A self‐organizing neural network approach for multiple traveling salesman and vehicle routing problems

Abstract

This paper addresses several algorithms based on self‐organizing neural network approach for routing problems. The algorithm for Traveling Salesman Problem is elaborated and the extension of the proposed algorithm to more complex problems namely, Multiple Traveling Salesmen and Vehicle Routing is discussed. In order to investigate the performance of the algorithms, a comprehensive empirical study has been provided. The simulations, which are conducted on standard data, evaluate the overall performance of this approach by comparing the results with the best known or the optimal solutions of the problems. The proposed algorithm shows significant advances in both qualities of the solution and computational efforts for most of the experimented data.

A Review: Machine Learning for Combinatorial Optimization Problems in Energy Areas

“…The search identified 274 documents containing the theoretical conclusions of various algorithms and the results of applicable approaches. Background information contains relevant knowledge in COPs [44][45][46][47][48][49][50][51][52][53][54], deep learning [55][56][57][58][59][60][61] and reinforcement learning [36,[62][63][64][65][66][67][68]. Supervised learning, reinforcement learning and game theoretic methods are introduced in learning methods, where supervised learning includes methods of B&B [69][70][71][72][73][74], sequence to vector [57,[75][76][77], GNN [78][79][80][81][82] and end-to-end architecture [83,84].…”

“…The objective of the traveling salesman problem (TSP) is to seek the shortest possible path that allows the salesman to visit each city only once and returns to the origin city given the city list and connection distances between any two city nodes. TSP is utilized as a basic formulation for many optimization approaches, such as vehicle routing [44], scheduling [45], path planning [46], logistics [47], DNA sequencing [48] and the computing system [49]. In these applications, the city nodes in the graph represent, for instance, customers, soldering points, or DNA fragments, and each city pair or the distance represents the traveling time duration or cost, or the measurement between DNA fragments.…”

Broken Bike Recycling Planning for Sharing Bikes System

“…To enable the algorithm to cope with our broken bike collection problem, a constraint satisfaction mechanism is incorporated. The output nodes compete to be the winner for a given broken sharing bike according to the following competitive rule [2], [4]:…”

“…where W j denotes the node j in route r [2]. G is the gain parameter and d is the cardinal distance measured along the ring between nodes j and J. .…”

Fast Scheduling of Autonomous Mobile Robots Under Task Space Constraints With Priorities

“…Starting with artificial neural networks designed by Hopfield and Tank [37], various different neural network methods have been used for the TSP such as elastic nets [38] and selforganizing maps [39][40][41][42]. Extensions of elastic nets and selforganizing maps have also been designed to handle the VRP [43][44][45][46]. Use of learning methods for the TSP/VRP has not been very popular in recent times, especially due to lack of results [47], but with the advent of sequence-to-sequence learning [48] and use of pointer networks [49], some research efforts have been made in this direction.…”