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Maurizio Boccia

    Maurizio Boccia

    We developed a mixed-integer linear programming model to plan exam sessions for external candidates in the Vestfold region, Norway. With our model, the administration planned the last session of 2018, the two sessions of 2019, and the... more
    We developed a mixed-integer linear programming model to plan exam sessions for external candidates in the Vestfold region, Norway. With our model, the administration planned the last session of 2018, the two sessions of 2019, and the first session of 2020. The plans produced are of high quality and saved three weeks of person effort per session.
    Several initiatives have been implemented worldwide to foster student interest towards STEM disciplines. These initiatives are based on the awareness that mathematics is essential for scientific and technological advancement: it trains to... more
    Several initiatives have been implemented worldwide to foster student interest towards STEM disciplines. These initiatives are based on the awareness that mathematics is essential for scientific and technological advancement: it trains to reasoning and reflection, stimulates logical capabilities and intuition, improve investigation attitude. Most of them recognize also that mathematical problem solving represents an effective way to support teachers and students in their teaching and learning activities, respectively. In this context, this work is aimed at presenting OPS4Math (Optimization and Problem Solving for Teaching of Mathematics), a training project for Secondary School teachers, supported by Italian Ministry of University and Research. The driving idea, widely discussed by the scientific community, is to operate a reversal of the didactical perspective: starting from phenomena/problems to introduce concepts of data, variables, relationships and functions in an appealing way...
    Logical Analysis of Data deals with the classification of huge data set by boolean formulas and their synthetic representation by ternary string, referred to as patterns. In this context, the simple pattern minimality problem (SPMP)... more
    Logical Analysis of Data deals with the classification of huge data set by boolean formulas and their synthetic representation by ternary string, referred to as patterns. In this context, the simple pattern minimality problem (SPMP) arises. It consists in determining the minimum number of patterns “explaining” an initial data set of binary strings. This problem is equivalent to the minimum disjunctive normal form problem and, hence, it has been widely tackled by set covering based heuristic approaches. In this work, we describe and tackle a particular variant of the SPMP coming from an application arising in the car industry production field. The main difference with respect to SPMP tackled in literature resides in the fact that the determined patterns must be partitions and not covers of the initial binary string data set. The problem is solved by an effective and fast heuristic, tested on several large size instances coming from a real application.
    Automated timetabling is a challenging area in the timetabling and scheduling theory and practice, intensively addressed in research papers in the last two decades. There are three main classes of problems, which are usually studied:... more
    Automated timetabling is a challenging area in the timetabling and scheduling theory and practice, intensively addressed in research papers in the last two decades. There are three main classes of problems, which are usually studied: school timetabling, course timetabling and examination timetabling. In this report, we address a case study of the Curriculum-Based Course Timetabling (CB-CTT) problem, arising at Engineering Department of Sannio University. In general, the problem consists of finding a feasible weekly assignment of course lectures to rooms and time periods while respecting a wide range of constraints, which have to be either strictly satisfied (hard constraints) or satisfied as much as possible (soft constraints). The case study here addressed here has many special requirements due to local organizational rules. We were able to model the complex requirements by an Integer Programming formulation. The solution approach consists of using an MIP solver, integrated with two local branching heuristics tailored for the problem. The effectiveness of the proposed approach is illustrated by the computational results on two real instances.
    Quantum computing (QC) represents a great challenge for both academia and private companies and it is currently pursuing the development of quantum algorithms and physical realizations of quantum computers. Quantum algorithms exploit the... more
    Quantum computing (QC) represents a great challenge for both academia and private companies and it is currently pursuing the development of quantum algorithms and physical realizations of quantum computers. Quantum algorithms exploit the concept of quantum bit (qubit). They are implemented by designing circuits which consider an ideal quantum computer where no interaction restriction between qubits is imposed. However, physical realizations of quantum computers are subject to several technological constraints and adjacency between interacting qubits is one of the most common one. To this end, additional gates, referred to as swap, can be added to a quantum circuit to make it nearest neighbour compliant. These additional gates have a cost in terms of reliability of the quantum system, hence their number should be minimized. In this paper we first give some hints about this cutting edge topic. Then we provide a review of the literature solving approaches for the swap minimization prob...
