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The genetic algorithm includes some parameters that should be adjusted, so as to get reliable results. Choosing a representation of the problem addressed, an initial population, a method of selection, a crossover operator, mutation…
The variational problem of the least uncomfortable journey between two locations on a straight line is simplified by a choice of the dependent variable. It is shown that taking the position, instead of the velocity, as the optimal function…
The travelling salesman problem (TSP) is one of the well-studied NP-hard problems in the literature. The state-of-the art inexact TSP solvers are the Lin-Kernighan-Helsgaun (LKH) heuristic and Edge Assembly crossover (EAX). A recent study…
A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…
This paper describes a formulation and develops a novel procedure for a fleet of unmanned aerial vehicles (UAVs) from the perspective of remotely executable tasks. In a complex mission environment, the characteristics of vehicles can be…
In this paper, we provide a novel strategy for solving Traveling Salesman Problem, which is a famous combinatorial optimization problem studied intensely in the TCS community. In particular, we consider the imitation learning framework,…
The ridesharing problem is that given a set of trips, each trip consists of an individual, a vehicle of the individual and some requirements, select a subset of trips and use the vehicles of selected trips to deliver all individuals to…
A fundamental variant of the classical traveling salesman problem (TSP) is the so-called multiple TSP (mTSP), where a set of $m$ salesmen jointly visit all cities from a set of $n$ cities. The mTSP models many important real-life…
We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag…
The quadratic traveling salesperson problem (QTSP) is a generalization of the traveling salesperson problem, in which all triples of consecutive customers in a tour determine the travel cost. We propose compact optimization models for QTSP…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
We study the Compositional Geometry Routing Problem (CGRP), a unified superclass of traditional routing problems that covers point-only, line-only, area-only, and arbitrary hybrid task geometries, providing a broad abstraction for…
We introduce a method based on the Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e. a NP-hard problem whose search space exponentially grows increasing the number of cities.…
In this paper, some preliminaries about signal flow graph, linear time-invariant system on F(z) and computational complexity are first introduced in detail. In order to synthesize the necessary and sufficient condition on F(z) for a general…
Hougardy and Schroeder (WG 2014) proposed a combinatorial technique for pruning the search space in the traveling salesman problem, establishing that, for a given instance, certain edges cannot be present in any optimal tour. We describe an…
Given a set $P$ of $n$ points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance…
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…
The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound,…
We develop an asymptotic approximation and bounds for the traveling salesman problem with time slots, i.e. when the time windows of points to visit are a partition of a given time horizon. Although this problem is relevant in several…
We introduce the Polychromatic Traveling Salesman Problem (PCTSP), where the input is an edge weighted graph whose vertices are partitioned into $k$ equal-sized color classes, and the goal is to find a minimum-length Hamiltonian cycle that…