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Ermittlung der optimalen Rundreise im Kontext der Tourenplanung – ein exemplarischer Anwendungsfall
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An electric vehicle, as the name suggests, runs purely on electricity provided by battery packs located under its floor. This electricity fuels the engine and converts electric power to mechanical motion. Accordingly, electric vehicles do not emit pollutants as no combustion process takes place within, making it an eco-friendly alternative to combustion vehicles. However, electric vehicles face one major issue and that is their limited range. Recharging electric vehicles’ batteries requires an important amount of time. Since time is an important factor, recent works started focusing more and more on optimizing the use of recharge within an electric vehicle to make the most of it while avoiding frequent stops at the charging stations. Another riddle to solve, is the routing of vehicles which gets more complicated when electric vehicles are thrown into the mix. Not only an electric vehicle has a limited range, adding charging stations location to the problem affects the final path, the time and the cost of the routing problem. To help researchers advance in this direction, our work discuss the recent methods used to solve the vehicle routing problem, as well as the issues facing charging of electric vehicles. This will help establish a picture of where improvements need to be made and inspire future works to accelerate the rate at which electric vehicles will be roaming our roads. Our review shows that literature focuses increasingly on adapting electric VRP to real life settings by adding more and more constraints. Moreover, recent works are considering the recharging patterns of electric vehicles in order to reduce the overall travel time, distance and cost. The results of this review prove that complexity of electric VRP stems from the difficulty of satisfying all imposed constraints, as well as the inability to predict the outcome of the solution proposed face to real-life scenarios.
The traveling salesman problem is a typical NP hard problem and a typical combinatorial optimization problem. Therefore, an improved artificial cooperative search algorithm is proposed to solve the traveling salesman problem. For the basic artificial collaborative search algorithm, firstly, the sigmoid function is used to construct the scale factor to enhance the global search ability of the algorithm; secondly, in the mutation stage, the DE/rand/1 mutation strategy of differential evolution algorithm is added to carry out secondary mutation to the current population, so as to improve the calculation accuracy of the algorithm and the diversity of the population. Then, in the later stage of the algorithm development, the quasi-reverse learning strategy is introduced to further improve the quality of the solution. Finally, several examples of traveling salesman problem library (TSPLIB) are solved using the improved artificial cooperative search algorithm and compared with the related algorithms. The results show that the proposed algorithm is better than the comparison algorithm in solving the travel salesman problem and has good robustness.
The traveling salesman problem (TSP) is one of the best-known combinatorial optimization problems. Many methods derived from TSP have been applied to study autonomous vehicle route planning with fuel constraints. Nevertheless, less attention has been paid to reinforcement learning (RL) as a potential method to solve refueling problems. This paper employs RL to solve the traveling salesman problem With refueling (TSPWR). The technique proposes a model (actions, states, reinforcements) and RL-TSPWR algorithm. Focus is given on the analysis of RL parameters and on the refueling influence in route learning optimization of fuel cost. Two RL algorithms: Q-learning and SARSA are compared. In addition, RL parameter estimation is performed by Response Surface Methodology, Analysis of Variance and Tukey Test. The proposed method achieves the best solution in 15 out of 16 case studies.
There are many sub-tour elimination constraint (SEC) formulations for the traveling salesman problem (TSP). Among the different methods found in articles, usually three apply more than others. This study examines the Danzig–Fulkerson–Johnson (DFJ), Miller–Tucker–Zemlin (MTZ), and Gavish–Graves (GG) formulations to select the best asymmetric traveling salesman problem (ATSP) formulation. The study introduces five criteria as the number of constraints, number of variables, type of variables, time of solving, and differences between the optimum and the relaxed value for comparing these constraints. The reason for selecting these criteria is that they have the most significant impact on the mathematical problem-solving complexity. A new and well-known multiple-criteria decision making (MCDM) method, the simultaneous evaluation of the criteria and alternatives (SECA) method was applied to analyze these criteria. To use the SECA method for ranking the alternatives and extracting information about the criteria from constraints needs computational computing. In this research, we use CPLEX 12.8 software to compute the criteria value and LINGO 11 software to solve the SECA method. Finally, we conclude that the Gavish–Graves (GG) formulation is the best. The new web-based software was used for testing the results.
