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University of Bologna (UOB) DEIS (Department of Electronics, Computer Science and Automatics) Faculty of Engineering Operations Research Unit
University of Bologna The University of Bologna (founded in 1088) is recognised as the oldest university in the western world. It has about 110000 students, and is divided in 23 faculties, 68 departments and 5 University Campus Branches (Bologna, Cesena, Forli`, Ravenna and Rimini) www.unibo.it
DEIS DEIS (Department of Electronics, Computer Science and Automatics) is composed by: 44 Full Professors 33 Associate Professors 35 Assistant Professors 90 PhD students 40 Post Doc researchers. It has sites in Bologna and Cesena. www.deis.unibo.it
DEIS The research and educational activities involve the following main fields: Automatics Biomedical Engineering Computer Science Electromagnetic Fields Electronics Operations Research Telecommunications
DEIS Undergraduate and Graduate Degrees: Automation Engineering Biomedical Engineering Computer Engineering Electronic Engineering Industrial Engineering Telecommunications Engineering PhD Degrees Automatics and Operations Research Electronics, Computer Science, Telecommunications Biomedical Engineering
DEIS- Operations Research Unit Research themes currently considered: Mathematical Programming methodologies (survey works on research areas and analysis of basic techniques) Specific subjects in Combinatorial Optimization and Graph Theory (design and implementation of effective exact, heuristic and metaheuristic algorithms for the solution of NP-hard problems and study of polyhedral structures in the solution space) Real-world applications (Crew Planning, Train Timetabling, Locomotive Scheduling, Train Platforming, Electric Power Dispatching, Staff Scheduling, Hydraulic Network Design, Vehicle Routing, Genome Comparison)
DEIS- Operations Research Unit Current International Collaborations: Universite’ Libre de Bruxelles, Belgium CRT, Montreal, Canada Carnegie Mellon University, Pittsburgh, USA University of Lancaster, UK Technical University of Graz, Austria University of Copenhagen, Denmark University of Colorado, Boulder, USA Universidad de La Laguna, Spain University of New Brunswick, Saint John, Canada Instituto Tecnologico de Aeronautica, Sao Jose’ dos Campos, SP Brazil …
DEIS- Operations Research Unit Staff members involved in the Project: Alberto Caprara • Associate Professor of Operations Research • Associate Editor of the journals: INFORMS Journal on Computing, Operations Research Letters • Co-Editor of Optima (the newsletter of the Mathematical Programming Society) • Conferred the “G.B. Dantzig Dissertation Award” (for the best applied O.R. PhD Thesis) from INFORMS (1996)
DEIS- Operations Research Unit Staff members involved in the Project: Andrea Lodi • Associate Professor of Operations Research • Associate Editor of the journals: Mathematical Programming, Algorithmic Operations Research • Conferred the ”2004-2005 IBM Herman Goldstine Postdoctoral Fellowship in Mathematical Sciences” (currently at the IBM T.S. Watson Research Centre, Yorktown Heights, NY, USA)
DEIS- Operations Research Unit Staff members involved in the Project: Silvano Martello • Professor of Operations Research • Co-Editor of the journal 4OR (Journal of the O.R. Societies of Belgium, France, Italy) • Associate Editor of the journals: INFOR, Journal of Heuristics, Discrete Optimization, SIAM Monographs in Discrete Mathematics and Applications • Co-Editor of the “Software Section” of the journal Discrete Applied Mathematics • Coordinator of ECCO (European Chapter in Combinatorial Optimization)
DEIS- Operations Research Unit Staff members involved in the Project: Paolo Toth • Professor of Combinatorial Optimization • Associate Editor of the journals: Transportation Science, Journal of Heuristics, Networks, European Journal of Operational Research, Journal of the Operational Research Society, Discrete Optimization, Algorithmic Operations Research, International Transactions in Operational Research • Co-Editor of the “Software Section” of the journal Discrete Applied Mathematics • President of IFORS (International Federation of the OR Societies) in the period 2001-2003
DEIS- Operations Research Unit Staff members involved in the Project: Daniele Vigo • Professor of Operations Research (Second Faculty of Engineering in Cesena) • Associate Editor of the journals: Operations Research Letters, Operations Research (period 2000-2003) • Chairman of the Organizing Committee of ROUTE 2005 (International Workshop on Vehicle Routing Problems, Bertinoro, June 23-26, 2005)
