zonal-based flexible transit service under demand uncertainties and dynamic cancellations

This paper introduces a comprehensive framework for planning and operating a zonal-based flexible transit (FT) service, a public transit mode designed to accommodate uncertain demand patterns. The framework addresses both offline planning based on stochastic demand distributions and cancellations, as well as online routing considering real-time orders and cancellation behaviour. Offline interzonal route planning is formulated as a two-stage recourse problem, while the intrazonal routing problem is modelled using a Markov decision process (MDP) that incorporates online information. To solve the problem, a service reliability-based decomposition method is employed to divide the problem into three mixed-integer subproblems. The first subproblem focuses on designing interzonal routes up to a specific demand level, taking into account a designated cancellation probability as determined by reliability measures. An insertion heuristic is developed for this subproblem to improve the solution efficiency. The second subproblem allocates passengers from certain categories to vehicles based on the passenger volume designated by reliability measures. Lastly, the third subproblem refines the vehicle intrazonal route according to the passenger assignment from the previous subproblem. The reliability measures are optimised iteratively until no further improvements are observed in consecutive iterations. The proposed FT service’s performance is evaluated using numerical simulations based on real New York City (NYC) taxi demand data, illustrating the effectiveness of the integrated planning and operational approach in accommodating uncertainties in on-demand transit systems.

Levy-Based Insertion Heuristics for Solving Travelling Salesman Problems

Levy-Based Insertion Heuristics for Solving Travelling Salesman Problems

METODE CHEAPEST INSERTION HEURISTIC PADA SISTEM INFORMASI GEOGRAFIS TEMPAT WISATA DI KABUPATEN DELI SERDANG BERBASIS ANDROID

Geographic Information System (GIS) is a system created using information derived from processing a number of data, namely geographic data or data located on the earth's surface. Geographic Information Systems can be used in various fields, one of which is as a travel planning and tourist location. The lack of information conveyed on tourism in Deli Serdang Regency is one of the obstacles for people who want to travel. In this thesis, a Geographic Information System application for tourism in Deli Serdang Regency is developed which has detailed tourist information and the selection of the shortest travel route and alternative tours. To determine the shortest route and alternative travel, use the Cheapest Insertion Heuristic Algorithm. Then it is hoped that the community can be helped in planning tourist trips in Deli Serdang Regency. This application utilizes the google maps API as a virtual map provider which will later display tourist location points in Deli Serdang Regency. In addition, this application is also equipped with tourist list information along with tourist details that can be accessed by the public as a reference for traveling.

A cooperative team orienteering optimisation model and a customised resolution metaheuristic

Workforce routing optimisation is an essential management task to achieve customer satisfaction and minimise costs in service-providing companies. A typical problem for an energy-saving company (ESCo) is to optimise the provisioning of maintenance services for the contracted buildings through a fleet of heterogeneous maintenance staff. This problem is modelled as a cooperative orienteering problem with time windows, operator qualification, and synchronisation constraints. A novel insertion heuristic is proposed and embedded in an adaptive large neighbourhood search algorithm and it is tested against a state-of-the-art algorithm using real-world data. The comparative study demonstrates the potential of the heuristic and a sensitivity analysis shows its robustness, focusing on time window length variation, and the number of synchronisation requirements. We consider managerial insights supported by results and concerns, e.g., the employment of further technicians to increase the number of served facilities. The proposed model and algorithm apply to similar problems as well.

Hybrid Variable Neighborhood Search for Solving School Bus-Driver Problem with Resource Constraints

The School Bus-Driver Problem with Resource Constraints (SBDP-RC) is an optimization problem with many practical applications. In the problem, the number of vehicles is prepared to pick a number of pupils, in which the total resource of all vehicles is less than a predefined value. The aim is to find a tour minimizing the sum of pupils’ waiting times. The problem is NP-hard in the general case. In many cases, reaching a feasible solution becomes an NP-hard problem. To solve the large-sized problem, a metaheuristic approach is a suitable approach. The first phase creates an initial solution by the construction heuristic based on Insertion Heuristic. After that, the post phase improves the solution by the General Variable Neighborhood Search (GVNS) with Random Neighborhood Search combined with Shaking Technique. The hybridization ensures the balance between exploitation and exploration. Therefore, the proposed algorithm can escape from local optimal solutions. The proposed metaheuristic algorithm is tested on a benchmark to show the efficiency of the algorithm. The results show that the algorithm receives good feasible solutions fast. Additionally, in many cases, better solutions can be found in comparison with the previous metaheuristic algorithms.

