University of Bologna (UOB)

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University of Bologna (UOB)

• DEIS (Department of Electronics, Computer Science
  and Automatics)
• Faculty of Engineering
• Operations Research Unit

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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

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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

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DEIS

• The research and educational activities involve
  the following main fields
• Automatics
• Biomedical Engineering
• Computer Science
• Electromagnetic Fields
• Electronics
• Operations Research
• Telecommunications

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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

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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)

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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

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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)

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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)

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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)

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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

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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)

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DEIS- Operations Research Unit

• Post-Doc Researchers
• Manuel Iori
• PhD Students
• Alessandro Carrotta (grant from ILOG, Paris)
• Matteo Fortini
• Valentina Cacchiani
• Enrico Malaguti

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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
• 
  

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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

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OR-DEIS Current Research Topics

• Knapsack Problems
• - 0 - 1 Knapsack Problem
• - Subset-Sum Problem
• - 2 - Constraint Knapsack Problem
• - 2 - Dimensional Knapsack Problem

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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

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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

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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

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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.

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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.

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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.

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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.

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OR-DEIS Current Research Topics

• Combinatorial Optimization Methods for Genome
  Comparison
• Two main objectives
• - study of the most used model to compare two
  genomes, 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.

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OR-DEIS Current Research Topics

• Design of Hydraulic Networks
• Design of exact and heuristic algorithms for the
  minimum cost design of hydraulic urban networks.

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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

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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)

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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.

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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).

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EXAMPLE

• 11 TRIPS TO BE COVERED EVERY DAY

T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
000 600 1200
1800 2400
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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)

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• The overall problem is approached in THREE
  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

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• 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)

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• 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
  (j1,,n)
• (w.l.o.g. cj gt 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 column j has an element of value 1 in
  row i Ai j 1).

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Train Timetabling Problem

• Defines the actual timetable for 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

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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

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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

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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

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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).

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Ideal timetable
Actual timetable
ideal_departure_instant
Shift
Station 1
stop
Station 2
Stretch
stop
Station 3
Station 4
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Objective of the problem

• Each train j is assigned an ideal profit pj
  depending 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 pj aj ( vj
  ) ßj (uj ) vj shift,
• uj stretch (sum of the stretches in all
  stations)
• The objective is to maximize the overall profit
  of the trains

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Optimization Algorithm

• Graph Theory Model
• Integer Linear Programming Formulation
• Lagrangian Relaxation
• Constructive Heuristic Algorithms
• Local Search Procedures

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Additional Characteristics

• Fixed block or Moving block signalling
• Capacities of the stations
• Full or Residual track capacity evaluation
• Maintenance operations