Dynamic Traveling Salesman Problem Research Articles

Traveling of multiple salesmen to dynamically changing locations for satisfying multiple goals

Polymer grade scheduling, maritime surveillance, e-food delivery, e-commerce, and military tactics necessitate multiple agents (e.g., extruders, speed boats, salesmen) capable of visiting (or completing) dynamically changing locations (or tasks) in minimum time and distance. This study proposes a novel methodology based on clustering and local heuristic-based evolutionary algorithms to address the dynamic traveling salesman problem (TSP) and the dynamic multi-salesman problem with multiple objectives. The proposed algorithm is evaluated on 11 benchmark TSP problems and large-scale problems with up to 10,000 instances. The results show the superior performance of the proposed methodology called the dynamic two-stage evolutionary algorithm as compared to the dynamic hybrid local search evolutionary algorithm. Furthermore, the algorithm's applicability is illustrated through various scenarios involving up to four salesmen and three objectives with dynamically changing locations. To demonstrate real-world relevance, a maritime surveillance problem employing a helideck monitoring system is solved, wherein the objective is to minimize the patrolling route while visiting faulty vessels that threaten marine vessels. This study provides a general framework of TSP which finds application in several sectors, including planning and scheduling in chemical and manufacturing industries, the defense sector, and the e-commerce sector. Finally, the results showcase the effectiveness of the proposed methodology in solving the dynamic multiobjective, and multiple salesmen problem, which represents a more generalized version of the TSP.

Searching for a Sub-Optimal Solution of the Dynamic Traveling Salesman Problem Using the Monte Carlo Method

The problem of drawing up a bypass plan for targets moving rectilinearly to one point for simple movements of an interceptor (traveling salesman) is considered. A new criterion of the problem is proposed based on the initial partition of the possible intercept area, as well as an algorithm for finding a sub-optimal bypass plan based on the construction of a solution search tree by the Monte Carlo method. A numerical implementation of the algorithm has been developed, modeling has been carried out and the obtained plans for bypassing targets have been statistically analyzed.

Measuring the Performance of Ant Colony Optimization Algorithms for the Dynamic Traveling Salesman Problem

Ant colony optimization (ACO) has proven its adaptation capabilities on optimization problems with dynamic environments. In this work, the dynamic traveling salesman problem (DTSP) is used as the base problem to generate dynamic test cases. Two types of dynamic changes for the DTSP are considered: (1) node changes and (2) weight changes. In the experiments, ACO algorithms are systematically compared in different DTSP test cases. Statistical tests are performed using the arithmetic mean and standard deviation of ACO algorithms, which is the standard method of comparing ACO algorithms. To complement the comparisons, the quantiles of the distribution are also used to measure the peak-, average-, and bad-case performance of ACO algorithms. The experimental results demonstrate some advantages of using quantiles for evaluating the performance of ACO algorithms in some DTSP test cases.

Solving Dynamic Traveling Salesman Problems With Deep Reinforcement Learning.

A traveling salesman problem (TSP) is a well-known NP-complete problem. Traditional TSP presumes that the locations of customers and the traveling time among customers are fixed and constant. In real-life cases, however, the traffic conditions and customer requests may change over time. To find the most economic route, the decisions can be made constantly upon the time-point when the salesman completes his service of each customer. This brings in a dynamic version of the traveling salesman problem (DTSP), which takes into account the information of real-time traffic and customer requests. DTSP can be extended to a dynamic pickup and delivery problem (DPDP). In this article, we ameliorate the attention model to make it possible to perceive environmental changes. A deep reinforcement learning algorithm is proposed to solve DTSP and DPDP instances with a size of up to 40 customers in 100 locations. Experiments show that our method can capture the dynamic changes and produce a highly satisfactory solution within a very short time. Compared with other baseline approaches, more than 5% improvements can be observed in many cases.

A Modified Ant Colony Optimization Algorithm with Pheromone Mutations for Dynamic Travelling Salesman Problem

Ant Colony Optimization (ACO) is an algorithm based on Meta-heuristics and swarm intelligence, taking inspiration from the exploring behavior of social insects like ants. Some very challenging optimization problems, like the vehicle routing problem, have been solved by Ant colony optimization. But, the Standard ACO algorithm has problems like trapping in local optimum. This paper discusses an improved version of the ACO algorithm, known as Modified ACO (M-ACO). The main motivation of the proposed algorithm is to use pheromone mutation techniques, such as swap and random, in dynamic environments, to overcome the problems of standard ACO and solve the Travelling Salesman Problem, which is a well-known NP-hard problem. Mutation allows better searching and exploring in other areas, for better results. Also, the exploitation is increased that uses local information to search local regions more intensively for finding minimum distance and increasing the rate of convergence. Evaporation-based Ant colony optimization (E-ACO) framework and population-based ant colony optimization (P-ACO) framework are the two groups into which the algorithms under study are separated. Both frameworks are evaluated on dynamic environments produced using TSPLIB base instances and updated for pheromone values using mutation technique. Experiments and Statistical tests were conducted on the TSPLIB datasets such as pr439 and lin318, in dynamic environments and on comparing ACO with M-ACO and P-ACO, better results were obtained for M-ACO and P-ACO. Metrics like offline have been considered to measure algorithm performance and behavior.