DEIS- Operations Research Unit Post-Doc Researchers; Manuel Iori PhD Students Alessandro Carrotta (grant from ILOG, Paris) Matteo Fortini Valentina Cacchiani Enrico Malaguti
OR-DEIS Papers in the last 3 years Mathematical Programming 7 Operations Research 2 INFORMS J. on Computing 7 Journal of Heuristics 3 SIAM J. on Optimization 1 Mathematics of Operat. Research 1 Networks 2 EJOR 6 Discrete Applied Mathematics 5 OR Letters 2
OR-DEIS Current Research Topics • Exact and Heuristic Algorithms for Combinatorial Optimization Problems • Design and implementation of effective enumerative, heuristic and metaheuristic algorithms for the following basic problems:
OR-DEIS Current Research Topics • Knapsack Problems: - 0 - 1 Knapsack Problem - Subset-Sum Problem - 2 - Constraint Knapsack Problem - 2 - Dimensional Knapsack Problem
OR-DEIS Current Research Topics • Bin Packing Problems: - Bin Packing Problem - 2 - Constraint Bin Packing Problem - 2 - Dimensional Bin Packing Problem - 3 - Dimensional Bin Packing Problem
OR-DEIS Current Research Topics • Graph Theory Problems: - Asymmetric Travelling Salesman Problem - Travelling Salesman Problem with Time Windows - Generalized Travelling Salesman Problem - Orienteering Problem - Graph Decomposition - Bandwith-2 Graphs
OR-DEIS Current Research Topics • Vertex Coloring Problem • Edge Coloring Problem • Vehicle Routing Problem • Valid Inequalities for Integer Linear Programming Models • Set Covering and Partitioning Problems • Scheduling Problems • Integration of Constraint Programming and Mathematical Programming Techniques
OR-DEIS Current Research Topics • Crew Planning in Railway Applications Design of bounds and heuristic algorithms, based on Lagrangian relaxations, for the solution of the “Crew Planning Problem”. The problem requires to determine a minimum cost set of crew “rosters” for covering a given timetabled set of trips.
OR-DEIS Current Research Topics • Train Timetabling Problem Design of exact and heuristic algorithms, based on Linear and Lagrangian relaxations, for the solution of real-world versions of the “Train Timetabling Problem”. Given a set of timetabled trains to be run along a “track”, find a feasible timetable so as to satisfy all the operational constraints with the minimum variations with respect to the given timetable.
OR-DEIS Current Research Topics • Train Platforming Problem Design of exact and heuristic algorithms for the solution of real-world versions of the “Train Platforming Problem”, in which one is required to assign an “itinerary” and a “platform” to each timetabled train visiting a station within a given time period.
OR-DEIS Current Research Topics • Optimization of the Electric Power Dispatching Study of models and design of heuristic algorithms for the optimization of the electric power dispatching in a competitive environment.
OR-DEIS Current Research Topics • Combinatorial Optimization Methods for Genome Comparison Two main objectives: - study of the most used model to compare twogenomes, namely the computation of the minimum number of inversions (“reversals”) of gene subsequences that leads from one genome to the other. - study of models to compare three or more genomes, recently proposed by computational biologists.
OR-DEIS Current Research Topics • Design of Hydraulic Networks Design of exact and heuristic algorithms for the minimum cost design of hydraulic urban networks.
OR-DEIS Cooperation with Industry: • Railway Crew Planning with Trenitalia SpA • Locomotive Assignment with Trenitalia SpA • Train Timetabling with Rete Ferroviaria Italiana SpA • Train Platforming with Rete Ferroviaria Italiana SpA • Train Traction Unit Assignment with MAIOR Srl and Ferrovie Nord Milano Esercizio SpA • Staff Scheduling with Beghelli SpA and the Municipality of Bologna • Vehicle Routing with ILOG (Paris) • Strategic Planning of Solid Waste Flows with HERA (Metropolitan area of Bologna) • Bus Scheduling in Low Demand Areas with ATC Bo
OR-DEIS European Union Projects: • Human Capital and Mobility (1992-2000) • TRIO (railway crew management, 1998-2000) • TRIS (train timetabling, 2000-2002) • PARTNER (train timetabling, 2003-2005) • REORIENT (freight rail corridors, 2005-2007)
RAILWAY CREW PLANNING • We are given a planned timetable for the train services (actual journeys with passengers or freight, and the transfers of empty trains or equipment between different stations) to be performed every day of a certain time period. • Each train service is split into a sequence of trips (segments of train journeys which must be serviced by the same crew without interruption). • Each trip is characterized by: • departure time, departure station, • arrival time, arrival station, • additional attributes. • Each daily occurrence of a trip has to be performed by a crew.
