Editorial for the special issue on “Algorithms for graphs and networks”

This Special Issue of Algorithms presents recent advances in the area of graphs and networks, focusing particularly on optimisation problems and their associated algorithms [...

The matching relaxation for a class of generalized set partitioning problems

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.Comment: 33 pages. A preliminary (4-page) version of this paper was presented at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial Optimization), with proceedings on Electronic Notes in Discrete Mathematic

Matheuristics: using mathematics for heuristic design

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development

Designing and Scheduling Cost-Efficient Tours by Using the Concept of Truck Platooning

Truck Platooning is a promising new technology to reduce the fuel consumption by around 15% via the exploitation of a preceding and digitally connected truck’s slipstream. However, the cost-efficient coordination of such platoons under consideration of mandatory EU driving time restrictions turns out to be a highly complex task. For this purpose, we provide a comprehensive literature review and formulate the exact EU-Truck Platooning Problem (EU-TPP) as an Integer Linear Program (ILP) which also features a hypothetical task-relieving effect for following drivers in a convoy. In order to increase the computational efficiency, we introduce an auxiliary constraint and two hierarchical planning-based matheuristic approaches: the Shortest Path Heuristic (SPH) and the Platoon Routing Heuristic (PRH). Besides a qualitative sensitivity analysis, we perform an extensive numerical study to investigate the impact of different critical influence factors on platooning, being of major political and economic interest. Our experiments with the EU-TPP suggest remarkable fuel cost savings of up to 10.83% without a 50% task relief, while its inclusion leads to additional personnel cost savings of up to even 31.86% at best with maximally 12 trucks to be coordinated in a recreated part of the European highway network. Moreover, we prove our matheuristics’ highly favorable character in terms of solution quality and processing time. Keywords: autonomous transport; Truck Platooning; driving time and rest periods; cost-efficient routing & scheduling; computational efficiency

A Literature Review On Combining Heuristics and Exact Algorithms in Combinatorial Optimization

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such benefits. This paper reviews existing techniques for such combinations and provides examples of using them for vehicle routing problems

Heuristics for a vehicle routing problem with information collection in wireless networks

International audienceWe consider a wireless network where a given set of stations is continuously generating information. A single vehicle, located at a base station, is available to collect the information via wireless transfer. The wireless transfer vehicle routing problem (WTVRP) is to decide which stations should be visited in the vehicle route, how long shall the vehicle stay in each station, and how much information shall be transferred from the nearby stations to the vehicle during each stay. The goal is to collect the maximum amount of information during a time period after which the vehicle returns to the base station. The WTVRP is NP-hard. Although it can be solved to optimality for small size instances, one needs to rely on good heuristic schemes to obtain good solutions for large size instances. In this work, we consider a mathematical formulation based on the vehicle visits. Several heuristics strategies are proposed, most of them based on the mathematical model. These strategies include constructive and improvement heuristics. Computational experiments show that a strategy that combines a combinatorial greedy heuristic to design a initial vehicle route, improved by a fix-and-optimize heuristic to provide a local optimum, followed by an exchange heuristic, affords good solutions within reasonable amount of running time