A Scheme Library-Based Ant Colony Optimization with 2-Opt Local Search for Dynamic Traveling Salesman Problem

The dynamic traveling salesman problem (DTSP) is significant in logistics distribution in real-world applications in smart cities, but it is uncertain and difficult to solve. This paper proposes a scheme library-based ant colony optimization (ACO) with a two-optimization (2-opt) strategy to solve the DTSP efficiently. The work is novel and contributes to three aspects: problem model, optimization framework, and algorithm design. Firstly, in the problem model, traditional DTSP models often consider the change of travel distance between two nodes over time, while this paper focuses on a special DTSP model in that the node locations change dynamically over time. Secondly, in the optimization framework, the ACO algorithm is carried out in an offline optimization and online application framework to efficiently reuse the historical information to help fast respond to the dynamic environment. The framework of offline optimization and online application is proposed due to the fact that the environmental change in DTSP is caused by the change of node location, and therefore the new environment is somehow similar to certain previous environments. This way, in the offline optimization, the solutions for possible environmental changes are optimized in advance, and are stored in a mode scheme library. In the online application, when an environmental change is detected, the candidate solutions stored in the mode scheme library are reused via ACO to improve search efficiency and reduce computational complexity. Thirdly, in the algorithm design, the ACO cooperates with the 2-opt strategy to enhance search efficiency. To evaluate the performance of ACO with 2-opt, we design two challenging DTSP cases with up to 200 and 1379 nodes and compare them with other ACO and genetic algorithms. The experimental results show that ACO with 2-opt can solve the DTSPs effectively.

Dynamic routing optimization with electric vehicles under stochastic battery depletion

ABSTRACT This paper addresses a dynamic traveling salesman problem with electric vehicles under stochastic battery depletion. In the problem, traffic density and battery consumption rate are not known precisely, and their probability distributions are subject to change during the transportation operations. The problem has been formulated and solved using the Dynamic Programming (DP) approach. We develop a DP-based heuristic, which combines Restricted DP and Prim’s algorithms, to solve larger instances. The provided algorithms can determine distribution plans that reduce energy consumption and range anxiety of electric vehicle drivers. The added values of the model and the solution approach have been shown based on a case study and 270 instance-setting pairs that involve relatively larger problems. The heuristic algorithm outperformed a benchmark heuristic by providing 6.87% lower calculated required energy on average. The provided decision support tools can be used to assure energy conservation and emission reduction for short-haul freight distribution systems.

A green dynamic TSP with detailed road gradient dependent fuel consumption estimation

The rapid transition to the digitalization of firms directs companies to speed up their decision-making processes and make technology-based decisions. The increasing environmental concerns and fossil-fuel scarcity force companies to employ new logistical aims, such as reducing fuel consumption and greenhouse gas emission in addition to the traditional cost minimization and profit maximization objectives. Traditional assumptions in fuel consumption calculation have been left not only to reach the objectives of the company and make consistent delivery plans but also to increase the solution quality of real-life problems. From this point of view, this study contributes to the related literature by developing a decision support model for a Travelling Salesman Problem that considers dynamic customer requests and realistic road gradients of the entire road network while calculating fuel consumption from transportation operations. The applicability of the developed model has been shown with a real-life case study in which laboratory samples have been collected and transferred from local family clinics to a central laboratory. Several objective functions are employed to demonstrate the benefits of considering realistic road gradients. The results of the numerical analyses on static and dynamic instances illustrate the benefits of respecting realistic road gradients in fuel consumption and addressing dynamic requests during delivery operations.

WireRoom

We present WireRoom , a computational framework for the intelligent design of abstract 3D wire art to depict a given 3D model. Our algorithm generates a set of 3D wire shapes from the 3D model with informative, visually pleasing, and concise structures. It is achieved by solving a dynamic travelling salesman problem on the surface of the 3D model with a multi-path expansion approach. We introduce a novel explorative computational design procedure by taking the generated wire shapes as candidates, avoiding manual design of the wire shape structure. We compare our algorithm with a baseline method and conduct a user study to investigate the usability of the framework and the quality of the produced wire shapes. The results of the comparison and user study confirm that our framework is effective for producing informative, visually pleasing, and concise wire shapes.

