Related papers: CycleFormer : TSP Solver Based on Language Modelin…

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…

Dynamic representation learning plays a pivotal role in understanding the evolution of linguistic content over time. On this front both context and time dynamics as well as their interplay are of prime importance. Current approaches model…

Sortformer is an encoder-based speaker diarization model designed for supervising speaker tagging in speech-to-text models. Instead of relying solely on permutation invariant loss (PIL), Sortformer introduces Sort Loss to resolve the…

We present a compact quantum encoding of the Traveling Salesperson Problem (TSP) based on a time-register representation of tours. A candidate route is represented as a sequence of $n$ city labels over discrete time steps, with one fixed…

This paper presents a novel and efficient heuristic framework for approximating the solutions to the multiple traveling salesmen problem (m-TSP) and other variants on the TSP. The approach adopted in this paper is an extension of the…

Transformers have achieved state-of-the-art performance in numerous tasks. In this paper, we propose a continuous-time formulation of transformers. Specifically, we consider a dynamical system whose governing equation is parametrized by…

Evolutionary algorithms have been shown to obtain good solutions for complex optimization problems in static and dynamic environments. It is important to understand the behaviour of evolutionary algorithms for complex optimization problems…

Finding the exact integrality gap $\alpha$ for the LP relaxation of the metric Travelling Salesman Problem (TSP) has been an open problem for over thirty years, with little progress made. It is known that $4/3 \leq \alpha \leq 3/2$, and a…

Let M be an nXn symetric matrix, n, even, T, an upper bound for T_OPT, an optimal tour, sigma_T, the smaller-valued perfect matching obtained from alternate edges of T expressed as a product of 2-cycles. Applying the modified Floyd-Warshall…

The characterization of strong valid inequalities for integer and mixed-integer programs is more of an artistic task than a systematic methodology, requiring inspiration that can sometimes be elusive. Frequently, this task is facilitated by…

We present an approach for the traveling salesman problem with graph metric based on Steiner cycles. A Steiner cycle is a cycle that is required to contain some specified subset of vertices. For a graph $G$, if we can find a spanning tree…

The travelling thief problem (TTP) is a representative of multi-component optimisation problems with interacting components. TTP combines the knapsack problem (KP) and the travelling salesman problem (TSP). A thief performs a cyclic tour…

The advent of Transformer-based models has surpassed the barriers of text. When working with speech, we must face a problem: the sequence length of an audio input is not suitable for the Transformer. To bypass this problem, a usual approach…

This work proposes a novel enumeration algorithm for computing the integrality gap of small instances of the subtour elimination formulation for the Asymmetric Traveling Salesman Problem (ATSP). The core idea is to enumerate pairs of…

We study GCS-TSP, a new variant of the Traveling Salesman Problem (TSP) defined over a Graph of Convex Sets (GCS) -- a powerful representation for trajectory planning that decomposes the configuration space into convex regions connected by…

In this paper, we present a new linear programming (LP) formulation of the Traveling Salesman Problem (TSP). The proposed model has O(n^8) variables and O(n^7) constraints, where n is the number of cities. Our numerical experimentation…

Effectively encoding multi-scale contextual information is crucial for accurate semantic segmentation. Existing transformer-based segmentation models combine features across scales without any selection, where features on sub-optimal scales…

Transformers have achieved great success in effectively processing sequential data such as text. Their architecture consisting of several attention and feedforward blocks can model relations between elements of a sequence in parallel…

We present an application of the tensor network generator-enhanced optimization (TN-GEO) framework to address the traveling salesman problem (TSP), a fundamental combinatorial optimization challenge. Our approach employs a tensor network…