GLNS: An effective large neighborhood search heuristic for the Generalized Traveling Salesman Problem

2017 ◽  
Vol 87 ◽  
pp. 1-19 ◽  
Author(s):  
Stephen L. Smith ◽  
Frank Imeson
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Neighborhood Search ◽  
Large Neighborhood Search ◽  
Search Heuristic ◽  
Large Neighborhood ◽  
Generalized Traveling Salesman Problem

scholarly journals Heterogeneous Task Allocation and Sequencing via Decentralized Large Neighborhood Search

2017 ◽  
Vol 05 (02) ◽  
pp. 79-95 ◽  
Author(s):  
Armin Sadeghi ◽  
Stephen L. Smith
Keyword(s):  
Traveling Salesman Problem ◽  
Task Allocation ◽  
Branch And Cut ◽  
Traveling Salesman ◽  
Neighborhood Search ◽  
Large Neighborhood Search ◽  
Solution Quality ◽  
Solution Approach ◽  
Large Neighborhood ◽  
Generalized Traveling Salesman Problem

This paper focuses on decentralized task allocation and sequencing for multiple heterogeneous robots. Each task is defined as visiting a point in a subset of the robot configuration space — this definition captures a variety of tasks including inspection and servicing. The robots are heterogeneous in that they may be subject to different differential motion constraints. Our approach is to transform the problem into a multi-vehicle generalized traveling salesman problem (GTSP). To solve the GTSP, we propose a novel decentralized implementation of large-neighborhood search (LNS). Our solution approach leverages the GTSP insertion methods proposed in Fischetti et al. [A branch-and-cut algorithm for the symmetric generalized traveling salesman problem, Oper. Res. 45(3) (1997) 378–394]. to repeatedly remove and reinsert tasks from each robot path. Decentralization is achieved using combinatorial-auctions between the robots on tasks removed from robot’s path. We provide bounds on the length of the dynamically feasible robot paths produced by the insertion methods. We also show that the number of bids in each combinatorial auction, a crucial factor in the runtime, scales linearly with the number of tasks. Finally, we present extensive benchmarking results to characterize both solution quality and runtime, which show improvements over existing decentralized task allocation methods.

Solving the Laser Cutting Path Problem Using Population-Based Simulated Annealing with Adaptive Large Neighborhood Search

2020 ◽  
Vol 833 ◽  
pp. 29-34 ◽  
Author(s):  
Makbul Hajad ◽  
Viboon Tangwarodomnukun ◽  
Chaiya Dumkum ◽  
Chorkaew Jaturanonda
Keyword(s):  
Simulated Annealing ◽  
Laser Cutting ◽  
Computing Time ◽  
Population Based ◽  
Neighborhood Search ◽  
Large Neighborhood Search ◽  
Adaptive Large Neighborhood Search ◽  
Large Neighborhood ◽  
Generalized Traveling Salesman Problem ◽  
Cutting Path

This paper presents an alternative algorithm for solving the laser cutting path problem which was modeled as Generalized Traveling Salesman Problem (GTSP). The objective is to minimize the traveling distance of laser cutting of all profiles in a given layout, where a laser beam makes a single visit and then does the complete cut of individual profile in an optimum sequence. This study proposed a hybrid method combining population-based simulated annealing (SA) with an adaptive large neighborhood search (ALNS) algorithm to solve the cutting path problem. Recombination procedures were executed alternately using swap, reversion, insertion and removal-insertion through a fitness proportionate selection mechanism. In order to reduce the computing time and maintain the solution quality, the 35% proportion of population were executed in each iteration using the cultural algorithm selection method. The results revealed that the algorithm can solve several ranges of problem size with an acceptable percentage of error compared to the best known solution.

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