A multiobjective combinatorial optimization (MOCO) formulation for the following location-routing problem in healthcare management is given: For a mobile healthcare facility, a closed tour with stops selected from a given set of population nodes has to be found. Tours are evaluated according to three criteria: (i) an economic efficiency criterion related to the tour length, (ii) the criterion o...

The Chinese postman problem (CPP) is that of finding the shortest postman tour covering all the roads in the network. The CPP is polynomial-time solvable on totally directed or undirected networks, but is NP-complete on mixed networks (MCPP). Several heuristic solution procedures including Mixed-1, Mixed-2, Modified Mixed-1, and Modified Mixed-2 algorithms, have been proposed to solve the probl...

Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem (TDTSP) consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The contribution of this paper is twofold. First, we describe a lower and upper bounding procedure that requires the solution of a simpler (yet NP-hard) Asymmetric Travelling Salesman Pro...

We are solving a tactical mail delivery problem by combining exact and heuristic methods. Routes for postpersons have to be planned visiting each customer exactly once at minimum cost. Four different modes (car, moped, bicycle, and walking) are available, but not all customers are accessible by all modes. In addition, it is possible to change the mode in the tour and walk a loop, which is calle...

The multi-vehicle covering tour problem (m-CTP) involves finding a minimumlength set of vehicle routes passing through a subset of vertices, subject to constraints on the length of each route and the number of vertices that it contains, such that each vertex not included in any route lies within a given distance of a route. This paper tackles a particular case of m-CTP where only the restrictio...

We study the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. In [3], the authors defined it as the Profitable Tour Problem (PTP). We present an (1 + log(n))-approximatio...

The covering salesman problem (CSP) is an extension of the well-known traveling salesman problem in which we are allowed to leave some vertices unvisited. The goal of the CSP is to construct a minimum length Hamiltonian cycle over a subset of vertices where those vertices not visited by the tour need to be within a pre-determined distance from at least one visited vertex. In this paper, we prop...

The motivation of this project is to solve a problem that we currently face working on a project called 27bards, which seeks to revolutionize the tour industry by constructing a database of currently existing tour operators with the Airbnb-like twist of allowing the average person to make money as a part-time tour guide. We wanted to apply machine-learning techniques to make sense of the largel...