Csci 658

Discrete Optimization

Spring 2015

CLASS MEETING TIMES. Jones 302, MWF 12-12:50

Office Hours: MW 2-4 p.m. or by appointment

PREREQUISITES. Csci 628 and C programming skills or their equivalent (linear programming theory, rudimentary compelxity theory, C++/Fortran programming and elementary data structures).

DESCRIPTION. Discrete optimization problems are those problems with decisions that are logical (yes/no) or countable. Both exact and heuristic methods for discrete optimization models will be presented in the course. Topics include relaxation techniques, constructive heuristics, improving search techniques (simplex method, simulated annealing, tabu search and genetic algorithms), branch and bound schemes, and valid inequalites for branch and cut methods.

TENTATIVE TOPIC OUTLINE

  1. Survey of Discrete Optimization Methods [11 lectures] (Ra Ch.11,12; MF Ch. 1-6)
    1. Introduction (MF Ch. 1-2)
    2. Enumeration and Relaxations (Ra 12; MF 3.1)
    3. Strengthening Relaxations
    4. Branch and Bound (Ra 12; MF 4.2,4.4)
    5. Refinements to Branch and Bound (Ra 12)
    6. Improving Search Heuristics (MF 3.2, 4.1)
    7. Constructive Heuristics
  2. Extending Discrete Improving Search [9 lectures]
    1. Simulated Annealing (JAMS, KY, Ra Ch.12, MF 5.1)
    2. Tabu Search (GL, Gl, KB, Ra Ch.12, MF 5.2)
    3. Genetic Algorithms (B, G, MF Ch. 6,7)
  3. Lagrangean Relaxation [8 lectures] (PR Ch.5, Be)
    1. Introduction
    2. Exposition
    3. Choosing Lagrange Multipliers
  4. More Branch and Bound [3 lectures] (PR Ch.5,6)
    1. Partial Solutions and Constructive Search
    2. Backtracking Search
    3. Branch and Bound
    4. Branch and Cut--Valid Inequalities
  • Student Paper Presentations [3 lectures]
    1. Examples include:
    2. Ant Colony Optimization
    3. Very Large Neighborhood Search
    4. Evolutionary Algorithms
    5. Greedy Randomized Adaptive Search Program (GRASP)

        REFERENCES.

        1. {MF} How to Solve It: Modern Heuristics, Z. Michalewicz andn D.B. Fogel, Springer (2000).
        2. {Ra} Optimization in Operations Research, Ronald L. Rardin, Prentice Hall (1998). Chapters 11 and 12.
        3. {B} Bean, J.C., ``Genetics and Random Keys for Sequencing and Optimization,'' (1992) Tech. Report 92-43, Dept. of Industrial and Operations Engr., U. of Michigan, Ann Arbor, MI 48109-2117.
        4. {Be} Beasley, J.E., ``Lagrangean Relaxation,'' (1992) 1-37, The Management School, Imperial College, London SW7 2AZ, England.
        5. {G} Goldberg, D.E. GAs in Search Optimization and Machine Learning, Addison Wesley (1989).
        6. {Gl} Glover, F., ``Tabu Search: A Tutorial,'' INTERFACES, 20 (1990) 74-94.
        7. {G2} Glover, F., ``Tabu Search--Part I,'' ORSA J. on Computing, 1 (1989) pp. 190-206.
        8. {G3} Glover, F., ``Tabu Search: New Options for Optimization,'' ORSA CSTS Newsletter, 15 (1994).
        9. {GL} Glover, F. and M. Laguna, ``Tabu Search," chapter in Modern Heuristics for Combinatorial Problems, (1993).
        10. {JAMS} Johnson, D.S., C.R. Aragon, L.A. McGeoch, and C. Schevon, ``Opimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning,'' Operations Research, 37 (1989) 865-892.
        11. {KY} Kincaid, R.K., and L.G. Yellin, ``The Discrete P-Dispersion-Sum Problem: Results on Trees and Graphs," Location Science, 1 (1993) pp. 171-186.
        12. {PR} Parker, R.G. and R.L. Rardin, ``Chapter 5: Nonpolynomial Algorithms--Partial Enumeration," Discrete Optimization}, Academic Press, Boston (1988).
        13. {Ra2} Rardin, R.L., Discrete Optimization, Chapter 106 in Handbook of Industrial Engineering, Wiley, NY (1992).
        14. {SK} Skorin-Kapov, J., ``Tabu Search Applied to the Quadratic Assignment Problem,'' ORSA J. on Computing, 2 (1990) pp. 33-42.
        HOMEWORK. Regular homework emphasizing and extending lecture material will be assigned and graded. Late homeworks are not accepted except in the case of an unanticipatable absence (e.g. serious illness, death in the family, loss of your favorite DVD etc.).

        GRADES. There will be a midterm exam and a final exam. Each exam will count 30% of the final course grade. The exams will be open notes. Our university scheduled final exam time slot is on Monday, May 4 from 9-noon. Homework assignments will be given periodically throughout the semester and together will count 30% of the final course grade. Some homework assignments will involve programming and the use of AMPL and an appropriate LP solver. The student paper presentations will count 10% of the final course grade.