Performance Evaluation of Convex Hull Node-Based Heuristics for Solving the Travelling Salesman Problem

Asani, Emmanuel Oluwatobi; Okeyinka, A. E.; Adebiyi, Ayodele Ariyo

doi:10.1007/978-981-16-2102-4_60

Cited by 1 publication

(2 citation statements)

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“…This process is iterated for all the nodes that are not yet part of the tour until the tour is fully built and a Hamiltonian circuit is formed. This pro-cess is greedy in nature; thus, the performance is relatively poor [18]. The pseudocode for the Nearest Neighbour Heuristic is as follow: Analytically, [19] had shown that for a TSP instance of nodes 𝑛, the approximation ratio/solution quality of the Nearest Neighbour Heuristic is at most…”

Section: The Nearest Neighbour Heuristicmentioning

confidence: 99%

“…Flood, the Travelling Salesman Problem has become the benchmark for several other techniques of optimization [1]. The TSP is a shortest tour (or path) problem to find the optimal route while visiting a set of cities (or nodes), ensuring each city (or node) is visited exactly once and regarding the Hamiltonian circuit, return to the start node or city [18]. The Travelling Salesman must traverse cities 1 𝑡𝑜 𝑛 in a Hamiltonian cycle that is; Start from city 1 and traverse the remaining 𝑛 − 1 cities in arbitrary order, and return to the starting point with the objective of touching the cities once at a minimal cost.…”

Section: Problem Formulationmentioning

confidence: 99%

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A Computation Investigation of the Impact of Convex Hull subtour on the Nearest Neighbour Heuristic

Asani

Okeyinka

Adebiyi

2023

2023 International Conference on Science, Engineering and Business for Sustainable Development Goals (SEB-SDG)

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This study investigated the computational effect of a Convex Hull subtour on the Nearest Neighbour Heuristic. Convex hull subtour has been shown to theoretically degrade the worstcase performances of some insertion heuristics from twice optimal to thrice optimal, although other empirical studies have shown that the introduction of the convex hull as a subtour is expected to minimize the occurrences of outliers, thereby potentially improving the solution quality. This study was therefore conceived to investigate the empirical effect of a convex-hull-based initial tour on the Nearest Neighbour Heuristic vis-a-vis the traditional use of a single node as the initial tour. The resulting hybrid Convex Hull-Nearest Neighbour Heuristic (CH-NN) was used to solve the Travelling Salesman Problem. The technique was experimented using publicly available testbeds from TSPLIB. The performance of CH-NN vis-à-vis that of the traditional Nearest Neighbour solution showed empirically that Convex Hull can potentially improve the solution quality of tour construction techniques.

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Section: The Nearest Neighbour Heuristicmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%