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Iterated Local Search (ILS) for the Quadratic Assignment Problem (QAP) Tim Daniëlse en Vincent Delvigne.

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Presentation on theme: "Iterated Local Search (ILS) for the Quadratic Assignment Problem (QAP) Tim Daniëlse en Vincent Delvigne."— Presentation transcript:

1 Iterated Local Search (ILS) for the Quadratic Assignment Problem (QAP) Tim Daniëlse en Vincent Delvigne

2 QAP

3 QAP (2)

4 Complexity

5 Iterated Local Search

6 Iterated Local Search (2) Generate Initial Solution – No known, well performing construction algorithm – Randomized assignment

7 Iterated Local Search (3)

8 Iterated Local Search (4)

9 Iterated Local Search (5) Acceptance Criterion – standard criterion: accept only improvements – varies among the algorithm-variants

10 QAP instance classes QAPLIB benchmark library 4 instance classes: – randomly generated (class i) – Manhattan distance matrix (class ii) – real-life instances (class iii) – random, resembling real-life (class iv)

11 QAP instance classes (2)

12 Analysis of search space

13 Analysis of search space (2)

14 Analysis of search space (3)

15 Distance-Fitness Correlation

16 Distance-Fitness Correlation (2)

17 Stagnation Detection Empirical run-time distribution (RTD) RTD develops below exponential distribution (stagnation) – perform restart

18 Algorithm Variations Soft Restarts – Use of history – Random new solution. Random Walk (RW) – Accept answer regardless of improvement – Combination with default “Better” might improve even more

19 Algorithm Variations (2)

20 Algorithm Variations (3)

21 Algorithm Variations (4)

22 Algorithm Comparison

23 Algorithm Comparison (2)

24 Algorithm Comparison (3)

25

26 Evolutionary Variant Variant of the Evolutionary Strategy. Optimized Local Search Different parameter settings

27

28 Evolutionary Variant (3)

29 Conclusions Fitness-Distance Correlation analysis ILS runtime analysis Acceptance Criteria analysis ES-MN best performing algorithm.

30 References Stutzle, Thomas (2006): Iterated Local Search for the Quadratic Assignment Problem. European Journal of Operational Research 174 (3), 1519-1539.

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