Solving large batches of traveling salesman problems with parallel and distributed computing

Abstract

In this paper, we describe and compare serial, parallel, and distributed solver implementations for large batches of Traveling Salesman Problems using the Lin-Kernighan Heuristic (LKH) and the Concorde exact TSP Solver. Parallel and distributed solver implementations are useful when many medium to large size TSP instances must be solved simultaneously. These implementations are found to be straightforward and highly efficient compared to serial implementations. Our results indicate that parallel computing using hyper-threading for solving 150-and 200-city TSPs can increase the overall utilization of computer resources up to 25 percent compared to single thread computing. The resulting speed-up/physical core ratios are as much as ten times better than a parallel and concurrent version of the LKH heuristic using SPC 3 in the literature. For variable TSP sizes, a longest processing time first heuristic performs better than an equal distribution rule. We illustrate our approach with an application in the design of order picking warehouses.

Vehicle Routing and Scheduling for Regular Mobile Healthcare Services

“…Such methods include metaheuristics like genetic algorithms [4], tabu search [5], simulated annealing, other bio-inspired optimizations [6]. Other types of approaches are machine learning [7] or distributed algorithms [8], [9].…”

Genetic algorithm and a double-chromosome implementation to the traveling salesman problem

“…In order to solve a TSP with even a moderate number of cities and in the interest of optimized tour, an extremely huge search space should be investigated and a massive computational time will be required. Although exact algorithms similar to the brute force approach (BFA) that allow for evaluating all possible solutions are guaranteed to find the optimal solution, they can only be applied to small TSPs up to 10 cities [7,8], and thus, for average and big TSPs the direct methods are, in fact, useless. Therefore, the development and application of heuristic algorithms that could find the optimal or near-optimal solution in a limited time frame [7] have been massively studied.…”

“…Although exact algorithms similar to the brute force approach (BFA) that allow for evaluating all possible solutions are guaranteed to find the optimal solution, they can only be applied to small TSPs up to 10 cities [7,8], and thus, for average and big TSPs the direct methods are, in fact, useless. Therefore, the development and application of heuristic algorithms that could find the optimal or near-optimal solution in a limited time frame [7] have been massively studied. Algorithms like but not limited to tabu search [9], Lin-Kernighan heuristic [10] have been significantly improved over years as successful methods for obtaining the optimal or near-optimal solutions [11] as well as genetic algorithm (GA) [8,[12][13][14][15][16][17].…”

Solving Traveling Salesman Problems with Ant Colony Optimization Algorithms in Sequential and Parallel Computing Environments: A Normalized Comparison

“…As ACOs are prone to local maxima, as-observed in many existing studies [9], [10], [19], we make a small change to the basic ACO for TSPs in Algorithm 1 to deal with such stagnation. In the probability-based stochastic controller (1), instead of directing ant k in city i to next city j according to the highest probability k ij p , we make a pool of three potential cities with the three highest probability …”

“…Avoiding local stagnation requires adding other disturbing operations into an ACO algorithm, but such an action inevitably prolongs the convergence [8], [9]. Given the multi-agent nature of ACOs, a few recent studies have explored the likelihood of efficiently applying parallel ACO algorithms to solve TSPs [14]- [19].…”