Exact Approaches for the Travelling Thief Problem

Cosolver2B: An Efficient Local Search Heuristic for the Travelling Thief Problem

Real-world problems are very difficult to optimize. However, many researchers have been solving benchmark problems that have been extensively investigated for the last decades even if they have very few direct applications. The Traveling Thief Problem (TTP) is a NP-hard optimization problem that aims to provide a more realistic model. TTP targets particularly routing problem under packing/loading constraints which can be found in supply chain management and transportation. In this paper, TTP is presented and formulated mathematically. A combined local search algorithm is proposed and compared …

旅行小偷问题的近似算法

Approximation Algorithms for the Traveling Thief Problem

研究旅行小偷问题，它融合了旅行商问题与背包问题。核心方法是设计算法。主要贡献是给出多项式时间计算(9 + ε,9 + ε)近似帕累托集的算法，还为加权旅行商问题给出(2e + ε)近似算法。

度量实例的旅行小偷问题的有效旅行

Effective Traveling for Metric Instances of the Traveling Thief Problem

本文研究了旅行小偷问题中固定打包计划下的旅行优化部分，将其转化为加权TSP变种，并探讨了不同距离度量和成本函数对计算复杂性的影响，提出了一种O(n²)时间动态规划算法及近似算法。

A Fully Polynomial Time Approximation Scheme for Packing While Traveling

Understanding the interactions between different combinatorial optimisation problems in real-world applications is a challenging task. Recently, the traveling thief problem (TTP), as a combination of the classical traveling salesperson problem and the knapsack problem, has been introduced to study these interactions in a systematic way. We investigate the underlying non-linear packing while traveling (PWT) problem of the TTP where items have to be selected along a fixed route. We give an exact dynamic programming approach for this problem and a fully polynomial time approximation scheme (FPTAS…

Closed form distance formula for the balanced multiple travelling salesmen

As a first contribution the mTSP is solved using an exact method and two heuristics, where the number of nodes per route is balanced. The first heuristic uses a nearest node approach and the second assigns the closest vehicle (salesman). A comparison of heuristics with test-instances being in the Euclidean plane showed similar solution quality and runtime. On average, the nearest node solutions are approximately one percent better. The closest vehicle heuristic is especially important when the nodes (customers) are not known in advance, e.g. for online routing. Whilst the nearest node is prefe…

On Solving Cycle Problems with Branch-and-Cut: Extending Shrinking and Exact Subcycle Elimination Separation Algorithms

In this paper, we extend techniques developed in the context of the Travelling Salesperson Problem for cycle problems. Particularly, we study the shrinking of support graphs and the exact algorithms for subcycle elimination separation problems. The efficient application of the considered techniques has proved to be essential in the Travelling Salesperson Problem when solving large size problems by Branch-and-Cut, and this has been the motivation behind this work. Regarding the shrinking of support graphs, we prove the validity of the Padberg-Rinaldi general shrinking rules and the Crowder-Padb…