RAILWAY CREW PLANNING (2) • Each crew performs a roster: sequence of trips whose operational cost and feasibility depend on several rules laid down by union contracts and company regulations (cyclic for “long” time periods). • The problem consists of finding a set of rosters, covering every daily occurrence of each trip in the given time period, so as to satisfy all the operational constraints with minimum cost (minimum number of crews). • Very complex and challenging problem due to both the size of the instances and the type and number of operational constraints. • In the Italian Railway Company (“Trenitalia - Ferrovie dello Stato FS”): about 8000 trains and 25000 drivers (largest problem involves about 5000 trips).
EXAMPLE * 11 TRIPS TO BE COVERED EVERY DAY: T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 0:00 6:00 12:00 18:00 24:00
EXAMPLE (2) * ROSTER OF A CREW COVERING THE 11 TRIPS Day #1 Day #2 Day #3 Day #4 Day #5 Day #6 T3 T9 T2 T5 T7 T10 week 1 day day 1 2 3 4 5 6 T1 T4 T8 T11 T6 week 2 7 8 9 10 11 12 Crew “weekly” rest • CYCLIC TRIP SEQUENCE SPANNING 12 DAYS • (REQUIRING 12 CREWS)
The overall problem is approached inTHREE PHASES: (C-F-T-V-G, Mathematical Programming 1997) • PAIRING GENERATION:a very large number of feasible PAIRINGS (duties) is generated. PAIRING: • sequence of trips to be covered by a single crew in 1-2 days; • starts and ends at the same depot; • cost depending on its characteristics. • PAIRING OPTIMIZATION: the best subset of the generated pairings is selected, so as to cover all the trips at minimum cost: solution of a SET COVERING – SET PARTITIONING PROBLEM. * PHASES 1 + 2: “CREW SCHEDULING PHASE”
3.ROSTERING OPTIMIZATION: the selected pairings are sequenced to obtain the final rosters (separately for each depot), defining a periodic duty assignment to each crew which guarantees that all the pairings are covered for a given number of consecutive days (i.e. one month)
The SET COVERING PROBLEM (SCP) Given: • a BINARY MATRIX Aij(very sparse) m = number of rows (i= 1,…, m) n = number of columns(j= 1,…, n) • a COST VECTOR (cj ): cj = cost of column j (j=1,…,n) (w.l.o.g.: cj > 0 and integer) * Select a subset of the n columns of Aij such that: • the sum of the costs of the selected columns is a minimum, • all the m rows are COVERED by the selected columns (i.e. for each row i at least one selected columnj has an element of value 1 in row i: Aij =1).
Train Timetabling Problem • Defines the actual timetablefor each train: • Departure time from the first station • Arrival time at the last station • Arrival and departure times for the intermediate stations • Separate timetabling problems are solved for distinct corridors in the network The trains are assumed to have different speeds
Train Timetabling: Constraints Basic Operational Constraints required in order to guarantee safety and regularity margin: • Minimum distance between a train and the next one along the corridor • Minimum distance between two consecutive arrivals (departures) in a station • Overtaking between trains can occur only within a station
Train Timetabling: Objectives Quality of service: • Minimum deviation of the actual timetable with respect to the ideal one • Robustness of the timetable with respect to random disturbances and failures
Optimization Methods • Heuristic algorithms possibly based on mathematical programming tools: • Mixed Integer Linear Programming formulations • Enumerative algorithms • Linear and Lagrangian relaxations • Aimed at finding an optimal timetable starting from the “ideal” one • Applicable at both Planning and Operational levels
Basic Train Timetabling Problem One single track is considered We are given on input a so-called ideal timetable which is typically infeasible. • To obtain a feasible (“actual”)timetable two kinds of modifications of the ideal timetable are allowed: • change the departure time of some trains from their first station (shift) and/or • increase the minimum stopping time in some of the intermediate stations (stretch).
Ideal timetable Actual timetable ideal_departure_instant Shift Station 1 stop Station 2 stop Stretch Station 3 Station 4
Objective of the problem • Each train j is assigned an ideal profit πjdepending on the type of the train (intercity, local, freight, etc). • If the train is shifted and/or stretched the profit is decreased. • If the profit becomes null or negative the train is cancelled. • Actual profit of train j = πj – αj (vj ) – βj (uj )vjshift, uj stretch (sum of the stretches in all stations) • The objective is to maximize the overall profit of the trains
Optimization Algorithm Graph Theory Model Integer Linear Programming Formulation Lagrangian Relaxation Constructive Heuristic Algorithms Local Search Procedures
Additional Characteristics “Fixed block” or “Moving block” signalling Capacities of the stations “Full “ or “Residual” track capacity evaluation Maintenance operations …