Most time-dependent vehicle routing problems are based on a similar modeling paradigm: travel time information is represented by travel time functions between pairs of points of interest (e.g., depot or customers). Only a few papers investigate how these functions can be computed using the available travel time information. Furthermore, most of them neglect the possibility that different paths could be selected in the road network depending on the compromises they offer between cost (distance) and travel time. In this paper, we propose a new setting where travel time functions are defined on road-network arcs. We consider the Time-Dependent Vehicle Routing Problem with Time Windows and solve it with a branch-and-price algorithm. As far as we know, this is the first exact approach for a time-dependent vehicle routing problem when travel time functions are initially defined on the segments of a road-network.
The task of the traveling salesman, which is to find the shortest or least costly circular route, is one of the most common optimization problems that need to be solved in various fields of practice. The article analyzes and demonstrates various methods for solving this problem using a specific example: heuristic (the nearest neighbor method, the most profitable neighbor method), metaheuristic (evolutionary algorithm), methods of mathematical programming. In addition to classic exact methods (which are difficult to use for large-scale tasks based on existing software) and heuristic methods, the article suggests using the innovative features of the commercially available MS Excel software using a meta-heuristic base. To find the optimal solution using exact methods, the Excel (Solver) software package was used, as well as the specialized GAMS software package. Comparison of different approaches to solving the traveling salesman problem using a practical example showed that the use of traditional heuristic approaches (the nearest neighbor method or the most profitable neighbor method) is not difficult from a computational point of view, but does not provide solutions that would be acceptable in modern conditions. The use of MS Excel for solving the problem using the methods of mathematical programming and metaheuristics enabled us to obtain an optimal solution, which led to the conclusion that modern tools are an appropriate addition to solving the traveling salesman problem while maintaining the quality of the solution.
A great challenge in operational research is to apply time-efficient algorithms to find the optimal solutions to the travelling salesman problem (TSP) and its many variations. The TSP with time windows (TSPTW) arises due to intense pressure for business to improve customer service. As online shopping becomes more popular, customer satisfaction increases if customers can decide when their orders are delivered to them. Customers may choose a time window, which is defined by an earliest delivery time and a latest delivery time, during which the package is delivered. Delivering packages to multiple customers is a typical TSPTW. One main challenge for a delivery business is to determine the size of the time window (i.e., the difference between the latest and earliest delivery times), which affects delivery cost and customer satisfaction. Although many previous studies investigated the TSPTW, none of those focused on the size of time windows. This study is the first that experiments with different time window sizes and determines their impact on tour duration, customer satisfaction, and solution time of the optimal delivery routes. The experiment results show that increasing the size of the time window decreases tour duration and customer satisfaction and increases solution time. Decreasing the size of the time window increases tour duration and customer satisfaction and decreases solution time. A small solution time is necessary for the scheduling of deliveries to many customers. A large solution time prevents a delivery business from delivering packages using optimal routes, which increases delivery cost and decreases customer satisfaction. The results of this study indicate that a general guideline for business is to allow customers to choose a time window size that is within the cost limit but is sufficiently small to maximize customer satisfaction and optimize delivery routes.
The Traveling Salesman Problem (TSP) is
a classical combinatorial optimization problem, which
is simple to state but very difficult to solve. The
problem is to find the shortest tour through a set of N
vertices so that each vertex is visited exactly once.
This problem is known to be NP-hard, and cannot be
solved exactly in polynomial time. Many exact and
heuristic algorithms have been developed in the field
of operations research (OR) to solve this problem. In
this paper we provide overview of different
approaches used for solving travelling salesman
problem.