    The paper describes models for scheduling the patterns that form a solution of a cutting stock problem. We highlight the problem of providing the required final products with the necessary items obtained from the cut, choosing which... more
    The paper describes models for scheduling the patterns that form a solution of a cutting stock problem. We highlight the problem of providing the required final products with the necessary items obtained from the cut, choosing which pattern feeds which lot of parts. This problem can be solved prior to schedule cuts, or in an integrated way. We present integer programming models for both approaches.
    Abstract The flying sidekick traveling salesman problem (FS-TSP) is a parcel delivery problem arising in the last-mile logistics, where the distribution plan of a driver-operated truck assisted by a drone (unmanned aerial vehicle, UAV)... more
    Abstract The flying sidekick traveling salesman problem (FS-TSP) is a parcel delivery problem arising in the last-mile logistics, where the distribution plan of a driver-operated truck assisted by a drone (unmanned aerial vehicle, UAV) has to be defined. The FS-TSP is a variant of the TSP where routing decisions are integrated with customer-to-drone and customer-to-truck assignment decisions and truck-and-drone synchronization constraints. The objective is the minimization of the time required to serve all the customers, taking into account drone payload capacity and battery power constraints. In this work we provide a new representation of the FS-TSP based on the definition of an extended graph. This representation allows to model the problem by a new and compact integer linear programming formulation, where the synchronization issue is tackled in a column generation fashion, thus avoiding the usage of big-M constraints, representing one of the main drawbacks of the models present in literature. The proposed formulation has been solved by an exact approach which combines a Branch-and-Cut algorithm and a column generation procedure, strengthened by variable fixing strategies and new valid inequalities specifically defined for the problem. The proposed method has been experienced on a large set of benchmark instances. Computational results show that the proposed approach either is competitive or outperforms the best exact approach present in literature for the FS-TSP. Indeed, it is able to provide the optimal solution for all small size instances with 10 customers and for several medium size instances with 20 customers, some of them never solved before.
    Abstract In this work we focus on the flying sidekick traveling salesman problem (FS-TSP). The FS-TSP arises in the last-mile distribution context and it is a variant of the TSP aimed at determining the distribution plan of a... more
    Abstract In this work we focus on the flying sidekick traveling salesman problem (FS-TSP). The FS-TSP arises in the last-mile distribution context and it is a variant of the TSP aimed at determining the distribution plan of a driver-operated truck assisted by a drone (unmanned aerial vehicle, UAV), where the synchronization between the two vehicles allows to parallelize the delivery operations, so providing a reduction of the overall completion time. Several variants of the FS-TSP have been considered in literature, most of them sharing the assumption that launching and rendezvous position of a drone sortie must be different. In this work, we relax this assumption allowing the truck to wait for the drone at the launching position (FS-TSP*). This introduces an important flexibility element to deal with deliveries in rural or in urban areas with no-fly zones. We propose an original and compact integer linear programming formulation which allows to exactly solve the FS-TSP* and consequently also the FS-TSP. The results on several test instances show that our method can effectively solve to optimality instances with up to 20 customers and quantify the advantages of the FS-TSP* with respect to FS-TSP in terms of overall completion time.
    The Inventory Routing Problem (IRP) involves the distribution of one or more products from a supplier to a set of clients over a discrete planning horizon. Each client has a known demand to be met in each period and can only hold a... more
    The Inventory Routing Problem (IRP) involves the distribution of one or more products from a supplier to a set of clients over a discrete planning horizon. Each client has a known demand to be met in each period and can only hold a limited amount of stock. The product is shipped through a distribution network by one or more vehicles of limited capacity. The objective is to find replenishment decisions minimizing the sum of the storage and distribution costs. In this paper, we present IRP reformulations under the Maximum Level replenishment policy, derived from a single-period substructure. We define a generic family of valid inequalities, and then introduce two specific subclasses for which the separation problem of generating violated inequalities can be effectively solved. A basic Branch-and-Cut algorithm has been implemented to demonstrate the strength of the single-period reformulations. We present computational results for the benchmark instances with 50 clients and 3 periods a...
