A deep reinforcement learning-assisted large neighbourhood dynamic robust algorithm for dynamic robust traveling salesman problems

This paper solves the dynamic traveling salesman problem (DTSP) using dynamic Gaussian Process Regression (DGPR) method. The problem of varying correlation tour is alleviated by the nonstationary covariance function interleaved with DGPR to generate a predictive distribution for DTSP tour. This approach is conjoined with Nearest Neighbor (NN) method and the iterated local search to track dynamic optima. Experimental results were obtained on DTSP instances. The comparisons were performed with Genetic Algorithm and Simulated Annealing. The proposed approach demonstrates superiority in finding good traveling salesman problem (TSP) tour and less computational time in nonstationary conditions.

In the dynamic traveling salesman problem (DTSP), the weights and vertices of the graph representing the TSP are allowed to change during the optimization. This work first discusses some issues related to the use of evolutionary algorithms in the DTSP. When efficient algorithms used for the static TSP are applied with restart in the DTSP, we observe that only some edges are generally inserted in and removed from the best solutions after the changes. This result indicates a possible beneficial use of memory approaches, usually employed in cyclic dynamic environments. We propose a memory approach and a hybrid approach that combines our memory approach with the elitism-based immigrants genetic algorithm (EIGA). We compare these two algorithms to four existing algorithms and show that memory approaches can be beneficial for the DTSP with random changes.

Dynamic multi-objective TSP (DMOTSP), a new research filed of evolutionary computation, is an NP-hard problem which comes from the applications of mobile computing, mobile communications. Currently, only a small number of literatures related to the research of static multi-objective TSP and dynamic single objective TSP. In this paper, an evaluation criterion of the algorithms for DMOTSP called Paretos-Similarity is first proposed, with which can evaluate the Pareto set and algorithms' performance for DMOTSP. A dynamic multi-objective evolutionary algorithm for DMOTSP, DMOTSP-EA, is also proposed, which embraces an effective operator, Inver-Over, for static TSP and dynamic elastic operators for dynamic TSP. It can track the Pareto front of medium-scale dynamic multi-objective TSP in which the number of cities is between 100 and 200. In experiment, taking CHN144+5 with two objectives for example, the algorithm is tested effective and the evaluation criterion, Paretos-Similarity, is available.

Deep reinforcement learning (DRL) methods have achieved remarkable success in solving static traveling salesman problems (TSP). However, dynamic TSP (DTSP), with the random appearance of new customers over time, introduces additional complexities that challenge DRL methods by the difficulty of obtaining optimized routing policy which lead to sub-optimal results and reduced training efficiency. To address these issues, we propose a decoupled training neural solver (DTNS) based on the encoder-decoder architecture, which is a novel approach that decouples the optimization of encoder and decoder, enhancing the model's ability to handle dynamic changes. Our method involves training under an Fore-Reveal condition first where the information of all customers nodes are known in advance to obtain optimized encoder and initialization for decoder and then fine-tuning the decoder in dynamic scenarios where dynamic customers are revealed over time. This training paradigm results in a flexible and globally optimized routing policy. Experimental results demonstrate that DTNS efficiently adapts to new customer requests in dynamic scenario, outperforming existing methods in dynamic routing environments.

In recent years, optimization in dynamic environments has attracted a growing interest from the genetic algorithm community due to the importance and practicability in real world applications. This paper proposes a new genetic algorithm, based on the inspiration from biological immune systems, to address dynamic traveling salesman problems. Within the proposed algorithm, a permutation-based dualism is introduced in the course of clone process to promote the population diversity. In addition, a memory-based vaccination scheme is presented to further improve its tracking ability in dynamic environments. The experimental results show that the proposed diversification and memory enhancement methods can greatly improve the adaptability of genetic algorithms for dynamic traveling salesman problems.

Dynamic traveling salesman problem with stochastic release dates

The problem presented in this paper was motivated by the need for a solution to be used in a search-and-rescue application and is formulated as a dynamic traveling salesman problem in a stochastic-state network setting. This problem formulation features a full-recourse decision framework and stochastic demands that are revealed only through direct observation. This problem is defined in a stochastic-state network setting, which allows the modeling of implicitly correlated demand stochasticity. The problem is then formulated as a Markovian decision process, and, finally, a heuristic solution is provided. The heuristic solution is based on a two-stage stochastic program with recourse solved on a set of aggregated networks generated by the use of an aggregating function. Subsets of the feasible solutions obtained at each stage are fixed, and the heuristic is used iteratively to further refine the routing policy.

