DM63 - Heuristics for Combinatorial Optimization Problems - Lecture Notes
Lecture 11, Fall 2006

Lecture October 30

We ended the description of Metaheuristics with Scatter Search and Path Relinking, Estimation of Distribution Algorithm and Cross Entropy Method.

We resumed the methods discussed and gave a concept map of the course so far.

The remaining lectures will be focused on Empirical Methods and Extended concepts in Optimisation.

We started with motivating the use of Empirical Analysis in this field and laying the Statistical Basis.

In the next lecture we continue with Empirical Methods. Two articls are reccomended readings:

C.C. McGeoch. Toward an Experimental Method for Algorithm Simulation. INFORMS Journal on Computing, Vol. 8 Issue 1, p1, 15p.

R.L. Rardin, R. Uzsoy. Experimental Evaluation of Heuristic Optimization Algorithms: A Tutorial. Journal of Heuristics 7(3): 261-304 (2001).</p>

Furtehr readings which could be helpful for the next lecture are:

M. Birattari, M. Zlochin, and M. Dorigo. (2005) Towards a Theory of Practice in Metaheuristics Design. A Machine Learning Perspective. Technical Report TR/IRIDIA/2005-030. IRIDIA, Université; Libre de Bruxelles, Brussels, Belgium. Available from the author's webpage.

M. Birattari, T. Stützle, L. Paquete, and K. Varrentrapp. (2002) A Racing Algorithm for Configuring Metaheuristics. In Proceedings of the Genetic and Evolutionary Computation Conference, pp. 11-18. Morgan Kaufmann, San Francisco, CA, USA. Available from the author's webpage.

The last lecture will be Thursday, 9th November.

Bibliographical Notes

The three metaheuristics encountered at the lecture are described here:

F. Glover, M. Laguna and R. Martí;. Fundaments of Scatter Search and Path Relinking. Control and Cybernetics, Volume 29, Number 3, pp. 653-684, 2000.

R. Martí (ed.) Feature Cluster on Scatter Search Methods for Optimization. European Journal of Operational Research. Volume 169, Issue 2, Pages 351-698

Rafael Martí, Manuel Laguna and Fred Glover, Principles of scatter search European Journal of Operational Research Volume 169, Issue 2, 1 March 2006, Pages 359-372.

Pelikan, M., Goldberg, D.E., Lobo, F. A Survey of Optimization by Building and Using Probabilistic Models. Tec. Rep. 99018. Illinois Genetic Algorithms Laboratory, University of Illinois. 1999.

P.T. de Boer, D. Kroese, S. Mannor and R.Y. Rubinstein. A Tutorial on the Cross-Entropy Method. 2003.

Basic concept of statistics can be found in any textbook of Applied Statistics, such as for example:

Petruccelli, Nandram & Chen: Applied Statistics for Engineers and Scientists, 1999, Prentice Hall Press.

Moreover the following web sites are worthwhile bookmarks:

• Electronic Statistics Textbook. StatSoft, Inc. (2006)

• NIST/SEMATECH e-Handbook of Statistical Methods

Exercises

Exercise 1

Classify the metaheuristics encountered in the lectures according to the following criteria:

• Trajectory methods vs discontinuous methods

  
  

• Population-based vs single-point search

  
  

• Memory usage vs memory-less methods

  
  

• One vs various neighborhood structures

  
  

• Dynamic vs static objective function

  
  

• Nature-inspired vs non-nature inspiration

  
  

• Instance based vs probabilistic modeling based

Exercise 2

There are different approaches to apply heuristic methods for solving the chromatic version of the graph coloring problem:

Number of colours	Candidate Solutions
$k$-fixed	complete	proper
$k$-fixed	partial	proper
$k$-fixed	complete	unproper
$k$-fixed	partial	unproper
$k$-variable	complete	proper
$k$-variable	partial	proper
$k$-variable	complete	unproper
$k$-variable	partial	unproper

Different choices for the candidate solutions, neighborhood structures and evaluation function are needed within each approach case. Which approach appears promising to you and which instead makes no sense? Could you design the application of the Metaheuristics within each approach?