    Research Interests:
    ABSTRACT In the aircraft industry structural components, referred to as part numbers (PN), have to be subject to an heat treatment in capacitated burn-in furnaces for a pre-defined period (exposure time) in order to provide them with... more
    ABSTRACT In the aircraft industry structural components, referred to as part numbers (PN), have to be subject to an heat treatment in capacitated burn-in furnaces for a pre-defined period (exposure time) in order to provide them with specific physic and chemical features (e.g. hardness, corrosion resistance, conductivity). Two or more part numbers can be grouped in a batch and treated simultaneously in the same furnace if it is possible to individuate a common exposure time. In order to minimize the total completion time (makespan) of the process it needs to determine the appropriate grouping of the part numbers into batches (batching problem) to be processed by each furnace (scheduling problem). The problem can be modeled as a batch scheduling problem on parallel machines where the batching and the scheduling problem are considered at the same time. Starting from a real case study, we present an original integer linear programming formulation in the case of two capacitated parallel machines and we provide the results obtained on two real instances coming from the aircraft industry.
    ABSTRACT
    ABSTRACT In this paper we report new computational results with an approach based on the generation of general cutting planes for several classes of Binary Integer Programming (BIP) Problems such as Generalized Assignment,... more
    ABSTRACT In this paper we report new computational results with an approach based on the generation of general cutting planes for several classes of Binary Integer Programming (BIP) Problems such as Generalized Assignment, Multi-Dimensional Knapsack, Capacitated P-median and Capacitated Network Location. These problems are characterized by a formulation including a great number of knapsack constraints, which, in general make these problems very hard to solve. The state of the art on these problems requires to use approaches based on Lagrangean Relaxation or decomposition approaches like Dantzig-Wolfe and Column Generation techniques. In this paper we present an approach based on the generation of general cutting planes of the polytope associated with each knapsack constraints. Computational experience on a wide set of benchamrk instances is carried out.
    Trains running through railway lines often accumulate some delay. When this happens, rescheduling and rerouting decisions must be quickly taken in real time. Despite the fact that even a single wrong decision may deteriorate the... more
    Trains running through railway lines often accumulate some delay. When this happens, rescheduling and rerouting decisions must be quickly taken in real time. Despite the fact that even a single wrong decision may deteriorate the performance of the whole railway network, this complex optimization task is still basically performed by human operators. In very recent years, the interest of train operators to implement automated decision systems has grown. Not incidentally, the railway application section (RAS) of INFORMS has issued a challenge devoted to this problem concomitantly with the INFORMS Annual Meeting 2012. In this article, we describe two heuristic approaches to solve the RAS problem based on a mixed integer linear programming formulation, and we report computational results on the three RAS instances and on an additional set of instances defined on a more congested network. Computational results on the challenge test bed show that our algorithms positively compare with other approaches to the RAS problem. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 62(4), 315–326 2013
    Abstract In the last 25 years a significant number of papers have treated the interesting case of the location of facilities which do not generate and/or attract flow, but intercept it. These facilities can be used by the flow units of... more
    Abstract In the last 25 years a significant number of papers have treated the interesting case of the location of facilities which do not generate and/or attract flow, but intercept it. These facilities can be used by the flow units of the network or proposed to/imposed on them along their ...
    The single-machine scheduling problem (SMSP) with release dates concerns the optimal allocation of a set of jobs on a single machine that is not able to process more than one job at a time. Each job is ready to be processed at a release... more
    The single-machine scheduling problem (SMSP) with release dates concerns the optimal allocation of a set of jobs on a single machine that is not able to process more than one job at a time. Each job is ready to be processed at a release date and without interruption. The goal is to minimize the total weighted completion time of the jobs. In this paper the time-indexed formulation is considered and a new lagrangean heuristic is proposed, based on the observation that lagrangean relaxation of job constraints leads to a weighted stable set problem on an interval graph. The relaxed problem is polynomially solvable by a dynamic-programming algorithm. We report computational experience, showing that instances up to 400 jobs and maximum processing time 50 (around 5,000,000 variables) are solved in less than 40 minutes on a personal computer, yielding duality gaps never exceeding 3%. We also test a set of hard instances, built to produce bad performances where we yield duality gaps less tha...