For a dynamic traveling salesman problem (DTSP), the weights (or traveling times) between two cities (or nodes) may be subject to changes. Ant colony optimization (ACO) algorithms have proved to be powerful methods to tackle such problems due to their adaptation capabilities. It has been shown that the integration of local search operators can significantly improve the performance of ACO. In this paper, a memetic ACO algorithm, where a local search operator (called unstring and string) is integrated into ACO, is proposed to address DTSPs. The best solution from ACO is passed to the local search operator, which removes and inserts cities in such a way that improves the solution quality. The proposed memetic ACO algorithm is designed to address both symmetric and asymmetric DTSPs. The experimental results show the efficiency of the proposed memetic algorithm for addressing DTSPs in comparison with other state-of-the-art algorithms.

The paper describes Ant Colony Communities (ACC) and verifies their usefulness for Dynamic Travelling Salesman Problem (DTSP). DTSP is a version of the classical TSP in which the distance matrix change in time. The ACC consists of a set of separate ant colonies with a server that coordinates their work and sends them cargos of data for processing. The colonies could be distributed over many computers working in a LAN or even over Internet. Such a mode of operation is especially useful for dynamic tasks where solutions must catch up with the changing environment. The ACC is used for the regular ACO and its version designed for dynamic environments: PACO and Immigrant ant colonies. The experiments show that for all types Ant Colonies the introduction of the community boots the performance. The routes are far shorter than in the case of original colonies.

An approach for solving the D-TSP (dynamic traveling salesman problem) is discussed. The difference between a TSP and a D-TSP is that, in the latter, traveling costs between cities change according to the time of day. A neural network was applied to a D-TSP. This D-TSP was given a two-dimensional representation. With several maps, minimum cost tours were found by computer simulation using a Hopfield-Tank-type neural network.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimization issues are often defined statically, assuming constant environmental conditions.However, in many real-world scenarios, problem environments are dynamic and continuously changing.Thus we need optimization algorithms that could solves those issues in dynamic environments as well.Dynamic optimization problems are change(s) that may occur through the time.Such environments are characterized by uncertainty, temporal changes, and structural complexities, which makes the optimization process a significant challenge.In addressing these challenges, evolutionary algorithms have emerged as one of the most effective approaches for solving dynamic optimization problems (DOPs).Among these algorithms, the Imperialist Competitive Algorithm (ICA), designed based on swarm intelligence and competition among imperialist countries, has garnered considerable attention due to its capability in solving static optimization issues.In this research, Imperialist Competitive Algorithms, inspired by the historical and political processes of colonization and assimilation, have been known as one of the efficient evolutionary algorithms.These algorithms face numerous challenges when dealing with dynamic problems , including reduced population diversity, performance degradation in conditions of rapid environmental changes, and limitations in optimal convergence.These cases indicate the need to develop improved and more adaptable versions of these algorithms.Using concepts such as memory, population clustering, and repulsion mechanisms, this algorithm has been able to maintain population diversity at all stages while increasing the speed of convergence in the face of environmental changes.The key feature of the proposed algorithm is the use of memory to store previous optimal solutions, a clustering mechanism to manage population diversity, and repulsion to prevent unnecessary accumulation of solutions in specific regions.Nevertheless, ICA exhibits poor performance in dynamic environments because it lacks mechanisms to maintain diversity, quick adaptation to environmental changes, and new optima track.This study presents an improved version of ICA aimed at overcoming these limitations.The proposed algorithm incorporates a combination of a memory mechanism and a clustering strategy to enhance its adaptability to environmental changes and preserve diversity within the population.The memory mechanism stores information about previous optima and utilizes it under appropriate conditions to accelerate the optimization process.forclustering method is used for clustering.Clustering in the proposed method ensures that diversity is maintained for the population during the execution of the algorithm.In this study, our goal is to solve problems that change the environment in a global way.That means, the fitness of all points in the environment changes.By testing just one point in the environment and comparing the fitness obtained with its previously stored value, we can detect a change in the environment.On the other hand, the clustering strategy, particularly the k-means technique, to maintain maintain population diversity and prevents the convergence of solutions to specific regions.Together, these two components create a balance between exploration and exploitation, thereby improving the algorithm's performance in dynamic environments.To evaluate the performance of the proposed algorithm, the Moving Peaks Benchmark (MPB) was used as a standard metric.Due to its capability to simulate complex and diverse changes in dynamic environmentsparticularly in Branke's second scenario-MPB is one of the most recognized tools for assessing the performance of dynamic optimization algorithms.The proposed algorithm was evaluated alongside advanced algorithms such as FTmPSO (TMO), RAmQSO-s4, RmNAFSA-s4, TFTmPSO, RFTmPSO, mQSO10 (5+5q), FMSO, CellularPSO, Multi-SwarmPSO, mCPSO, AmQSO*, FTMPSO, almPSO, and CDEPSA.Experimental results demonstrated that the proposed algorithm outperformed other methods in areas such as convergence speed, adaptability to environmental changes, and population diversity preservation.A key feature of the proposed algorithm is its ability to retain identified optima even after environmental changes.Additionally, the use of the k-means clustering technique has ensured that the algorithm effectively avoids excessive focus on specific regions and maintains population diversity while facing complex environmental changes.Another advantage of this algorithm is its scalability in handling dynamic optimization issues with high dimensions and complexities.These findings indicate that the proposed algorithm is not only effective in laboratory settings but also suitable for real-world applications with fast and dynamic changes.

