Papers by Aristide Mingozzi
Lower Bounds and an Exact Method for the Heterogeneous Vehicle Routing Problem
Decomposition , relaxation and metaheuristic generation
Large part of combinatorial optimization research has been devoted to the study of exact methods ... more Large part of combinatorial optimization research has been devoted to the study of exact methods leading, most notably during the years 60s and 70s, to a number of very diversified approaches to the solution of the problems of interest. Several of these approaches have by now lost their thrust in the literature as newer, more powerful exact optimization techniques appeared and proved their effectiveness. However, some of those older framework can now be revisited in a metaheuristic perspective, as they are quite general frameworks for dealing with optimization problems. In this work we propose to investigate the possibility of reinterpreting decomposition, with special emphasis on the related Dantzig-Wolfe, Benders and Lagrangean relaxation techniques. We show how these techniques, when applied in a heuristic context, can be framed as a “master process that guides and modifies the operations of subordinate heuristics”, i.e., as metaheuristics [3]. Obvious advantages arise from these...
An exact method for the vehicle routing problem with time windows
A new exact algorithm for the vehicle muting problem based on q-paths and k-shortest paths relaxations
Annals or, 1995
Networks, 2015
In the traveling salesman problem with pickup, delivery, and ride-time constraints (TSPPD-RT), a ... more In the traveling salesman problem with pickup, delivery, and ride-time constraints (TSPPD-RT), a vehicle located at a depot is required to service a number of requests where the requests are known before the route is formed. Each request consists of (i) a pickup location (origin), (ii) a delivery location (destination), and (iii) a maximum allowable travel time from the origin to the destination (maximum ride-time). The problem is to design a tour for the vehicle that (i) starts and ends at the depot, (ii) services all requests, (iii) ensures that each request's ride-time does not exceed its maximum ride-time, and (iv) minimizes the total travel time required by the vehicle to service all requests (objective function). A capacity constraint that may be present is that the weight or volume of the undelivered requests on the vehicle must always be no greater than the vehicle's capacity. In this article, we concurrently analyze the TSPPD-RT with capacity constraints and without capacity constraints. We describe two mathematical formulations of the problem. These formulations are used to derive new lower bounds on the solution to the problem. Then, we provide two exact methods for finding the optimal route that minimizes the total travel cost. Our extensive computational analysis on both versions of the TSPPD-RT shows that the proposed algorithms are capable of solving to optimality instances involving up to 50 requests.
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The Traveling Salesman Problem with Precedence Constraints
Operations Research Proceedings, 1992
The Traveling Salesman Problem with Precedence Constraints is to find an hamiltonian tour of mini... more The Traveling Salesman Problem with Precedence Constraints is to find an hamiltonian tour of minimum cost in a graph G=(X,A) of n vertices, starting from vertex 1, visiting every vertex that must precede i before i (i=2,3,...,n) and returning to vertex 1. In this paper we describe a new bounding procedure and a new optimal algorithm based on dynamic programming. Computational results are given for two classes of randomly generated test problems, including the Dial-A-Ride problem with the classical TSP objective function.
The Multi-depot Periodic Vehicle Routing Problem
Lecture Notes in Computer Science, 2005
The Multi-Depot Periodic Vehicle Routing Problem (MDPVRP) is the problem of designing, for an hom... more The Multi-Depot Periodic Vehicle Routing Problem (MDPVRP) is the problem of designing, for an homogeneous fleet of vehicles of capacity Q, a set of routes for each day of a given p-day period. The routes of day k must be executed by mk vehicles based at the depot assigned ...
Real world finite capacity planning: A partial enumeration - Based optimizer
IFAC Proceedings Volumes (IFAC-PapersOnline), 2009
Abstract Finite capacity planning is a central problem in manufacturing industries. At the heart ... more Abstract Finite capacity planning is a central problem in manufacturing industries. At the heart of it lies a scheduling optimization problem, which has been so far studied in the optimization literature mainly in abstract forms, like job shop scheduling. There is a huge gap between the job shop instances used as benchmark in the literature and the scheduling instances met in real-world planning, this both with respect to instance size and to instance complexity, meaning the type of constraints and of variables considered. We present here the algorithmic core of a package primarily targeted to metallic carpentry industries, where instance types and CPU time constraints pose severe burdens on the optimization methods which can be used. We report about the results obtained by means of partial enumeration, a mathematic programming technique, here included in an Ant Colony Optimization framework.
Combinatorial optimization
A Set Partitioning Approach to the Crew Scheduling Problem
Operations Research, 1999
The crew scheduling problem (CSP) appears in many mass transport systems (e.g., airline, bus, and... more The crew scheduling problem (CSP) appears in many mass transport systems (e.g., airline, bus, and railway industry) and consists of scheduling a number of crews to operate a set of transport tasks satisfying a variety of constraints. This problem is formulated as a set partitioning problem with side constraints (SP), where each column of the SP matrix corresponds to a feasible duty, which is a subset of tasks performed by a crew. We describe a procedure that, without using the SP matrix, computes a lower bound to the CSP by finding a heuristic solution to the dual of the linear relaxation of SP. Such dual solution is obtained by combining a number of different bounding procedures. The dual solution is used to reduce the number of variables in the SP in such a way that the resulting SP problem can be solved by a branch-and-bound algorithm. Computational results are given for problems derived from the literature and involving from 50 to 500 tasks.