Improved sequential insertion heuristics for berth allocation problems

AbstractBerth allocation decisions affect all subsequent decisions in port terminals. Thus assigning berthing positions and berthing times to vessels—known as the berth allocation problem (BAP)—is one of the most important problems in port terminals. Because this is an NP‐hard problem, most of the solution methods proposed for solving it are heuristics. Although very different, some heuristics applied to the continuous BAP share a common step usually performed several times: the insertion of vessels from an insertion sequence in the time‐space diagram that represents a BAP solution. This process is frequently done by using minimum cost sequential insertion heuristics such as bottom‐left‐based heuristics. Although fast and simple, these heuristics may not lead to high‐quality solutions. In this paper, we propose improved sequential insertion heuristics that generally outperform the traditional ones and keep their simplicity and speed. The proposed heuristics are tested on a large set of instances of BAPs with different optimization objectives, and the obtained results show that they can lead to solutions up to 70% better than those obtained by traditional sequential insertion heuristics.

Adaptive large neighborhood search algorithm for the Unmanned aerial vehicle routing problem with recharging

The applications of Unmanned aerial vehicles (UAVs) in both civilian and military fields are drawing increasing attention recently. This paper investigates a new routing problem of small UAVs for information collection with time windows, where UAVs can be recharged at platforms (e.g. ground vehicles or stations) distributed in a given area. Different from the previous works on UAV routing, the UAVs are allowed to partially recharge their batteries according to the requirement in the following route. A mixed integer nonlinear programming model is developed to formulate the problem, where the overall time for completing all targets’ observation and the number of UAVs are minimized. An improved adaptive large neighborhood search (ALNS) algorithm with simulated annealing strategies is designed, and a recharging platform insertion heuristic is developed to determine the recharging strategy and construct feasible solutions. To verify the efficiency of the proposed algorithms, a set of new benchmark instances are designed based on the well-known Solomon data set and solved. The computational results are compared with those obtained by the ant colony optimization and variable neighborhood search, which shows that ALNS performs significantly better and stable. Furthermore, experimental analysis indicates that important advantages can be obtained through introducing the recharging strategy for small UAVs.

Probabilistic Analysis of Optimization Problems on Sparse Random Shortest Path Metrics

Simple heuristics for (combinatorial) optimization problems often show a remarkable performance in practice. Worst-case analysis often falls short of explaining this performance. Because of this, “beyond worst-case analysis” of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many (combinatorial) optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained in recent years, where random shortest path metrics generated from dense graphs (either complete graphs or Erdős–Rényi random graphs) have been used so far. In this paper we extend these findings to sparse graphs, with a focus on sparse graphs with ‘fast growing cut sizes’, i.e. graphs for which |delta (U)|=Omega (|U|^varepsilon ) for some constant varepsilon in (0,1) for all subsets U of the vertices, where delta (U) is the set of edges connecting U to the remaining vertices. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances generated from a sparse graph with fast growing cut sizes, we prove that the greedy heuristic for the minimum distance maximum matching problem, and the nearest neighbor and insertion heuristics for the traveling salesman problem all achieve a constant expected approximation ratio. Additionally, for instances generated from an arbitrary sparse graph, we show that the 2-opt heuristic for the traveling salesman problem also achieves a constant expected approximation ratio.

Perbandingan Algoritma Cheapest Insertion Heuristic Dan Nearest Neighbor Dalam Menyelesaikan Traveling Salesman Problem

The main problem of the Traveling Salesman Problem is that a salesman travels to several places to go with a known distance and then returns to his original place by using the shortest route from his journey, and all the places the salesman goes to are only allowed once. This research focuses on the problem of distributing goods at PT. The Medan Nugraha Ekakurir (JNE) route with the destination delivery address in the Medan area. The Cheapest Insertion Heuristic Algorithm is an algorithm used to form tours (travels) by gradually building the shortest path route with minimal weight, by adding new points one at a time. One. The Nearest Neighbor Algorithm is a simple and fast algorithm to build a feasible initial tour length from TSP where the technique takes the shortest distance from the initial position regardless of other distances. This study resulted in the conclusion that the application of the cheapest insertion heuristic and nearest neighbor algorithms in terms of finding the distance to the problem of shipping goods at PT. The Medan Nugraha Ekakurir (JNE) route starts with finding the distance between addresses with the help of google maps, then continues with the help of the WinQSB software. Based on the research results obtained using the cheapest insertion heuristic and nearest neighbor algorithms, it is obtained that the search for the shortest route distance for shipping goods at PT. The smaller Medan Nugraha Ekakurir (JNE) route is generated by the nearest neighbor algorithm. This shows that the nearest neighbor algorithm is more effective in terms of finding the traveling distance on the Traveling Salesman Problem problem of shipping goods at PT. Medan's Nugraha Ekakurir (JNE) Line.