In this paper we consider a problem related to deliveries assisted by an unmanned aerial vehicle, so-called drone. In particular we consider the Flying Sidekick Traveling Salesman Problem, in which a truck and a drone cooperate to deliver parcels to customers minimizing the completion time. In the following we improve the formulation found in the related literature. We propose three-indexed and two-indexed formulations and a set of inequalities that can be implemented in a branch-and-cut fashion. The methods that we propose are able to find the optimal solution for most of the literature instances. Moreover, we consider two versions of the problem: one in which the drone is allowed to wait at the customers, as in the literature, and one in which waiting is allowed only in flying mode. The solving methodologies are adapted to both versions and a comparison between the two is provided.
This paper addresses the traveling salesman problem with drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years reflecting the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms two existing methods in terms of solution quality and improves many best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to investigate their sensitivity to the performance of our method.
List-based simulated annealing (LBSA) algorithm is a novel simulated annealing algorithm where list-based cooling scheme is used to control the change of parameter temperature. Aiming to improve the efficiency of the LBSA algorithm for largescale optimization problems, this paper proposes an enhanced LBSA (ELBSA) algorithm for solving large-scale traveling salesman problem (TSP). The ELBSA algorithm can drive more sampling at more suitable temperatures and from more promising neighborhoods. Specifically, heuristic augmented sampling strategy is used to ensure that more neighbors are from promising neighborhoods, systematic selection strategy is proposed to guarantee that each component of the current solution has a chance to be improved, and variable Markov chain length (VMCL), based on arithmetic sequence, is used to sample more neighbors at more suitable temperatures. Extensive experiments were performed to show the contribution of the heuristic augmented sampling strategy, and to verify the advantage of using systematic selection and VMCL. Comparative experiments, which were conducted on a wide range of large-scale TSP instances, show that the ELBSA algorithm is better than or competitive with most other state-ofthe-art metaheuristics.
With the fast growth of the parcel volume of online shopping, home delivery (delivering parcels to customers’ homes or workplaces) has accentuated the pressure on last mile delivery actors. Customer pickup, which allows customers to pick up their parcels from shared delivery facilities near them, has become widely popular. This study introduces a novel travelling salesman problem with time windows for the last mile delivery in online shopping. The purpose is to find a minimum cost tour over given customers and/or shared delivery facilities (SDFs) in which unvisited customers are assigned to the SDFs. A general variable neighbourhood search heuristic is developed to solve the problem. Computational results corroborate that the proposed heuristic is competitive relative to well-known algorithms.
The development of e-commerce has led to a surge in the quantity of online shopping parcels. However, given the lack of “scale effect” last mile delivery is inefficient, expensive and produces a considerable amount of carbon emissions, which has become an obstacle to the development of a sustainable economy. This work proposes a travelling salesman problem with carbon emission reduction in last mile delivery. The proposed problem aims to reduce the total costs and carbon emissions of last mile delivery by deciding on the allocation of parcel lockers whilst scheduling delivery routes. In addition, we take the customer self-collection intention into consideration and translate it into self-collection costs, which are included in the objective. An iterated local search (ILS) algorithm is proposed, and four new local search operators are designed to improve customer allocation. The proposed method is tested on a set of scattered and clustered instances, including a real-world instance. Computational results show the superiority and competitiveness of the proposed algorithm.
An innovative model of parcel distribution is emerging from the accelerated evolution of drones and the effort of logistic companies to proceed faster deliveries at a reduced cost. This new modality originated the Flying Sidekick Traveling Salesman Problem (FSTSP) in which customers are served either by a truck or a drone. Additionally, this variant of the Traveling Salesman Problem (TSP) presents several new restrictions concerning the drone such as endurance and payload capacity. This work proposes a hybrid heuristic that the initial solution is created from the optimal TSP solution reached by a Mixed-Integer Programming (MIP) solver. Next, an implementation of the General Variable Neighborhood Search is used to obtain the delivery routes of truck and drone. Computational experiments show the potential of the algorithm to improve the total delivery time up to 67.79%. New best-known solutions (BKS) are established for all FSTSP instances that results are reported in the literature. Furthermore, a new set of instances based on well-known TSPLIB instances is provided.
