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INNOVIZATION-Innovative solutions through Optimization

INNOVIZATION-Innovative solutions through Optimization. Prof. Kalyanmoy Deb & Aravind Srinivasan Kanpur Genetic Algorithm Laboratory (KanGAL) Department of Mechanical Engineering Indian Institute of Technology Kanpur. Innovization.

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INNOVIZATION-Innovative solutions through Optimization

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  1. INNOVIZATION-Innovative solutions through Optimization Prof. Kalyanmoy Deb & Aravind Srinivasan Kanpur Genetic Algorithm Laboratory (KanGAL) Department of Mechanical Engineering Indian Institute of Technology Kanpur

  2. Innovization Identification of commonalities amongst optimal solutions or Knowledge discovery. • Optimal Solutions satisfy - KKT conditions. • Single Objective optimization • No global information about any property that the optimal solutions may carry. • No flexibility for the decision maker. • Multi-Objective Optimization • Need for Evolutionary Algorithms(GA) • NSGA-2: Established Algorithm for EMO March 10, KanGAL

  3. EMO • Principle: • Find multiple Pareto-optimal solutions simultaneously • Three main reasons: • For a better decision-making • For unveiling salient optimality properties of solutions • For assisting in other problem solving March 10, KanGAL

  4. Potentials • Better Understanding of the problem. • Reduces Cost. • Eliminates the need for new optimization for small change in parameters. • Deciphers innovative ideas for further design. • Benchmark Designs for industries. March 10, KanGAL

  5. Innovization Procedure • Choose two or more conflicting objectives (e.g., size and power) • Usually, a small sized solution is less powered • Obtain Pareto-optimal solutions using an EMO • Investigate for any common properties manually or automatically March 10, KanGAL

  6. Minimize brake mass Minimize stopping time 16 non-linear constraints 5 variables: Discrete (ri,ro,t,,F,Z) ri in 60:1:80, ro in 90:1:110 mm t in 1:0.5:3 mm, F in 600:10:1000 N Z in 2:1:10 Multi-Disk Brake Design March 10, KanGAL

  7. Innovized Principles • t = 1.5 mm • F = 1,000 N • ro-ri=20mm • Z = 3 till 9 (monotonic) • Starts with small ri and smallest ro • Both increases with brake mass • ri reaches max limit, ro increases March 10, KanGAL

  8. Innovized Principles (cont.) • Surface area, S=Π(ro2-ri2)n • T ∞ 1/S • May be intuitive, but comes out as an optimal property • r_i,max reduces the gap, but same T-S relationship March 10, KanGAL

  9. Mechanical Spring Design • Minimize material volume • Minimizedeveloped stress • Three variables: (d, D, N): discrete, real, integer • Eight non-linear constraints • Solid length restriction • Maximum allowable deflection (P/k≤6in) • Dynamic deflection (Pm-P)/k≥1.25in • Volume and stress limitations March 10, KanGAL

  10. Innovized Principles • Pareto-optimal front have niches with d • Only 5 (out of 42) values of d (large ones) are optimal • Spring stiffness more or less identical • (k=560 lb/in) • 559.005, 559.877, 559.998 lb/in March 10, KanGAL

  11. Optimal Springs, Optimal Recipe d=0.283 in k=559.9 lb/in k=559.0 lb/in d=0.331 in k=559.5 lb/in d=0.394 in Increased stress Increased volume d=0.4375 in k=559.6 lb/in k=560.0 lb/in d=0.5 in March 10, KanGAL

  12. Innovized Principles (cont.) • Investigation reveals: S∞1/(kV0.5) • Two constraints reveal: 50≤k≤560 lb/in • Largest allowable k attains optimal solution • Dynamic deflection constraint active March 10, KanGAL

  13. Higher-Level Innovizations • All optimal solutions have identical spring constant • Constraint g_6 is active: • (P_max-P)/k ≥ δw • k=(p_max-P)/δw • k=(1000-300)/1.25 or 560 lb/in • Change δw • k values change March 10, KanGAL

  14. Welded-Beam Design • Minimize cost and deflection • Four variables and four constraints • Shear stress • Bending stress • b≥h • Buckling load March 10, KanGAL

  15. Innovizations • Two properties • Very small cost solutions behave differently than rest optimal solutions March 10, KanGAL

  16. Innovizations (cont.) • All solutions make shear stress constraint active • Minimum deflection at t=10, b=5 (upper bounds) • Transition when buckling constraint is active • Minimum cost when all four are active March 10, KanGAL

  17. Variations in Variables • Small-cost: t reduces, b, l, h increases • Otherwise: t constant, b reduces, l increases, h reduces March 10, KanGAL

  18. Reliability of this procedure • Confidence in the obtained Pareto front • Benson’s method, Normal Constraint method, KKT conditions. • Confidence in the obtained principles. • KKT Analysis • Big proof and Benchmark results. March 10, KanGAL

  19. Higher Level Innovization • Innovization principles for • Robust Optimization • Reliability Based Optimization • Innovization principles considering • Different pairs of objectives. March 10, KanGAL

  20. Further Challenges: Automated Innovization • Find principles from Pareto-optimal data • Objectives and decision variables • A complex data-mining task • Clustering cum concept learning • Rule extraction • Difficulties • Multiple relationships • Relationships span over a partial set • Mathematical forms not known a-priori • Dealing with inexact data March 10, KanGAL

  21. Thank You Questions and suggestions are welcome March 10, KanGAL

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