Large TSP Research Articles

An efficient benders decomposition for the [formula omitted]-median problem

The p-median problem is a classic discrete location problem with numerous applications. It aims to open p sites while minimizing the sum of the distances of each client to its nearest open site. We study a Benders decomposition of the most efficient formulation in the literature. We show that the Benders cuts can be separated in linear time. The Benders reformulation leads to a compact formulation for the p-median problem. We implement a two-phase Benders decomposition algorithm that outperforms state-of-the-art methods on benchmark instances by an order of magnitude and allows to exactly solve for the first time several instances among which are large TSP instances and BIRCH instances. We also show that our implementation easily applies to the uncapacitated facility location problem.

An Optimized Discrete Dragonfly Algorithm Tackling the Low Exploitation Problem for Solving TSP

Optimization problems are prevalent in almost all areas and hence optimization algorithms are crucial for a myriad of real-world applications. Deterministic optimization algorithms tend to be computationally costly and time-consuming. Hence, heuristic and metaheuristic algorithms are more favoured as they provide near-optimal solutions in an acceptable amount of time. Swarm intelligence algorithms are being increasingly used for optimization problems owing to their simplicity and good performance. The Dragonfly Algorithm (DA) is one which is inspired by the swarming behaviours of dragonflies, and it has been proven to have a superior performance than other algorithms in multiple applications. Hence, it is worth considering its application to the traveling salesman problem which is a predominant discrete optimization problem. The original DA is only suitable for solving continuous optimization problems and, although there is a binary version of the algorithm, it is not easily adapted for solving discrete optimization problems like TSP. We have previously proposed a discrete adapted DA algorithm suitable for TSP. However, it has low effectiveness, and it has not been used for large TSP problems. In this paper, we propose an optimized discrete adapted DA by using the steepest ascent hill climbing algorithm as a local search. The algorithm is applied to a TSP problem modelling a package delivery system in the Kuala Lumpur area and to benchmark TSP problems, and it is found to have a higher effectiveness than the discrete adapted DA and some other swarm intelligence algorithms. It also has a higher efficiency than the discrete adapted DA.

Improving Ant Colony Optimization efficiency for solving large TSP instances

Ant Colony Optimization (ACO) is a family of nature-inspired metaheuristics often applied to finding approximate solutions to difficult optimization problems. Despite being significantly faster than exact methods, the ACOs can still be prohibitively slow, especially if compared to basic problem-specific heuristics. As recent research has shown, it is possible to significantly improve the performance through algorithm refinements and careful parallel implementation benefiting from multi-core CPUs and dedicated accelerators. In this paper, we present a novel ACO variant, namely the Focused ACO (FACO). One of the core elements of the FACO is a mechanism for controlling the number of differences between a newly constructed and a selected previous solution. The mechanism results in a more focused search process, allowing to find improvements while preserving the quality of the existing solution. An additional benefit is a more efficient integration with a problem-specific local search. Computational study based on a range of the Traveling Salesman Problem instances shows that the FACO outperforms the state-of-the-art ACOs when solving large TSP instances. Specifically, the FACO required less than an hour of an 8-core commodity CPU time to find high-quality solutions (within 1% from the best-known results) for TSP Art Instances ranging from 100000 to 200000 nodes.

Parallel iterative hill climbing algorithm to solve TSP on GPU

SummaryTraveling Salesman Problem (TSP) is an NP‐hard combinatorial optimization problem. Heuristic algorithms provide satisfactory solutions to large instance TSP in a reasonable amount of time. However, heuristic methods result in suboptimal solutions as they do not cover the search space adequately. Sequential heuristic approaches spend significant CPU time in neighborhood generation for large input instances. Neighborhood generation time can be reduced by generating in parallel. GPUs have been shown to be effective in exploiting data and memory level parallelism in large complex problems. This work presents a GPU‐based Parallel Iterative Hill Climbing (PIHC) algorithm using the nearest neighborhood heuristic to arrive at near‐optimal solutions of large TSPLIB instances in a reasonable amount of time. Multiple construction heuristics approaches, thread mapping strategies, and data structures for TSPLIB instances have been evaluated. We demonstrate improved cost quality on symmetric TSPLIB instances up to 85,900 cities. The PIHC GPU implementation gives up to 193× speedup over its sequential counterpart and up to 979.96× speedup over a state‐of‐the‐art GPU‐based TSP solver. The PIHC implementation gives a cost quality with error rate 0.72% in the best case and 8.06% in the worst case.

Generalization of the restricted planar location problems: Unified metaheuristic algorithms

In the restricted planar location problems, facilities cannot be located inside certain areas on the plane. We define congested regions as polygonal areas on the plane inside which locating a facility is infeasible but through which traveling is possible at an additional fixed cost. The location problem with congested regions on the Euclidean plane is shown to be a generalization of the two most studied problems in the literature, i.e. the restricted planar facility location problems with forbidden regions and with barriers. We propose three metaheuristic algorithms enhanced with a local search procedure to solve the restricted planar location problem. A user interface module is also developed to implement the algorithms on the test instances and analyze computational experiments. The test problem instances include those from the restricted planar facility location literature as well as modified large TSP and VRP instances from the routing literature. The presented computational results show the performance of the proposed algorithms and their effectiveness on solving problems with large size.

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

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% 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 SPC3 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.

A CLUSTERING AND GENETIC SCHEME FOR LARGE TSP OPTIMIZATION PROBLEMS

A novel hybrid genetic scheme to solve the traveling salesman problem is presented in this paper. The proposed scheme has two major steps: clustering and global optimization. The clustering step is used to obtain an initial solution that is used as seed. The global optimization uses this seed to produce a better result using genetic operators. A number of benchmarks have been used to evaluate the proposed scheme. The solutions to these benchmarks which include 105-, 318-, 1060-, 2152-, 3038-, and 5934-city TSPs are extremely close to the best known solutions. This scheme is the first genetic approach that deals with large TSP benchmarks.

Improved Large-Step Markov Chain Variants for the Symmetric TSP

The large-step Markov chain (LSMC) approach is the most effective known heuristic for large symmetric TSP instances; cf. recent results of [Martin, Otto and Felten, 1991] and [Johnson, 1990]. In this paper, we examine relationships among (i) the underlying local optimization engine within the LSMC approach, (ii) the “kick move” perturbation that is applied between successive local search descents, and (iii) the resulting LSMC solution quality. We find that the traditional “double-bridge” kick move is not necessarily optimum: stronger local optimization engines (e.g., Lin-Kernighan) are best matched with stronger kick moves. We also propose use of an adaptive temperature schedule to allow escape from deep basins of attraction; the resulting hierarchical LSMC variant outperforms traditional LSMC implementations that use uniformly zero temperatures. Finally, a population-based LSMC variant is studied, wherein multiple solution paths can interact to achieve improved solution quality.