The purpose of this paper is to show how to use the Alldifferent constraint in Solver in MS Excel to solve the traveling salesman problem (TSP). Previous research on the topic uses the Alldifferent constraint in combination with the INDEX function in MS Excel to select the shortest path that reaches all customers. This paper offers another approach in solving the TSP with the MS Excel Solver tool using the VLOOKUP function. Constraints for a minimal travel distance and visiting each place once are satisfied. The solution of the TSP is given as a consequence of places that may be visited. The practical implication of the proposed approach is in the sphere of distribution and transportation logistics. The example described in this paper is innovative. It may be used by other researchers and business organizations to extend their software products by adapting the proposed technology.
Traveling Salesman Problem with Time Windows (TSPTW) serves as one of the most important variants of the Traveling Salesman Problem (TSP). The main objective functions expressed in the literature of the TSPTW consist of the following: (1) to minimize total distance travelled (or to minimize total travel time spent on the arcs), (2) to minimize total cost of traveling on the arcs and cost of waiting before services, or (3) to minimize total time passed from depot to depot (tour duration). When the unit cost of traveling and unit cost of waiting appear equal, then one may solve the problem just minimizing tour duration. According to our best knowledge, only one formulation with nonlinear constraints considers the aim of minimizing tour duration for symmetric case. However, for just minimizing tour duration, we haven’t seen any linear formulation for symmetric and any general formulation for asymmetric TSPTW. In this paper, for minimizing tour duration, we propose polynomial size integer linear programming formulation for symmetric and asymmetric TSPTW separately. The performances of our proposed formulations are tested on well-known benchmark instances used to minimize total travel time spent on the arcs. For symmetric TSPTW, our proposed formulation sufficiently and capably finds optimal solutions for all instances (the biggest are with 400 customers) in an extremely short time with CPLEX 12.4. For asymmetric TSPTW, we used instances generated from a real life problem which were used for minimizing total arc cost. We used these instances for minimizing tour duration and observe that, optimal solutions of the most of the instances up to 232 nodes are obtained within seconds. In addition, the proposed formulation for asymmetric case obtained 7 new best known solutions.
Travel Salesman Problem is one of the most known optimization problems. While an optimal solution cannot be reached, non-optimal solutions approach optimality and keep running time fast. In this paper, the most used algorithms to solve this problem are comparedin terms of route length, elapsed time and number of iterations. The TSP is simulated using different scenarios examples and the convergence is checked for each case.
Torespondto the reduction of greenhouse gas emissions and global warming, this paper investigates the minimal-carbon-footprint time-dependent heterogeneous-fleet vehicle routing problem with alternative paths (MTHVRPP). This finds a route with the smallestcarbon footprint, instead of the shortestroute distance, which is the conventional approach, to serve a number of customers with a heterogeneous fleet of vehicles in cases wherethere may not be only one path between each pair of customers, and the vehicle speed differs at different times of the day. Inheriting from the NP-hardness of the vehicle routing problem, the MTHVRPP is also NP-hard. This paper further proposes a genetic algorithm (GA) to solve this problem. The solution representedbyour GA determines the customer serving ordering of each vehicle type. Then, the capacity check is used to classify multiple routes of each vehicle type, and the path selection determines the detailed paths of each route. Additionally, this paper improves the energy consumption model used for calculating the carbon footprint amount more precisely. Compared with the results without alternative paths, our experimental results show that the alternative path in this experimenthas a significant impact on the experimental results in terms of carbon footprint.
This paper presents a survey of the research on the vehicle routing problem with time windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval, all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. Both traditional heuristic route construction methods and recent local search algorithms are examined. The basic features of each method are described, and experimental results for Solomon's benchmark test problems are presented and analyzed. Moreover, we discuss how heuristic methods should be evaluated and propose using the concept of Pareto optimality in the comparison of different heuristic approaches. The metaheuristic methods are described in the second part of this article.
