arXiv subjects

Manuel Iori

Publications and source records attributed to Manuel Iori.

23 records · Page 2Linked to original sources

arXiv2019

Solution of minimum spanning forest problems with reliability constraints

We propose the reliability constrained k-rooted minimum spanning forest, a relevant optimization problem whose aim is to find a k-rooted minimum cost forest that connects given customers to a number of supply vertices, in such a way that a minimum required reliability on each path between a customer and a supply vertex is satisfied and the cost is a minimum. The reliability of an edge is the probability that no failure occurs on that edge, whereas the reliability of a path is the product of the reliabilities of the edges in such path. The problem has relevant applications in the design of networks, in fields such as telecommunications, electricity and transports. For its solution, we propose a mixed integer linear programming model, and an adaptive large neighborhood search metaheuristic which invokes several shaking and local search operators. Extensive computational tests prove that the metaheuristic can provide good quality solutions in very short computing times.

math.OC↗

arXiv2019

A Branch-and-Price Algorithm for the Temporal Bin Packing Problem

We study an extension of the classical Bin Packing Problem, where each item consumes the bin capacity during a given time window that depends on the item itself. The problem asks for finding the minimum number of bins to pack all the items while respecting the bin capacity at any time instant. A polynomial-size formulation, an exponential-size formulation, and a number of lower and upper bounds are studied. A branch-and-price algorithm for solving the exponential-size formulation is introduced. An overall algorithm combining the different methods is then proposed and tested trough extensive computational experiments.

math.OC↗

arXiv2018

Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines

We consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical formulations, some of which require the implementation of tailored branch-and-price methods. In our work, we solve the problem instead by means of new arc-flow formulations, by first representing it on a capacitated network and then invoking a mixed integer linear model with a pseudo-polynomial number of variables and constraints. According to our computational tests, existing formulations from the literature can solve to proven optimality benchmark instances with up to 100 jobs, whereas our most performing arc-flow formulation solves all instances with up to 400 jobs and provides very low gap for larger instances with up to 1000 jobs.

cs.DS↗

arXiv2018

Mathematical models and search algorithms for the capacitated $p$-center problem

The capacitated p-center problem requires to select p facilities from a set of candidates to service a number of customers, subject to facility capacity constraints, with the aim of minimizing the maximum distance between a customer and its associated facility. The problem is well known in the field of facility location, because of the many applications that it can model. In this paper, we solve it by means of search algorithms that iteratively seek the optimal distance by solving tailored subproblems. We present different mathematical formulations for the subproblems and improve them by means of several valid inequalities, including an effective one based on a 0-1 disjunction and the solution of subset sum problems. We also develop an alternative search strategy that finds a balance between the traditional sequential search and binary search. This strategy limits the number of feasible subproblems to be solved and, at the same time, avoids large overestimates of the solution value, which are detrimental for the search. We evaluate the proposed techniques by means of extensive computational experiments on benchmark instances from the literature and new larger test sets. All instances from the literature with up to 402 vertices and integer distances are solved to proven optimality, including 13 open cases, and feasible solutions are found in 10 minutes for instances with up to 3038 vertices.

cs.DS↗

arXiv2016

A heuristic algorithm for a single vehicle static bike sharing rebalancing problem

The static bike rebalancing problem (SBRP) concerns the task of repositioning bikes among stations in self-service bike-sharing systems. This problem can be seen as a variant of the one-commodity pickup and delivery vehicle routing problem, where multiple visits are allowed to be performed at each station, i.e., the demand of a station is allowed to be split. Moreover, a vehicle may temporarily drop its load at a station, leaving it in excess or, alternatively, collect more bikes from a station (even all of them), thus leaving it in default. Both cases require further visits in order to meet the actual demands of such station. This paper deals with a particular case of the SBRP, in which only a single vehicle is available and the objective is to find a least-cost route that meets the demand of all stations and does not violate the minimum (zero) and maximum (vehicle capacity) load limits along the tour. Therefore, the number of bikes to be collected or delivered at each station should be appropriately determined in order to respect such constraints. We propose an iterated local search (ILS) based heuristic to solve the problem. The ILS algorithm was tested on 980 benchmark instances from the literature and the results obtained are quite competitive when compared to other existing methods. Moreover, our heuristic was capable of finding most of the known optimal solutions and also of improving the results on a number of open instances.

cs.AI↗