Parallelization Strategies for GPU-Based Ant Colony Optimization Solving the Traveling Salesman Problem

Ant colony optimization (ACO) algorithm is a metaheuristic inspired by the behavior of real ants in their search for the shortest path to food sources. The ACO algorithm takes on these characteristics of robust, positive feedback distributed computing, easy fusing with other algorithms. But the basic ACO algorithm has some deficiencies of premature and stagnation phenomenon in the evolution process, and is easily trapped into local optimal solution. And it is difficult to explore other solutions in the neighbor space. So a improved ACO(DPSEMACO) algorithm based on dual population strategy, bi-directional dynamic adjust evaporation factor strategy of the pheromone and parallel strategy is proposed to solve the traveling salesman problem(TSP). In the DPSEMACO algorithm, the ants are divided into the two subpopulations by borrowing the mutual cooperation mechanism of biological community, which evolve separately and exchange information timely. The bi-directional dynamic adjusting evaporation factor strategy of the pheromone is used to change the corresponding path pheromone of different subpopulations in order to avoid to trap into a local optimum. The parallel strategy can avoid falling into a local optimum. And the DPSEMACO algorithm can expand the search space and improve the overall searching performance by repeated changing the pheromone of the each subpopulation and adaptive adjusting evaporation factor. Finally, in order to prove the optimization performance of the proposed DPSEMACO algorithm, some classic TSP instances are selected from the TSPLIB in this paper. And some existing methods are selected to compare the optimization performance with the proposed DPSEMACO algorithm. The experimental results demonstrate that the proposed DPSEMACO algorithm is feasible and effective in solving TSP, and takes on a good global searching ability and high convergence speed.

Objectives: A well-known NP-complete problem is the travelling salesman problem (TSP). It has numerous engineering and scientific applications. In this article, we have proposed a multi-conveyance TSP where different conveyances are present to travel from one city to another city. This is an extension to classical TSP. In this TSP, the salesman visits all the cities only once during his/her tour, using different conveyances to travel from one city to another. The cost of travelling between cities using various modes of conveyance varies. The objective of this research is to find the minimum cost tour using an ant colony optimization (ACO) based approach by satisfying the constraints of the proposed multi-conveyance TSP. Method: The considered TSP has been solved using a novel ACO technique. The proposed ACO is adopted with the Roulette-wheel selection and “tuning solution” techniques. We have used a few benchmark datasets from TSPLIB to check the effectiveness of the proposed algorithm. The experimental findings for a few benchmarks TSP instances show that almost always, the proposed ACO is able to find a better result. Then, we used some redefined and randomly generated datasets for experiments. The experimental outcomes for various input datasets are also very encouraging. Findings: The goal of the proposed TSP is to find a complete tour with a minimum cost without exceeding the total travel cost and total travel time. Thus, there are two novel constraints in the classical TSP. Novelty: A unique aspect of the proposed research is the use of several conveyance facilities and a fixed total travel time and cost. This is new, as these three factors are integrated into a single TSP model. Keywords: Travelling Salesman Problem; Travel Cost; Travel Time; MultiConveyance TSP; Ant Colony Optimization

Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm has been applied. However, relatively few results on the runtime analysis of the ACO on the TSP are available. This paper presents the first rigorous analysis of a simple ACO algorithm called (1 + 1) MMAA (Max-Min ant algorithm) on the TSP. The expected runtime bounds for (1 + 1) MMAA on two TSP instances of complete and non-complete graphs are obtained. The influence of the parameters controlling the relative importance of pheromone trail versus visibility is also analyzed, and their choice is shown to have an impact on the expected runtime.

Meta-heuristics Genetic Algorithms (GA) and Ant Colony Optimisation (ACO) have both shown success when applied to permutation problems such as the Traveling Salesman Problem (TSP). Therefore, combining the approaches could prove beneficial. This paper presents an ACO inspired mutation operator for use in a GA based on Partial-ACO. Applied to a range of TSP instances the ACO mutation operator demonstrates considerable improvements over standard GA mutation operators finding solutions within a few percent of optimal for TSP instances of nearly 4000 cities. In fact, experiments demonstrate performance close to that of local search with standard mutation operators. Moreover, when integrating local search the ACO inspired mutation operator continues to provide improved results over standard mutation and local search.KeywordsAnt colony optimisationGenetic algorithmMutation

Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are independent and identically distributed. However, the existing literature fails to solve TSP instances when training and testing data have different distributions. Concretely, we find that different training and testing distribution will result in more difficult TSP instances, i.e., the solution obtained by the model has a large gap from the optimal solution. To tackle this problem, in this work, we study learning-based TSP methods when training and testing data have different distributions using adaptive-hardness, i.e., how difficult a TSP instance can be for a solver. This problem is challenging because it is non-trivial to (1) define hardness measurement quantitatively; (2) efficiently and continuously generate sufficiently hard TSP instances upon model training; (3) fully utilize instances with different levels of hardness to learn a more powerful TSP solver. To solve these challenges, we first propose a principled hardness measurement to quantify the hardness of TSP instances. Then, we propose a hardness-adaptive generator to generate instances with different hardness. We further propose a curriculum learner fully utilizing these instances to train the TSP solver. Experiments show that our hardness-adaptive generator can generate instances ten times harder than the existing methods, and our proposed method achieves significant improvement over state-of-the-art models in terms of the optimality gap. The codes are publicly available.

Over the years, Metaheuristic algorithms have proven significant efficacy in handling None- Deterministic polynomial hard (NP-hard) combinatorial optimization problems, mainly the Traveling Salesman Problem (TSP) which has been used to evaluate and test many metaheuristics algorithms such as Ant Colony optimizations. This paper contributes a new optimization algorithm to the famous-family of swarm and evolutionary techniques named Scuba Diver Optimization Algorithm (SDOA) which is a novel population-based metaheuristic optimization algorithm inspired by the behavioural and physiological dynamics of scuba divers in the open water environments. SDOA simulates main diving factors including (depth, tank pressure/oxygen, bottom time, and ascent strategies) for keeping a balance between explorations and exploitations during the search process. SDOA novelty appears in its adaptive control of solution diversity using pressure and oxygen level thresholds, enabling robust avoidance of local optima and faster convergence. The SDOA algorithm was evaluated on a range of TSP instances from the TSPLIB library, which were categorized into three groups: Group 1, comprising instances with 1–99 cities; Group 2, including instances with 100–999 cities; and Group 3, consisting of large-scale instances with 1000 or more cities. And the results of SDOA is compared with established metaheuristics algorithms such as Ant Colony Optimization, Artificial Bee Colony, and Genetic Algorithm. The study results showing that SDOA consistently produces shorter (near optimal) tour lengths with significantly minimum computational time in larger problem sizes (Group 3). The proposed algorithm also demonstrates better scalability and stability in different initialization and population sizes. Future directions include adapting SDOA for solving other optimization problems including multi-objective or dynamic optimization contexts.

Many real-world problems, like microchip design, can be modeled by means of the well-known traveling salesman problem (TSP). Many instances of this problem can be found in the literature. Although several optimization algorithms have been applied to TSP instances, the selection of the more promising algorithm is, in practice, a difficult decision. In this paper, a new meta-learning-based approach is investigated for the selection of optimization algorithms for TSP instances. Essentially, a learning model is trained with TSP instances for which the performance of a set of optimization algorithms is known a priori. Then, the learned model is used to predict the best algorithm for a new TSP instance. Each instance is described by meta-features that capture characteristics of the TSP that affect the performance of the optimization algorithms. Given that the best solution for a given TSP instance can be obtained by several algorithms, the meta-learning problem is considered here to be a multi-label classification problem. Several experiments illustrate the performance of the proposed approach, with promising results.

The traveling salesman problem (TSP) is an NP-hard problem. Thus far, a large number of researchers have proposed different ant colony optimization (ACO) algorithms to solve the TSP. These algorithms inevitably encounter problems such as long convergence time and the tendency to easily fall into local optima. On the basis of the ACO algorithm, this study proposes a dynamic adaptive ACO algorithm (DAACO). DAACO realizes the diversity of initialization of the ACO algorithm by dynamically determining the number of ants to be prevented from falling into local optimization. DAACO also adopts a hybrid local selection strategy to increase the quality of ant optimization and reduce the optimization time. Among the 20 instances of the TSPLIB dataset, the DAACO algorithm obtains 19 optimal values, and the solutions of 10 instances are better than those of other algorithms. The experimental results on the TSPLIB dataset show that the DAACO algorithm has obvious advantages in terms of convergence time, solution quality, and average value relative to existing state-of-the-art ACO algorithms.

Ant Colony Optimization (ACO) algorithm has a wide array of applications to solve combinatorial optimization problems, especially Traveling Salesman Problems (TSPs). The major limitations of ACO algorithm are premature convergence, the possibility that trapped in the local optima. In this paper, an improved Ant Colony Optimization algorithm is proposed which uses fractional order difference for pheromone updating and a weighted combined transition probability. The fractional order difference with the characteristic of long-term memory helps the algorithm make full use of the historical information, and the combined transition probability enhances the exploration ability of the algorithm by using the information of a few steps forward. The performance of the proposed algorithm is tested on various data sets from the standard TSP Library compared with the corresponding integer order algorithm and some evolutionary algorithms. According to the empirical results, our algorithm based on fractional order difference overcomes the classic integer order. Furthermore, the results on a number of TSP instances demonstrate that compared with other evolutionary algorithms, the proposed method can obtain the better solutions on most instances with stronger robustness.

