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Recent papers on approximation algorithms for the traveling salesman problem (TSP) have given a new variant on the well-known Christofides' algorithm for the TSP, called the Best-of-Many Christofides' algorithm. The algorithm involves…

Data Structures and Algorithms · Computer Science 2015-06-26 Kyle Genova , David P. Williamson

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

Data Structures and Algorithms · Computer Science 2022-05-31 Amey Gohil , Manan Tayal , Tezan Sahu , Vyankatesh Sawalpurkar

In this paper, we study optimization problems where the cost function contains time-varying parameters that are unmeasurable and evolve according to linear, yet unknown, dynamics. We propose a solution that leverages control theoretic tools…

Optimization and Control · Mathematics 2025-03-20 Shivanshu Tripathi , Abed AlRahman Al Makdah , Fabio Pasqualetti

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that aims to find the shortest possible route that visits each city exactly once and returns to the starting point. This paper explores the application…

Neural and Evolutionary Computing · Computer Science 2025-01-28 Kael Silva Araújo , Francisco Márcio Barboza

Evolutionary deep neural networks have emerged as a rapidly growing field of research. This paper studies numerical integrators for such and other classes of nonlinear parametrizations $ u(t) = \Phi(\theta(t)) $, where the evolving…

Numerical Analysis · Mathematics 2025-01-22 Christian Lubich , Jörg Nick

Asymmetric Travelling Salesman Problem (ATSP) and its special case Directed Hamiltonicity are among the most fundamental problems in computer science. The dynamic programming algorithm running in time $O^*(2^n)$ developed almost 60 years…

Data Structures and Algorithms · Computer Science 2020-10-02 Łukasz Kowalik , Konrad Majewski

Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to…

Neural and Evolutionary Computing · Computer Science 2024-08-23 Frank Neumann , Carsten Witt

When globally optimal solutions of complicated optimization problems cannot be located by evolutionary algorithms (EAs) in polynomial expected running time, the hitting time/running time analysis is not flexible enough to accommodate the…

Neural and Evolutionary Computing · Computer Science 2020-12-01 Cong Wang , Yu Chen , Jun He , Chengwang Xie

Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a…

Neural and Evolutionary Computing · Computer Science 2019-08-12 Patrick Spettel , Hans-Georg Beyer

Many real-world problems can be formulated as a constrained Traveling Salesman Problem (TSP). However, the constraints are always complex and numerous, making the TSPs challenging to solve. When the number of complicated constraints grows,…

Artificial Intelligence · Computer Science 2024-03-11 Jingxiao Chen , Ziqin Gong , Minghuan Liu , Jun Wang , Yong Yu , Weinan Zhang

Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…

Discrete Mathematics · Computer Science 2016-01-06 Jens Vygen

In distributed evolutionary algorithms, migration interval is used to decide migration moments. Nevertheless, migration moments predetermined by intervals cannot match the dynamic situation of evolution. In this paper, a scheme of setting…

Neural and Evolutionary Computing · Computer Science 2017-01-06 Chengjun Li , Jia Wu

Given a traveling salesman problem (TSP) tour $H$ in graph $G$ a $k$-move is an operation which removes $k$ edges from $H$, and adds $k$ edges of $G$ so that a new tour $H'$ is formed. The popular $k$-OPT heuristics for TSP finds a local…

Data Structures and Algorithms · Computer Science 2017-08-02 Marek Cygan , Lukasz Kowalik , Arkadiusz Socala

The moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting…

Robotics · Computer Science 2025-04-24 Anoop Bhat , Geordan Gutow , Bhaskar Vundurthy , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

This paper explores the enhancement of solution diversity in evolutionary algorithms (EAs) for the maximum matching problem, concentrating on complete bipartite graphs and paths. We adopt binary string encoding for matchings and use Hamming…

Neural and Evolutionary Computing · Computer Science 2024-04-19 Jonathan Gadea Harder , Aneta Neumann , Frank Neumann

Most evolutionary algorithms have multiple parameters and their values drastically affect the performance. Due to the often complicated interplay of the parameters, setting these values right for a particular problem (parameter tuning) is a…

Neural and Evolutionary Computing · Computer Science 2024-10-08 Denis Antipov , Maxim Buzdalov , Benjamin Doerr

In this work we introduce an implementation for which machine learning techniques helped improve the overall performance of an evolutionary algorithm for an optimization problem, namely a variation of robust minimum-cost path in graphs. In…

Neural and Evolutionary Computing · Computer Science 2021-02-04 Ricardo Di Pasquale , Javier Marenco

The $(1+(\lambda,\lambda))$ genetic algorithm, first proposed at GECCO 2013, showed a surprisingly good performance on so me optimization problems. The theoretical analysis so far was restricted to the OneMax test function, where this GA…

Neural and Evolutionary Computing · Computer Science 2017-04-17 Maxim Buzdalov , Benjamin Doerr

Robust iterative methods for solving large sparse systems of linear algebraic equations often suffer from the problem of optimizing the corresponding tuning parameters. To improve the performance of the problem of interest, specific…

Numerical Analysis · Mathematics 2023-10-18 Andrey Petrushov , Boris Krasnopolsky

We consider the time-dependent traveling salesman problem (TDTSP), a generalization of the asymmetric traveling salesman problem (ATSP) to incorporate time-dependent cost functions. In our model, the costs of an arc can change arbitrarily…

Optimization and Control · Mathematics 2018-05-04 Christoph Hansknecht , Imke Joormann , Sebastian Stiller
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