    We study an exact separation procedure—SEP-MK—for the knapsack set with a single continuous variable XMK. Then, we address the question of whether SEP-MK can be of practical use in tightening mixed-integer programming (MIP) formulations... more
    We study an exact separation procedure—SEP-MK—for the knapsack set with a single continuous variable XMK. Then, we address the question of whether SEP-MK can be of practical use in tightening mixed-integer programming (MIP) formulations when using standard (floating-point) MIP solvers. To this purpose, we present a separation procedure for MIP problems—SEP-MIPMK—where we derive knapsack sets of the form XMK by aggregating the continuous variables in the mixed knapsack inequalities of the formulation. Then, we use SEP-MK to generate cutting planes. Before the continuous variables are aggregated, the mixed knapsack inequalities are modified through the use of a bound substitution procedure to take into account fixed and variable bounds on the continuous variables. Bound substitution is made according to some heuristic rules, so even if its basic component SEP-MK is “exact,” the overall separation procedure for MIP problems, SEP-MIPMK, is heuristic. We perform a computational study on ...
    In this paper we study the case of a company that delivers different types of fuel to a set of fuel pumps. The company has one warehouse and supplies the pumps by a fleet of trucks with several tanks of differing capacities.The company’s... more
    In this paper we study the case of a company that delivers different types of fuel to a set of fuel pumps. The company has one warehouse and supplies the pumps by a fleet of trucks with several tanks of differing capacities.The company’s aim is to satisfy the orders using the available resources (trucks and drivers) with the minimum total
    The Median-Path problem consists of locating a st-path on a network, minimizing a function of two parameters: accessibility to the path and total cost of the path. Applications of this problem can be found in transportation planning,... more
    The Median-Path problem consists of locating a st-path on a network, minimizing a function of two parameters: accessibility to the path and total cost of the path. Applications of this problem can be found in transportation planning, water resource management and fluid transportation.
    ... installation and assignment. Concentrators can have capacity con-straints. Deng and Simchi-Levi [DSL92], Yaman [Yam05] and Yaman and Labbè [LYG05] study the polyhedral structure of this problem. In [LY06] Yaman and ...
    Research Interests:
    In this paper we tackle a three-dimensional non-convex domain loading problem. We have to efficiently load identical small boxes into a highly irregular non-convex domain. The boxes to be loaded have a particular shape. If d is the length... more
    In this paper we tackle a three-dimensional non-convex domain loading problem. We have to efficiently load identical small boxes into a highly irregular non-convex domain. The boxes to be loaded have a particular shape. If d is the length of the smallest edge of the box, its dimensions are d × nd × md, n ≤ m, with n and
    ... Pasquale Avella1, Maurizio Boccia2, Carmine Di Martino3, Giuseppe Oliviero3, Antonio Sforza4, and Igor Vasil'ev5⋆ 1 RCOST – Research Center on Software Technology ... Whitaker (1983) and Resende and Werneck... more
    ... Pasquale Avella1, Maurizio Boccia2, Carmine Di Martino3, Giuseppe Oliviero3, Antonio Sforza4, and Igor Vasil'ev5⋆ 1 RCOST – Research Center on Software Technology ... Whitaker (1983) and Resende and Werneck (2002b) described a way to ac-celerate this algorithm. ...
    The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic... more
    The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic for large-scale instances of CFLP. It is based on a Lagrangean relaxation, which is used to select a subset of “promising” variables, forming the core problem, and on a Branch-and-Cut algorithm that solves the core problem. We report on computational experience showing that instances up to 2000 facilities and 2000 clients are solved to 1%-optimality in less than 8 minutes of CPU time on a personal computer.