Operations Research, 2013
In the two-echelon capacitated vehicle routing problem (2E-CVRP), the delivery to customers from ... more In the two-echelon capacitated vehicle routing problem (2E-CVRP), the delivery to customers from a depot uses intermediate depots, called satellites. The 2E-CVRP involves two levels of routing problems. The first level requires a design of the routes for a vehicle fleet located at the depot to transport the customer demands to a subset of the satellites. The second level concerns the routing of a vehicle fleet located at the satellites to serve all customers from the satellites supplied from the depot. The objective is to minimize the sum of routing and handling costs. This paper describes a new mathematical formulation of the 2E-CVRP used to derive valid lower bounds and an exact method that decomposes the 2E-CVRP into a limited set of multidepot capacitated vehicle routing problems with side constraints. Computational results on benchmark instances show that the new exact algorithm outperforms the state-of-the-art exact methods.
Operations Research, 2011
The capacitated location-routing problem (LRP) consists of opening one or more depots on a given ... more The capacitated location-routing problem (LRP) consists of opening one or more depots on a given set of a-priori defined depot locations, and designing, for each opened depot, a number of routes in order to supply the demands of a given set of customers. With each depot are associated a fixed cost for opening it and a capacity that limits the quantity that can be delivered to the customers. The objective is to minimize the sum of the fixed costs for opening the depots and the costs of the routes operated from the depots. This paper describes a new exact method for solving the LRP based on a set-partitioning-like formulation of the problem. The lower bounds produced by different bounding procedures, based on dynamic programming and dual ascent methods, are used by an algorithm that decomposes the LRP into a limited set of multicapacitated depot vehicle-routing problems (MCDVRPs). Computational results on benchmark instances from the literature show that the proposed method outperform...
New upper bounds for the two-dimensional orthogonal non-guillotine cutting stock problem
IMA Journal of Management Mathematics, 2002
... AND ELENI HADJICONSTANTINOU The Management School, Imperial College, 53 Prince&a... more ... AND ELENI HADJICONSTANTINOU The Management School, Imperial College, 53 Prince's Gate, Exhibition Road, London SW7 2PG, UK ... The two-dimensional orthogonal non-guillotine cutting stock problem (NGCP) appears in many industries (eg the wood and steel ...
The Two-Dimensional Finite Bin Packing Problem. Part II: New lower and upper bounds
Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 2003
This paper is the second of a two part series and describes new lower and upper bounds for a more... more This paper is the second of a two part series and describes new lower and upper bounds for a more general version of the Two-Dimensional Finite Bin Packing Problem (2BP) than the one considered in Part I (see Boschetti and Mingozzi 2002). With each item is associated an input parameter specifying if it has a fixed orientation or it can
Mathematical Programming, 2007
This paper presents a new exact algorithm for the Capacitated Vehicle Routing Problem (CVRP) base... more This paper presents a new exact algorithm for the Capacitated Vehicle Routing Problem (CVRP) based on the set partitioning formulation with additional cuts that correspond to capacity and clique inequalities. The exact algorithm uses a bounding procedure that finds a near optimal dual solution of the LP-relaxation of the resulting mathematical formulation by combining three dual ascent heuristics. The first dual heuristic is based on the q-route relaxation of the set partitioning formulation of the CVRP. The second one combines Lagrangean relaxation, pricing and cut generation. The third attempts to close the duality gap left by the first two procedures using a classical pricing and cut generation technique. The final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between an upper bound and the lower bound achieved. The resulting problem is solved by an integer programming solver. Computational results over the main instances from the literature show the effectiveness of the proposed algorithm.
In [1] we introduced a new state-space relaxation, called ng-path relaxation, to compute lower bo... more In [1] we introduced a new state-space relaxation, called ng-path relaxation, to compute lower bounds to routing problems, such as the Capacitated Vehicle Routing Problem (CVRP) and the VRP with Time Windows (VRPTW). This relaxation consists of partitioning the set of all possible paths ending at a generic vertex according to a mapping function that associates with each path a subset of the visited vertices that depends on the order in which such vertices are visited. The subset of vertices associated with each ng-path is used to impose partial elementarity. This relaxation proved to be particularly effective in computing lower bounds on the CVRP, the VRPTW and the Traveling Salesman Problem with Time Windows (TSPTW) [2]. In this talk, we propose a new dynamic method to improve the ng-path relaxation which consists of defining, iteratively, the mapping function of the ng-path relaxation using the results achieved at the previous iteration. This method is analogous to cutting plane methods, where the cuts violated by the ng-paths at a given iteration are incorporated in the new ng-path relaxation at the next iteration. The new technique has been used to solve the Traveling Salesman Problem with Cumulative Costs (CTSP) and to produce new benchmark results for the TSPTW. The results obtained show the effectiveness of the proposed method.
Transportation Science, 2017
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Discrete Optimization, 2008
The set partitioning problem is a fundamental model for many important real-life transportation p... more The set partitioning problem is a fundamental model for many important real-life transportation problems, including airline crew and bus driver scheduling and vehicle routing. In this paper we propose a new dual ascent heuristic and an exact method for the set partitioning problem. The dual ascent heuristic finds an effective dual solution of the linear relaxation of the set partitioning problem and it is faster than traditional simplex based methods. Moreover, we show that the lower bound achieved dominates the one achieved by the classic Lagrangean relaxation of the set partitioning constraints. We describe a simple exact method that uses the dual solution to define a sequence of reduced set partitioning problems that are solved by a general purpose integer programming solver. Our computational results indicate that the new bounding procedure is fast and produces very good dual solutions. Moreover, the exact method proposed is easy to implement and it is competitive with the best branch and cut algorithms published in the literature so far.
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Papers by Aristide Mingozzi