Nowadays, truck‐and‐drone problems represent one of the most studied classes of vehicle routing problems. The Flying Sidekick Traveling Salesman Problem ( FS‐TSP ) is the first optimization problem defined in this class. Since its definition, several variants have been proposed differing for the side constraints related to the operating conditions and for the structure of the hybrid truck‐and‐drone delivery system. However, regardless the specific problem under investigation, determining the optimal solution of most of these routing problems is a very challenging task, due to the vehicle synchronization issue. On this basis, this work provides a new arc‐based integer linear programming formulation for the FS‐TSP . The solution of such formulation required the development of a branch‐and‐cut solution approach based on new families of valid inequalities and variable fixing strategies. We tested the proposed approach on different sets of benchmark instances. The experimentation shows that the proposed method is competitive or outperforms the state‐of‐the‐art approaches, providing either the optimal solution or improved bounds for several instances unsolved before.
Effective trip planning should consider the location of vehicle charging stations. Optimizing the route of electric vehicles should be carried out taking into account the location of the charging stations. The article presents a proposal of a method for optimizing electric vehicle journeys with the use of genetic algorithms. The method developed by the authors considers the range of the electric vehicle, the location of the charging stations and the parameters of the slow / fast charging station. Initial verification of the method was carried out on the example of a travel route in Poland, taking into account the actual locations of fast and slow charging stations. The criterion adopted was the minimization of the traveled distance.
This paper introduces the Electric Vehicle Routing Problem with Drones (EVRPD), the first VRP combining electric ground vehicles (EVs) with unmanned aerial vehicles (UAVs), also known as drones, in order to deliver packages to customers. The problem’s objective is to minimize the total energy consumption, focusing on the main non-constant and controllable factor of energy consumption on a delivery vehicle, the payload weight. The problem considers same-sized packages, belonging to different weight classes. EVs serve as motherships, from which drones are deployed to deliver the packages. Drones can carry multiple packages, up to a certain weight limit and their range is depended on their payload weight. For solving the EVRPD, four algorithms of the Ant Colony Optimization framework are implemented, two versions of the Ant Colony System and the Min-Max Ant System. A Variable Neighborhood Descent algorithm is utilized in all variants as a local search procedure. Instances for the EVRPD are created based on the two-echelon VRP literature and are used to test the proposed algorithms. Their computational results are compared and discussed. Practical, real-life scenarios of the EVRPD application are also presented and solved.
We consider a consistent vehicle routing problem for the delivery of parcels with electric vehicles. Stemming from a real-world problem, we assume that vehicles can only be charged with electricity between their delivery tours in the morning and their pickup tours in the afternoon. For this purpose, a charging station with a limited amount of charging slots is available at the depot. We aim at generating a set of vehicle routes that are driver- and time-consistent and efficiently use limited charging resources, while optimizing the sum of vehicle fixed cost, vehicle/driver operating time, arrival time consistency and driver consistency. We present a mathematical model to describe the problem in detail. For solving the real-world problem, a template-based Adaptive Large Neighborhood Search is developed, complemented with constraint programming for charging management and quadratic programming for delivery and pickup trip scheduling. Computational experiments for different settings and scenarios, based on data from an Austrian parcel delivery company, are presented and analysed.
Gegenstand des Kapitels sind Aufgaben, Planungsprobleme, Lösungsverfahren und Softwaresysteme der lang-, mittel- und kurzfristigen Transportplanung. Für die Gestaltung von Transportnetzen auf der langfristigen Planungsebene und die Festlegung der Transportwege und -mittel auf der mittelfristigen Ebene werden Modelle und Lösungsansätze diskutiert, die auf dem Mehrgüter-Netzwerkflussproblem basieren. Es folgt eine Betrachtung der mittel- und kurzfristigen Probleme der Fahrzeugeinsatzplanung und des Einflusses der Transportplanung auf die Bestandsplanung, bevor die Tourenplanung hinsichtlich auftretender Planungsprobleme, existierender Lösungsverfahren und Softwarelösungen ausführlich behandelt wird.