Swarm intelligence is a relatively new approach to problem solving that takes inspiration from the social behaviors of insects and other animals. Ants, in particular, have inspired a number of methods and techniques among which the most studied and successful is the general-purpose optimization technique, also known as ant colony optimization, In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. Ant Colony Optimization (ACO) algorithm is used to arrive at the best solution for TSP. In this article, the researcher has introduced ways to use a great deluge algorithm with the ACO algorithm to increase the ability of the ACO in finding the best tour (optimal tour). Results are given for different TSP problems by using ACO with great deluge and other local search algorithms.

Traveling salesman problem (TSP) is a well-known NP-hard combinatorial optimization problem. It has been solved by a number of exact and approximate algorithms and serves as a testbed for new heuristic and metaheuristic optimization algorithms. However, it is often not easy to evaluate the hardness (complexity) of a TSP instance. Simple measures such as the number of cities or the minimum (maximum) route length do not capture the internal structure of a TSP instance sufficiently. In this work, we propose a new method for the assessment of TSP instance complexity based on clustering. The new approach is evaluated on a set of randomized TSP instances with different structure and its relation to the performance of a selected metaheuristic TSP solver is studied.

Beam-ACO, a modification of the traditional Ant Colony Optimization (ACO) algorithms that incorporates a modified beam search, is one of the most effective ACO algorithms for solving the Traveling Salesman Problem (TSP). Although adding beam search to the ACO heuristic search process is effective, it also increases the amount of work (in terms of partial paths) done by the algorithm at each step. In this work, we introduce a greedy variant of Beam-ACO that uses a greedy path selection heuristic. The exploitation of the greedy path selection is offset by the exploration required in maintaining the beam of paths. This approach has the added benefit of avoiding costly calls to a random number generator and reduces the algorithms internal state, making it simpler to parallelize. Our experiments demonstrate that not only is our greedy Beam-ACO (gBeam-ACO) faster than traditional Beam-ACO, in some cases by an order of magnitude, but it does not sacrifice quality of the found solution, especially on large TSP instances. We also found that our greedy algorithm, which we refer to as gBeam-ACO, was less dependent on hyperparameter settings.

The traveling salesman problem (TSP) is a classic problem in optimization, frequently used for measuring the performance of optimization algorithms. The goal in solving the TSP is to determine the lowest-cost circuit through a set of cities on a graph. Ant colony optimization (ACO) algorithms, inspired by nature, use simulated ants that modify their environment through laying and removing pheromone, represented by weights on the edges of the graph connecting each city. In this study, a novel algorithm is developed, Multi-Colony System (MCS), which uses multiple colonies of simulated ants in combination to produce superior solutions to the TSP. In comparison with Ant Colony System (ACS), a standard well-performing ACO algorithm, MCS has displayed improved performance, producing tours up to 19.4% shorter than those of ACS in the same amount of time. The performance of MCS in this study presents potential advantages in applications beyond the TSP, including the ability of multiple colonies to both develop a greater number of solutions simultaneously and to more efficiently avoid local maxima in the search space.

We propose an end-to-end learning framework based on hierarchical reinforcement learning, called H-TSP, for addressing the large-scale Traveling Salesman Problem (TSP). The proposed H-TSP constructs a solution of a TSP instance starting from the scratch relying on two components: the upper-level policy chooses a small subset of nodes (up to 200 in our experiment) from all nodes that are to be traversed, while the lower-level policy takes the chosen nodes as input and outputs a tour connecting them to the existing partial route (initially only containing the depot). After jointly training the upper-level and lower-level policies, our approach can directly generate solutions for the given TSP instances without relying on any time-consuming search procedures. To demonstrate effectiveness of the proposed approach, we have conducted extensive experiments on randomly generated TSP instances with different numbers of nodes. We show that H-TSP can achieve comparable results (gap 3.42% vs. 7.32%) as SOTA search-based approaches, and more importantly, we reduce the time consumption up to two orders of magnitude (3.32s vs. 395.85s). To the best of our knowledge, H-TSP is the first end-to-end deep reinforcement learning approach that can scale to TSP instances of up to 10000 nodes. Although there are still gaps to SOTA results with respect to solution quality, we believe that H-TSP will be useful for practical applications, particularly those that are time-sensitive e.g., on-call routing and ride hailing service.

Discrete Spider Monkey Optimization for Travelling Salesman Problem