Urban On-Demand Delivery via Autonomous Aerial Mobility: Formulation and Exact Algorithm

The implementation of the autonomous unmanned aerial mobility is a game changer for the on-demand delivery service in the crowded urban setting. In this study, the first of its kind commercial unmanned aerial vehicle (UAV) urban delivery program in China is targeted. Different from the traditional ground pickup and delivery services, the aerial mode considers not only the time window constraints, but also the spatial conflicts incurred during the take-off and landing operations of UAVs. To obtain the optimal flying routes of the focused problem, a mixed integer programming model is formulated. Due to its inherent complexity, the optimal schedule cannot be attained within acceptable time via the off-the-shelf solvers. To help speed up the solving process, a branch-and-cut based exact algorithm is proposed, together with a series of customized valid inequalities. To further accelerate, a greedy insertion heuristic is designed to secure high-quality initial solutions. In the numerical section, it is observed that the algorithm proposed in this paper can help solve the real-life on-demand UAV delivery problem to near optimum (within 5% optimality gap) within reasonable computation time (in 5 minutes). <i>Note to Practitioners</i>&#x2014;With the increase of labor cost, the distribution cost increases very rapidly. In the meantime, the employment of automated vehicles for logistics reshapes the landscape of the urban last-mile delivery. As an efficient courier carrier, the unmanned aerial vehicle (UAV) is trending the autonomous delivery endeavour. When integrating UAVs into the urban delivery program, practitioners need to pay special attention to the scheduling of UAVs at the operational level in addition to the hardware of the UAVs. To help solve the UAV dispatch problem, we propose an online scheduling scheme, considering the spatial conflict constraints in the actual UAV operations. And an exact algorithm is designed to accelerate the solving process. Numerical experiments demonstrate that the proposed algorithm can achieve near optimal dispatch plan with 5% optimality gap in 5 minutes. Furthermore, it is discovered that the demand pooling is an essential decision to make for UAV-based delivery. Longer pooling time can increase the UAV efficiency with more realized demand information, but too much pooling could lead to prolonged customer waiting and a low service level.

Variable neighborhood search for a new practical dynamic pickup and delivery problem

In today's manufacturers, a large number of cargoes like materials, semi-finished products and finished products have to be delivered among factories during the manufacturing process. Thus, this paper first introduces a new Dynamic Pickup and Delivery Problem (DPDP), which has more practical constraints like dock, time windows, capacity and last-in-first-out loading. This DPDP model can fit the practical scenarios more, which cannot be directly solved by the existing optimization algorithms. To solve this problem, this paper proposes a new V ariable N eighborhood S earch Algorithm with M ultiple local search strategies and an E fficient disturbance, called VNSME. Specifically, each new optimization period is activated when new orders are coming, in which a variable neighborhood search is used to find the best solution for this period. At each start of a period, the best solution found in the previous period is reconstructed as an initial solution for the new period by using exhaustion and cheapest insertion heuristics. Next, four different local search strategies (couple-exchange*, block-exchange*, block-relocate* and multi-relocate*) are designed to search around the initial solution, and then the currently found best solution is further perturbed by a modified 2-opt-L* method. At last, the performance of VNSME is studied on the real-world DPDP benchmarks offered by Huawei in the competition at ICAPS 2021, where the advantages of VNSME are confirmed in the competition as its final score gets the first rank among 153 teams.

