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The Problem

Resource-Based Fitness Sharing Jeffrey Horn Northern Michigan University Department of Mathematics and Computer Science Marquette, MI USA jhorn@nmu.edu http://cs.nmu.edu/~jeffhorn PPSN VII September 10, 2002. The Problem.

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The Problem

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  1. Resource-Based Fitness SharingJeffrey HornNorthern Michigan UniversityDepartment of Mathematics and Computer ScienceMarquette, MI USAjhorn@nmu.eduhttp://cs.nmu.edu/~jeffhornPPSN VII September 10, 2002

  2. The Problem • We want to exploit the “covering” capabilities of niching/speciation. Idea is to make fitness a function of converage. • Example applications: shape nesting, cutting stock trim minimization, layout, packing, etc. • Goal is to cover a finite, uniform surface (the substrate) with the maximum number of shapes (or pieces). • All pieces are identical.

  3. Resource Sharing Defined Example Scenario: Three overlapping Niches A, B, C Shared fitness

  4. Resource Sharing on One-Dimension Nesting Problem Bold rectangle is substrate to be covered by small squares (selection only) All squares represented initially Final coverage still contains overlapping squares, and is missing some globals

  5. Fitness Sharing Define The shared fitness is where is the sharing function

  6. RESOURCE SHARING+ FITNESS SHARING=RESOURCE-BASED FITNESS SHARING

  7. Resource-based Fitness Sharing Defined Shared fitness . Example for three Overlapping niches Note how RFS combines the simpler structure (a ratio) of fitness sharing with the resource-based niche overlap calculation of resource sharing.

  8. RFS on the One-Dimension Shape Nesting Problem (selection only) Blue rectangle is substrate to be covered by smaller, green, squares All squares represented initially Note edge effect Perfect Coverage (indicates high selection pressure)

  9. f(x) 1 0 Fitness Sharing on a “Hat” Function (selection only) “off-substrate” Individuals have died off. Niches at edges do well (the edge effect) Initial population covers entire domain Ideal solution. Nine remaining species exactly cover the “top” of The “hat” Edge effects propogate toward center, reinforce each other Success of FS in One Dimension Nesting

  10. Cooperative Behavior? Here lines connect species that seem to cooperate in trying to cover the surface together (they do not overlap)

  11. RFS in Two Dimensions (selection only) All overhanging pieces have been eliminated Distribution of Entire Population Blue square is the substrate to be covered Globals Only Initial distribution, including globals, is uniform. Beginning of corner effect…

  12. All 16,000 population slots are filled (fairly evenly) with copies of the 16 globals Still some overlap left in the population…

  13. RFS with Mutation Much smaller pop size (N=500). Some globals must be discovered by mutation (some are NOT in Initial pop.) Pop has converged on the 16 globals, with mutation still producing some “misfits” Distribution of Entire Population

  14. The Approaches • FITNESS SHARING (FS)established • Fast and simple • Some success (e.g., niching on the Pareto front in multi-objective EC) • LIMITATION: fixed niche radius implies spherically-shaped niches/pieces ONLY (also constrains shape of substrate) • RESOURCE SHARING (RS)natural • Based on actual, arbitrarily shaped pieces and substrate • Natural • LIMITATION: introduces complex dynamics that often prevent convergence to “optimal” equilibrium distribution • RESOURCE-BASED FITNESS SHARING (RFS)new • Combines benefits of both FS and RS • Overcomes above limitations of FS and RS • Simpler dynamics (so more robust convergence) than RS, but based directly on actual coverage of resources (substrate) by pieces (shapes)

  15. Summary • RFS seems to have the simplicity and efficiency of fitness sharing • But also has the “natural fit” of resource sharing (with niches based entirely on resource coverage) • Potential for success on harder shape nesting problems (e.g., irregular shapes, irregular substrates, rotated pieces, etc.)

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