1. “Hard” Optimization Problems
Goal: Find
where S is often multi-dimensional; real-valued or binary
Many classes of optimization problems (and algorithms) exist.
When might it be worthwhile to consider metaheuristic or machine learning approaches?
Marcus Gallagher - MASCOS Symposium, 26/11/04

2. Marcus Gallagher - MASCOS Symposium, 26/11/04
Finding an “exact” solution is intractable.
Limited knowledge of f()
No derivative information.
May be discontinuous, noisy,…
Evaluating f() is expensive in terms of time or cost.
f() is known or suspected to contain nasty features
Many local minima, plateaus, ravines.
The search space is high-dimensional.
Marcus Gallagher - MASCOS Symposium, 26/11/04

3. Marcus Gallagher - MASCOS Symposium, 26/11/04
What is the “practical” goal of (global) optimization?
“There exists a goal (e.g. to find as small a value of f() as possible), there exist resources (e.g. some number of trials), and the problem is how to use these resources in an optimal way.”
A. Torn and A. Zilinskas, Global Optimisation. Springer-Verlag, Lecture Notes in Computer Science, Vol. 350.
Marcus Gallagher - MASCOS Symposium, 26/11/04

4. Marcus Gallagher - MASCOS Symposium, 26/11/04
Heuristics
Heuristic (or approximate) algorithms aim to find a good solution to a problem in a reasonable amount of computation time – but with no guarantee of “goodness” or “efficiency” (cf. exact or complete algorithms).
Broad classes of heuristics:
Constructive methods
Local search methods
Marcus Gallagher - MASCOS Symposium, 26/11/04

5. Marcus Gallagher - MASCOS Symposium, 26/11/04
Metaheuristics
Metaheuristics are (roughly) high-level strategies that combinine lower-level techniques for exploration and exploitation of the search space.
An overarching term to refer to algorithms including Evolutionary Algorithms, Simulated Annealing, Tabu Search, Ant Colony, Particle Swarm, Cross-Entropy,…
C. Blum and A. Roli. Metaheuristics in Combinatorial Optimization: Overview and Conceptual Comparison. ACM Computing Surveys, 35(3), 2003, pp
Marcus Gallagher - MASCOS Symposium, 26/11/04

6. Learning/Modelling for Optimization
Most optimization algorithms make some (explicit or implicit) assumptions about the nature of f().
Many algorithms vary their behaviour during execution (e.g. simulated annealing).
In some optimization algorithms the search is adaptive
Future search points evaluated depend on previous points searched (and/or their f() values, derivatives of f() etc).
Learning/modelling can be implicit (e.g, adapting the step-size in gradient descent, population in an EA).
Marcus Gallagher - MASCOS Symposium, 26/11/04

7. EDAs: Probabilistic Modelling for Optimization
Idea is to convert the optimization problem into a search over probability distributions.
P. Larranaga and J. A. Lozano (eds.). Estimation of Distribution Algorithms: a new tool for evolutionary computation. Kluwer Academic Publishers, 2002.
The probabilistic model is in some sense an explicit model of (currently) promising regions of the search space.
Marcus Gallagher - MASCOS Symposium, 26/11/04

8. Marcus Gallagher - MASCOS Symposium, 26/11/04
Summary
The field of metaheuristics (including Evolutionary Computation) has produced
A large variety of optimization algorithms
Demonstrated good performance on a range of real-world problems.
Metaheuristics are considerably more general:
can even be applied when there isn’t a “true” objective function (coevolution).
Can evolve non-numerical objects.
Marcus Gallagher - MASCOS Symposium, 26/11/04

9. Marcus Gallagher - MASCOS Symposium, 26/11/04
Summary
EDAs take an explicit modelling approach to optimization.
Existing statistical models and model-fitting algorithms can be employed.
Potential for solving challenging problems.
Model can be more easily visualized/interpreted than a dynamic population in a conventional EA.
Although the field is highly active, it is still relatively immature
Improve quality of experimental results.
Make sure research goals are well-defined.
Lots of preliminary ideas, but lack of comparative/followup research.
Difficult to keep up with the literature and see connections with other fields.
Marcus Gallagher - MASCOS Symposium, 26/11/04