Efficient convex-elastic net algorithm to solve the Euclideantraveling salesman problem

This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extension

Efficient convex-elastic net algorithm to solve the Euclideantraveling salesman problem

This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extension

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

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 worst-case 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

People Efficiently Explore the Solution Space of the Computationally Intractable Traveling Salesman Problem to Find Near-Optimal Tours

Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution (“good” edges) were significantly more likely to stay than other edges (“bad” edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants “ran out of ideas.” In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics

An Application of Self-Organizing Map for Multirobot Multigoal Path Planning with Minmax Objective

In this paper, Self-Organizing Map (SOM) for the Multiple Traveling Salesman Problem (MTSP) with minmax objective is applied to the robotic problem of multigoal path planning in the polygonal domain. The main difficulty of such SOM deployment is determination of collision-free paths among obstacles that is required to evaluate the neuron-city distances in the winner selection phase of unsupervised learning. Moreover, a collision-free path is also needed in the adaptation phase, where neurons are adapted towards the presented input signal (city) to the network. Simple approximations of the shortest path are utilized to address this issue and solve the robotic MTSP by SOM. Suitability of the proposed approximations is verified in the context of cooperative inspection, where cities represent sensing locations that guarantee to “see” the whole robots’ workspace. The inspection task formulated as the MTSP-Minmax is solved by the proposed SOM approach and compared with the combinatorial heuristic GENIUS. The results indicate that the proposed approach provides competitive results to GENIUS and support applicability of SOM for robotic multigoal path planning with a group of cooperating mobile robots. The proposed combination of approximate shortest paths with unsupervised learning opens further applications of SOM in the field of robotic planning

Modeling and Optimization for Transportation Systems Planning and Operations

In this paper, we focus on a number of applications of network optimization techniques to transportation systems analysis. In particular, network analysis problems, network design problems, and network management problems are discussed in some detail. The intent is to survey important application areas.*To be presented at the International Symposium on Large Engineering Systems, University of Manitoba, Winnipeg, Manitoba, Canada, August 9-12, 197

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

End-to-End Decision Focused Learning using Learned Solvers

Achieving fusion of deep learning with combinatorial algorithms promises transformativechanges to AI. Creating an impact in a real-world setting requires AI techniques to span a pipeline from data, to predictive models, to decisions. Aligning these components together requires careful consideration, as having these components trained separately does not account for the end goal of the model. This work surveys general frameworks for melding these components, we focus on the integration of optimization methods with machine learning architectures. We address some challenges and limitations associated with these methods and propose a novel approach to address some of the bottlenecks that arise