Dieses Lehrbuch ermöglicht dem Leser einen leichten Einstieg in die Matrixrechnung. Matrizen und Vektoren bilden eine wesentliche Grundlage vieler quantitativer Modelle und Methoden sowohl in der ökonomischen Forschung als auch in der industriellen Praxis. Grundelemente der Matrixrechnung werden anschaulich erläutert und anhand ökonomischer Anwendungen vertieft. Darauf aufbauend führt das Buch in die Vektorraumtheorie und lineare Optimierung ein. Zu jedem Kapitel finden sich zahlreiche Übungsaufgaben mit Lösungen. Die 6. Auflage wurde um ein Kapitel zur Anwendung des Simplex-Algorithmus in MS Excel ergänzt.
Der Inhalt
• Grundlegende und weiterführende Matrixrechnung
• Ökonomische Anwendungen der Matrixrechnung
• Allgemeine lineare Gleichungssysteme
• Vektorraumtheorie
• Lineare Optimierung allgemein und mit MS Excel<
Die Autoren
Prof. Dr. Christoph Mayer ist Professor für Betriebswirtschaftslehre / Investition und Finanzierung an der Hochschule für Technik und Wirtschaft Dresden. Einer seiner Forschungsschwerpunkte ist die stochastische Modellierung und Monte-Carlo-Simulation der Chancen und Risiken von Unternehmen zur Abbildung der gesamthaften Wirkung von Unsicherheiten auf relevante Zielgrößen.
Dr. Carsten Weber arbeitet seit über 10 Jahren in verschiedenen leitenden Funktionen im Bereich Vergütung & betriebliche Altersversorgung beim Ludwigshafener Chemiekonzern BASF. Seine wissenschaftlichen Arbeiten befassen sich mit der Bewertung der privaten Rentenversicherung und alternativen Entsparmodellen.
Prof. Dr. David Francas ist Professor für ABWL und Logistische Informationssysteme an der Hochschule Heilbronn. Seine Forschungs- und Beratungsschwerpunkte liegen in den Bereichen Logistik, Supply Chain Management, Operations Research und Business Analytics.
In diesem Lehrbuch werden die Grundlagen im Umgang mit Excel-VBA, von der Erstellung von Makros über beispielhafte Anwendungen des Solvers bis zur Erstellung von benutzerdefinierten Funktionen, Schritt für Schritt dargestellt. Dabei werden wertvolle Tipps zur Gestaltung und Dokumentation von Excel-Berechnungsblättern gegeben. Auf dieser Basis erfolgt die angeleitete Erstellung von Flash-Berechnungen realer Dampf-Flüssig- und Flüssig-Flüssig-Gleichgewichte. Die wichtigsten Grundoperationen der Thermischen Verfahrenstechnik werden in den nachfolgenden Kapiteln verständlich und strukturiert behandelt: Ausgehend von den Phasengleichgewichten und Erhaltungsgleichungen erfolgt die Herleitung der Berechnungsgleichungen und darauf aufbauend die Erstellung von Excel-Berechnungsblättern zur Lösung der praxisnahen Aufgabenstellungen. Zusätzlich werden u. a. die Auslegung von Anlagen zur Flüssigkeitsförderung und Partikelsysteme behandelt.
Der InhaltExcel mit VBA für verfahrenstechnische Anwendungen - Thermodynamik der Gemische - Batch-Destillation, Batch-Rektifikation - Flüssig-Flüssig-Extraktion - Absorption - Auslegung von Packungskolonnen - Rektifikation - Zustände feuchter Luft und Trocknungsprozesse im h,X-Diagramm - Förderung inkompressibler Fluide - Partikelsysteme
Die Zielgruppen
Studierende und Anwender aus Maschinenbau und Verfahrenstechnik sowie chemisch-technischer Fachrichtungen. Geeignet auch für VBA-Anfänger.