Machine Learning–Based Feasibility Checks for Dynamic Time Slot Management

Online grocers typically let customers choose a delivery time slot to receive their goods. To ensure reliable service, the retailer may want to close time slots as capacity fills up. The number of customers that can be served per slot largely depends on the specific order sizes and delivery locations. Conceptually, checking whether it is possible to serve a certain customer in a certain time slot given a set of already accepted customer orders involves solving a vehicle routing problem with time windows. This is challenging in practice as there is little time available and not all relevant information is known in advance. We explore the use of machine learning to support time slot decisions in this context. Our results on realistic instances using a commercial route solver suggest that machine learning can be a promising way to assess the feasibility of customer insertions. On large-scale routing problems it performs better than insertion heuristics. History: This paper has been accepted for the Transportation Science Special Issue on Machine Learning Methods and Applications in Large-Scale Route Planning Problems. Funding: This research was funded by the Netherlands Organization for Scientific Research under the City Logistics Living Laboratory project [Grant 439.18.424].

A multi-stage heuristic algorithm based on task grouping for vehicle routing problem with energy constraint in disasters

In recent years, serious disasters have happened frequently, causing significant loss of lives and substantial economic consequences. Considering that rescue vehicles are mainly powered by electricity, they cannot compete with the conventional ones in terms of the cruising range. Therefore, it is of great significance to study how rescue vehicles can execute multiple rescue tasks quickly and efficiently with energy constraint. In this paper, a multi-stage vehicle routing algorithm based on task grouping (MSVR-TG) is proposed for the rescue vehicle routing problem with energy constraint (VRPEC) in disasters. In the task grouping stage, a novel K-means algorithm based on angular density (K-means-ad) is suggested to address the instability of the result of K-means caused by the random selection of initial cluster centers. It can balance the travel distance of each vehicle as much as possible, which is critical when vehicles are energy constrained. In the sequence planning stage, a problem-specific genetic algorithm (PSGA) with multiple population initialization rules and the route improvement strategy is introduced to balance the convergence speed and population diversity, achieving a promising planning result. In the route adjusting stage, various removal and insertion heuristics in the large neighborhood search (LNS) are designed to adjust the routes, thereby further improving the planning result. The routes participating in adjustment are obtained via the developed route selection rule. The validity of each stage in MSVR-TG has been verified in a series of scenarios. A comparison about the proposed algorithm against several advanced algorithms is constructed, and results reveal that MSVR-TG is superior over compared algorithms for VRPEC.

A machine learning-driven two-phase metaheuristic for autonomous ridesharing operations

This paper contributes to the intersection of operations research and machine learning in the context of autonomous ridesharing. In this work, autonomous ridesharing operations are reproduced through an event-based simulation approach and are modeled as a sequence of static subproblems to be optimized. The optimization framework consists of a novel data-driven metaheuristic within a two phase approach. The first phase consists of a greedy insertion heuristic that assigns new online requests to vehicles. The second phase consists of a local-search based metaheuristic that iteratively revisits previously-made vehicle-trip assignments through intra- and inter-vehicle route exchanges. These exchanges are performed by selecting from a pool of destroy–repair operators using a machine learning approach that is trained offline on a large dataset composed of more than one and a half million examples of previously-solved autonomous ridesharing subproblems.Computational results are performed on multiple dynamic instances extracted from real ridesharing data published by Uber Technologies Inc. Results show that the proposed machine learning-based optimization approach outperforms benchmark state-of-the-art data-driven metaheuristics by up to about nine percent, on average. Managerial insights highlight the correlation between selected vehicle routing features and the performance of the metaheuristics in the context of autonomous ridesharing operations.

A Multi-Depot Dynamic Vehicle Routing Problem with Stochastic Road Capacity: An MDP Model and Dynamic Policy for Post-Decision State Rollout Algorithm in Reinforcement Learning

In the event of a disaster, the road network is often compromised in terms of its capacity and usability conditions. This is a challenge for humanitarian operations in the context of delivering critical medical supplies. To optimise vehicle routing for such a problem, a Multi-Depot Dynamic Vehicle-Routing Problem with Stochastic Road Capacity (MDDVRPSRC) is formulated as a Markov Decision Processes (MDP) model. An Approximate Dynamic Programming (ADP) solution method is adopted where the Post-Decision State Rollout Algorithm (PDS-RA) is applied as the lookahead approach. To perform the rollout effectively for the problem, the PDS-RA is executed for all vehicles assigned for the problem. Then, at the end, a decision is made by the agent. Five types of constructive base heuristics are proposed for the PDS-RA. First, the Teach Base Insertion Heuristic (TBIH-1) is proposed to study the partial random construction approach for the non-obvious decision. The heuristic is extended by proposing TBIH-2 and TBIH-3 to show how Sequential Insertion Heuristic (SIH) (I1) as well as Clarke and Wright (CW) could be executed, respectively, in a dynamic setting as a modification to the TBIH-1. Additionally, another two heuristics: TBIH-4 and TBIH-5 (TBIH-1 with the addition of Dynamic Lookahead SIH (DLASIH) and Dynamic Lookahead CW (DLACW) respectively) are proposed to improve the on-the-go constructed decision rule (dynamic policy on the go) in the lookahead simulations. The results obtained are compared with the matheuristic approach from previous work based on PDS-RA.

