Comparative Study of Algorithms Metaheuristics Based Applied to the Solution of the Capacitated Vehicle Routing Problem

This chapter presents the best-known heuristics and metaheuristics that are applied to solve the capacitated vehicle routing problem (CVRP), which is the generalization of the TSP, in which the nodes are visited by more than one route. To find out which algorithm obtains better results, there are 30 test instances used, which are grouped into 3 sets of problems according to the position of the nodes. The study begins with an economic impact analysis of the transportation sector in companies, which represents up to 20% of the final cost of the product. This case study focuses on the CVRP for its acronym capacitated vehicle routing problem, analyzing the best-known heuristics such as Clarke & Wright and sweep, and the algorithms GRASP and simulated annealing metaheuristics based.

Solution Attractor of Local Search System: A Method to Reduce Computational Complexity of the Traveling Salesman Problem

The traveling salesman problem (TSP) is presumably difficult to solve exactly using local search algorithms. It can be exactly solved by only one algorithm—the enumerative search algorithm. However, the scanning of all possible solutions requires exponential computing time. Do we need exploring all the possibilities to find the optimal solution? How can we narrow down the search space effectively and efficiently for an exhausted search? This chapter attempts to answer these questions. A local search algorithm is a discrete dynamical system, in which a search trajectory searches a part of the solution space and stops at a locally optimal point. A solution attractor of a local search system for the TSP is defined as a subset of the solution space that contains all locally optimal tours. The solution attractor concept gives us great insight into the computational complexity of the TSP. If we know where the solution attractor is located in the solution space, we simply completely search the solution attractor, rather than the entire solution space, to find the globally optimal tour. This chapter describes the solution attractor of local search system for the TSP and then presents a novel search system—the attractor-based search system—that can solve the TSP much efficiently with global optimality guarantee.

CUDA Accelerated 2-OPT Local Search for the Traveling Salesman Problem

This research involves the development of a compute unified device architecture (CUDA) accelerated 2-opt local search algorithm for the traveling salesman problem (TSP). As one of the fundamental mathematical approaches to solving the TSP problem, the time complexity has generally reduced its efficiency, especially for large problem instances. Graphic processing unit (GPU) programming, especially CUDA has become more mainstream in high-performance computing (HPC) approaches and has made many intractable problems at least reasonably solvable in acceptable time. This chapter describes two CUDA accelerated 2-opt algorithms developed to solve the asymmetric TSP problem. Three separate hardware configurations were used to test the developed algorithms, and the results validate that the execution time decreased significantly, especially for the large problem instances when deployed on the GPU.

Accelerating DNA Computing via PLP-qPCR Answer Read out to Solve Traveling Salesman Problems

An asymmetric, fully-connected 8-city traveling salesman problem (TSP) was solved by DNA computing using the ordered node pair abundance (ONPA) approach through the use of pair ligation probe quantitative real time polymerase chain reaction (PLP-qPCR). The validity of using ONPA to derive the optimal answer was confirmed by in silico computing using a reverse-engineering method to reconstruct the complete tours in the feasible answer set from the measured ONPA. The high specificity of the sequence-tagged hybridization, and ligation that results from the use of PLPs significantly increased the accuracy of answer determination in DNA computing. When combined with the high throughput efficiency of qPCR, the time required to identify the optimal answer to the TSP was reduced from days to 25 min.