Der Autor
Professor Dr.-Ing. Uwe Feuerriegel lehrt seit 1997 an der Fachhochschule Aachen Thermodynamik, Wärme- und Stoffübertragung sowie Thermische Verfahrenstechnik. Davor war er mehrere Jahre als Projektleiter im Anlagenbau im In- und Ausland tätig.
The traveling-salesman problem is that of finding a permutation P = (1 i2 i3 … in) of the integers from 1 through n that minimizes the quantity where the aαβ are a given set of real numbers. More accurately, since there are only (n − 1)′ possibilities to consider, the problem is to find an efficient method for choosing a minimizing permutation. This problem was posed, in 1934, by Hassler Whitney in a seminar talk at Princeton University. There are as yet no acceptable computational methods, and surprisingly few mathematical results relative to the problem.
The reverse logistics problem of the simultaneous distribution of commodities and the collection of reusable empty packages
with a single depot and a single vehicle with limited capacity is addressed in this paper. Commodities to be distributed are
loaded at the depot and the empty packages are transported back to the depot. This is called the traveling salesman problem
with simultaneous delivery and pick-up (TSDP), a variant of the classical traveling salesman problem (TSP), where nodes require
both delivery and pick-up. The objective is to minimize the total distance traveled by servicing of the all customers. We
develop a mathematical programming model and a two-phase heuristic to solve the TSDP. In the first phase, we use an agglomerative
procedure to find an initial solution. In the second phase, we develop an enhanced version of simulated annealing (SA) to
search for the best solution. We tested the heuristic on standard, derived, and randomly generated data-sets and obtained
encouraging results.
This report describes an implementation of the Lin-Kernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solutions for all solved problem instances we have been able to obtain, including a 7397-city problem (the largest nontrivial problem instance solved to optimality today). Furthermore, the algorithm has improved the best known solutions for a series of large-scale problems with unknown optima, among these an 85900-city problem.
In this paper, some of the main known algorithms for the traveling salesman problem are surveyed. The paper is organized as follows: 1) definition; 2) applications; 3) complexity analysis; 4) exact algorithms; 5) heuristic algorithms; 6) conclusion.
The combination of genetic and local search heuristics has been shown to be an effective approach to solving the traveling salesman problem (TSP). This paper describes a new hybrid algorithm that exploits a compact genetic algorithm in order to generate high-quality tours, which are then refined by means of the Lin-Kernighan (LK) local search. The local optima found by the LK local search are in turn exploited by the evolutionary part of the algorithm in order to improve the quality of its simulated population. The results of several experiments conducted on different TSP instances with up to 13,509 cities show the efficacy of the symbiosis between the two heuristics
This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem. The procedure is based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems. The procedure produces optimum solutions for all problems tested, “classical” problems appearing in the literature, as well as randomly generated test problems, up to 110 cities. Run times grow approximately as n ² ; in absolute terms, a typical 100-city problem requires less than 25 seconds for one case (GE635), and about three minutes to obtain the optimum with above 95 per cent confidence.
The paper is concerned with the optimum routing of a fleet of gasoline delivery trucks between a bulk terminal and a large number of service stations supplied by the terminal. The shortest routes between any two points in the system are given and a demand for one or several products is specified for a number of stations within the distribution system. It is desired to find a way to assign stations to trucks in such a manner that station demands are satisfied and total mileage covered by the fleet is a minimum A procedure based on a linear programming formulation is given for obtaining a near optimal solution. The calculations may be readily performed by hand or by an automatic digital computing machine. No practical applications of the method have been made as yet. A number of trial problems have been calculated, however.
Solution of a large scale traveling salesman problem. The Rand Cooperation Institute for Operational Research
- G Dantzig
- R Fulkerson
- S Johnson
Step-By-Step Optimization With Excel Solver - The Excel Statistical Master
- M Harmon