Nowadays manipulators are widely used in logistics systems, thus being important to improve the efficiency. In this paper, we transform the task sequencing problem of manipulator into a dynamic traveling salesman problem (DTSP), and use the Monte Carlo tree search (MCTS) approach to determine the execution order of the tasks. MCTS is an effective self-learning algorithm, which consists of four phases, i.e., initialization, simulation, selection and back propagation. Furthermore, to fit the dynamic feature of real-life applications, we introduce a dynamic mechanism using the information of historically found solutions. Finally, we carry out experiments based on 30 randomly generated task sets. The results show that, compared to the most popular method which executes all the tasks in sequence, MCTS is able to save 14.37%, 15.68%, 18.10% execution time (respectively on the small-scale, mid-scale and large-scale task sets), indicating its ability in improving the efficiency of manipulator.

Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC) and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we’re going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has significantly improved routes optimization.

Many real-world problems involve the coordination of multiple agents in dynamic environments, where characteristics of the problem being solved change over time. In such problems, adaptive, self-organizing agent approaches have been shown to provide very robust solutions. However, these approaches often require non-trivial amounts of time to respond to large environmental shifts. Considering this limitation, we observe that environmental changes in a given dynamic problem are generally not completely random; similar states in the environment tend to reappear over time. Memory is one way to leverage this past information and improve the adaptive efficiency of the agent system. In this paper, we explore the use of memory as a means of boosting the performance of self-organizing agents in solving dynamic coordination problems. We consider the specific problem of coordinating product flows in a factory that is subject to changing job mixes over time, which has been previously solved using a computational model of the task allocation behavior of wasps. We augment this base procedure with a number of memory systems, the most sophisticated of which exploit memory models inspired by estimation of distribution algorithms (EDAs) to manage computational cost. An experimental analysis is presented which demonstrates the advantage of using memory. Configurations using the EDA-inspired memory models are shown to substantially outperform configurations with more standard and infinite-sized memory models, and all are shown to improve the performance of the baseline task allocation procedure.

Among all combinatorial optimization problems, traveling salesman problem (TSP) is one of the widely studied problems. Though the optimization version of this problem is NP-hard, practical solution techniques don't require optimality. And many different heuristics and approximation algorithms are used to solve this problem. Cellular competitive decision algorithm (CCDA) is a new heuristic for solving hard problem, especially those NP-hard problems. One of the biggest characteristic of CCDA is easy to integrate the mathematical feature with the problem itself together. Firstly, mathematical properties of traveling salesman problem are analyzed to calculate the lower bound of the problem. Then a CCDA for traveling salesman problem is presented. In order to test its validity, we carry out extensive computational experiments. From the results we know the presented algorithm has a satisfactory behavior both in running time and the quality of the solution found.