About Construction of Realizability Arias of Salesman Strategies in Dynamic Salesmen Problem

The dynamic travelling salesman problem, where we assume that all objects can move with constant velocity, is considered. To solve this NPhard problem we use a game-theoretic approach and well-known solution concepts of pursuit games. We identify the realizability areas of salesman strategies depending on the initial positions of customers and their velocities. We present different cases of realizability areas of salesman strategies constructing in Python program with several numbers of customers.

Hybrid Algorithm Based on Ant Colony Optimization and Simulated Annealing Applied to the Dynamic Traveling Salesman Problem.

The dynamic traveling salesman problem (DTSP) falls under the category of combinatorial dynamic optimization problems. The DTSP is composed of a primary TSP sub-problem and a series of TSP iterations; each iteration is created by changing the previous iteration. In this article, a novel hybrid metaheuristic algorithm is proposed for the DTSP. This algorithm combines two metaheuristic principles, specifically ant colony optimization (ACO) and simulated annealing (SA). Moreover, the algorithm exploits knowledge about the dynamic changes by transferring the information gathered in previous iterations in the form of a pheromone matrix. The significance of the hybridization, as well as the use of knowledge about the dynamic environment, is examined and validated on benchmark instances including small, medium, and large DTSP problems. The results are compared to the four other state-of-the-art metaheuristic approaches with the conclusion that they are significantly outperformed by the proposed algorithm. Furthermore, the behavior of the algorithm is analyzed from various points of view (including, for example, convergence speed to local optimum, progress of population diversity during optimization, and time dependence and computational complexity).

The predictive value of quantitative sensory testing: a systematic review on chronic postoperative pain and the analgesic effect of pharmacological therapies in patients with chronic pain.

Studies have suggested that quantitative sensory testing (QST) might hold a predictive value for the development of chronic postoperative pain and the response to pharmacological interventions. This review systematically summarizes the current evidence on the predictive value of QST for chronic postoperative pain and the effect of pharmacological interventions. The main outcome measures were posttreatment pain intensity, pain relief, presence of moderate-to-severe postoperative pain, responders of 30% and 50% pain relief, or validated questionnaires on pain and disability. A systematic search of MEDLINE and EMBASE yielded 25 studies on surgical interventions and 11 on pharmacological interventions. Seventeen surgical and 11 pharmacological studies reported an association between preoperative or pretreatment QST and chronic postoperative pain or analgesic effect. The most commonly assessed QST modalities were pressure stimuli (17 studies), temporal summation of pain (TSP, 14 studies), and conditioned pain modulation (CPM, 16 studies). Of those, the dynamic QST parameters TSP (50%) and CPM (44%) were most frequently associated with chronic postoperative pain and analgesic effects. A large heterogeneity in methods for assessing TSP (n = 4) and CPM (n = 7) was found. Overall, most studies demonstrated low-to-moderate levels of risk of bias in study design, attrition, prognostic factors, outcome, and statistical analyses. This systematic review demonstrates that TSP and CPM show the most consistent predictive values for chronic postoperative pain and analgesic effect, but the heterogeneous methodologies reduce the generalizability and hence call for methodological guidelines.

Solving dynamic TSP by parallel and adaptive ant colony communities

Solving dynamic TSP by parallel and adaptive ant colony communities

Genetic algorithm‐based multiple moving target reaching using a fleet of sailboats

This study addresses the problem of Dynamic Travelling Salesman Problem for a multi-agent system using a fleet of sailboats. A genetic algorithm (GA) is proposed, which attributes to each agent a varying number of targets to be collected. GA allows obtaining a suboptimal solution in the shortest time possible. Moreover, this study adapts it to the specific problem involving a fleet of sailboats, which is a challenging task with comparison to autonomous underwater vehicles or motorised vehicles in terms of the propulsion. Therein motors can be flexibly controlled while sailboat movements are constrained by available wind direction and speed. Thus the method takes into account wind conditions at various locations of the sailboat. Simulation results demonstrate the effectiveness of the proposed approach.

GORTS: genetic algorithm based on one-by-one revision of two sides for dynamic travelling salesman problems

The dynamic travelling salesman problem (DTSP) is a natural extension of the standard travelling salesman problem, and it has attracted significant interest in recent years due to is practical applications. In this article, we propose an efficient solution for DTSP, based on a genetic algorithm (GA), and on the one-by-one revision of two sides (GORTS). More specifically, GORTS combines the global search ability of GA with the fast convergence feature of the method of one-by-one revision of two sides, in order to find the optimal solution in a short time. An experimental platform was designed to evaluate the performance of GORTS with TSPLIB. The experimental results show that the efficiency of GORTS compares favourably against other popular heuristic algorithms for DTSP. In particular, a prototype logistics system based on GORTS for a supermarket with an online map was designed and implemented. It was shown that this can provide optimised goods distribution routes for delivery staff, while considering real-time traffic information.