SISTEM REKOMENDASI TEMPAT WISATA MENGGUNAKAN ALGORITMA CHEAPEST INSERTION HEURISTIC DAN NAÏVE BAYES

Bali is one of the best tourism areas in Indonesia, as evidenced in 2016 Bali received a number of awards on the TripAdvisor Travelers Choice Award in global and Asian scope. However, the Corona virus outbreak from 2019, caused the tourism sector in Bali to decline, thus a solution is needed to restore the tourism sector in Bali, where one solution is to increase cultural tourism to the maximum, as the main attraction of tourist destinations in Bali. Bali. So the author proposes a tourism recommendation system, which aims to recommend tourist attractions that are suitable for tourists, which in this recommendation system is also recommended cultural tourism destinations that are directly recommended by the community, and there is also a mapping of tourist attractions as part of a tourist recommendation system, mapping of tourist attractions public and cultural attractions. In this tourism recommendation system, using the Naïve Bayes Algorithm to recommend general tourist destinations based on the personal motivation of tourists, which is based on the attributes of age, gender, natural interest, artificial interest, cultural interest of tourists, using 200 training data consisting of 14 classes of tourist attractions. . In addition, this tourist recommendation system is equipped with recommendations for routing tourist attractions using the Cheapest Insertion Heuristic Algorithm, to arrange a list of tourist attractions.&#x0D; Keywords: Recommendation System, Naïve Bayes Algorithm, Cheapest Insertion Heuristic Algorithm, Personal Motivation, Place Mapping.

Heuristic Approach For Robust Counterpart Open Capacitated Vehicle Routing Problem With Time Windows

Garbage is one of the environmental problems. The process of transporting garbage sometimes occurs delays such as congestion and engine failure. Robust optimization model called a robust counterpart open capacitated vehicle routing problem (RCOCVRP) with time windows was formulated to get over this delays. This model has formulated with the limitation of vehicle capacity and time windows with an uncertainty of waste volume and travel time. The RCOCVRP model with time windows is solved by a heuristic approach. The heuristic approach used to solve the RCOCVRP model with time windows uses the nearest neighbor and the cheapest insertion heuristic algorithm. The RCOCVRP with time windows model is implemented on the problem of transporting waste in Sako sub-district. The solutions of these two heuristic approaches are compared and analyzed. The RCOCVRP model with time windows to optimize the route problems of waste transport vehicles that is solved using the cheapest insertion heuristics algorithm is more effective than the nearest neighbor method.

Probabilistic analysis of optimization problems on generalized random shortest path metrics

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, “beyond worst-case analysis” of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms.The instances of many optimization problems are essentially a discrete metric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained by Bringmann et al. (Algorithmica, 2013), who have used random shortest path metrics constructed using complete graphs to analyze heuristics.The goal of this paper is to generalize these findings to non-complete graphs, especially Erdős–Rényi random graphs. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances, we prove that the greedy heuristic for the minimum distance maximum matching problem, the nearest neighbor and insertion heuristics for the traveling salesman problem, and a trivial heuristic for the k-median problem all achieve a constant expected approximation ratio. Additionally, we show a polynomial upper bound for the expected number of iterations of the 2-opt heuristic for the traveling salesman problem.

Step cost functions in a fleet size and mix vehicle routing problem with time windows

The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several specificities have been tackled by dedicated methods in order to better reflect real-world situations. Following this trend, this article addresses the fleet size and mix vehicle routing problem with time windows in which companies hire a third-party logistics company. The shipping charges considered in this work are calculated using step cost functions, in which values are determined according to the type of vehicle and the total distance traveled, with fixed values for predefined distance ranges. A mixed integer linear programming model is introduced and two sequential insertion heuristics are proposed. The introduced methods are examined through a computational comparative analysis in small-sized instances with known optimal solution, 168 benchmark instances from the literature, and 3 instances based on a real-world problem from the civil construction industry. The numerical experiments show that the proposed methods are efficient and show good performance in different scenarios.