Dynamic traveling salesman problem with stochastic release dates

The dynamic traveling salesman problem with stochastic release dates (DTSP-srd) is a problem in which a supplier has to deliver parcels to its customers. These parcels are delivered to its depot while the distribution is taking place. The arrival time of a parcel to the depot is called its release date. In the DTSP-srd, release dates are stochastic and dynamically updated as the distribution takes place. The objective of the problem is the minimization of the total time needed to serve all customers, given by the sum of the traveling time and the waiting time at the depot. The problem is represented as a Markov Decision Process and is solved through a reoptimization approach. Two models are proposed for the problem to be solved at each stage. The first model is stochastic and exploits the entire probabilistic information available for the release dates. The second model is deterministic and uses an estimation of the release dates. An instance generation procedure is proposed to simulate the evolution of the information to perform computational tests. The results show that a more frequent reoptimization provides better results across all tested instances and that the stochastic model performs better than the deterministic model. The main drawback of the stochastic model lies in the computational time required to evaluate a solution, which makes an iteration of the heuristic substantially more time-consuming than in the case where the deterministic model is used.

A Self-Adaptive Discrete PSO Algorithm with Heterogeneous Parameter Values for Dynamic TSP.

This paper presents a discrete particle swarm optimization (DPSO) algorithm with heterogeneous (non-uniform) parameter values for solving the dynamic traveling salesman problem (DTSP). The DTSP can be modeled as a sequence of static sub-problems, each of which is an instance of the TSP. In the proposed DPSO algorithm, the information gathered while solving a sub-problem is retained in the form of a pheromone matrix and used by the algorithm while solving the next sub-problem. We present a method for automatically setting the values of the key DPSO parameters (except for the parameters directly related to the computation time and size of a problem).We show that the diversity of parameters values has a positive effect on the quality of the generated results. Furthermore, the population in the proposed algorithm has a higher level of entropy. We compare the performance of the proposed heterogeneous DPSO with two ant colony optimization (ACO) algorithms. The proposed algorithm outperforms the base DPSO and is competitive with the ACO.

Solution attractor of local search in travelling salesman problem (part 2): computational study

This paper is the second part of our study. In the first part, we introduced the concept of solution attractor of local search system for the travelling salesman problem (TSP), described a procedure for constructing the solution attractor, and presented an attractor-based search system to solve the dynamic multi-objective TSP. In this paper, we report the results of our recent empirical study on some important properties of the solution attractor of local search system for the TSP. These properties include the nature of convergence of local search trajectories, the size of the constructed solution attractor, the relationship between the size of the problem and the size of the constructed solution attractor, the best tour in the solution attractor, and computational complexity in the attractor-based search system.

A modified Ant Colony Optimization algorithm to solve a dynamic traveling salesman problem: A case study with drones for wildlife surveillance

Abstract This study presents a novel Ant Colony Optimization (ACO) framework to solve a dynamic traveling salesman problem. To maintain diversity via transferring knowledge to the pheromone trails from previous environments, Adaptive Large Neighborhood Search (ALNS) based immigrant schemes have been developed and compared with existing ACO-based immigrant schemes available in the literature. Numerical results indicate that the proposed immigrant schemes can handle dynamic environments efficiently compared to other immigrant-based ACOs. Finally, a real life case study for wildlife surveillance (specifically, deer) by drones has been developed and solved using the proposed algorithm. Results indicate that the drone service capabilities can be significantly impacted when the dynamicity of deer are taken into consideration. Highlights Proposed a novel ACO-ALNS based metaheuristic. Four variants of the proposed metaheuristic is developed to investigate the efficiency of each of them. A real life case study mirroring the behavior of DTSP is developed.

Novel local restart strategies with hyper-populated ant colonies for dynamic optimization problems

The emergence of novel metaheuristic algorithms and the impracticality of exact algorithms led to the increased application of stochastic optimization techniques to solve combinatorial optimization problems. Determination of population size, stopping criteria, selection of optimal parameter values, getting out of the local optima and most importantly the interplay between various parameters are yet to be addressed. In this work, the significance of population size and how it interplays with other parameters in determining the effective convergence of the system in both static and dynamic scenarios for travelling salesman problem (TSP) are explained. This work utilizes a more complex variant of introducing dynamism in TSP, by swapping existing nodes with new nodes. This work proposes novel local restart strategies for efficient search space reset during node replacements in dynamic TSP. The proposed local restart strategy in combination with hyper-populated ant systems is found to outperform existing state-of-the-art solutions on benchmark datasets including Oliver30, Eilon51 and KROA100 from TSPLIB.