INNOVIZATION-Innovative solutions through Optimization

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INNOVIZATION-Innovative solutions through
Optimization

• Prof. Kalyanmoy Deb Aravind Srinivasan
• Kanpur Genetic Algorithm Laboratory (KanGAL)
• Department of Mechanical Engineering
• Indian Institute of Technology Kanpur

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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

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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

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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.

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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

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Multi-Disk Brake Design

• Minimize brake mass
• Minimize stopping time
• 16 non-linear constraints
• 5 variables Discrete (ri,ro,t,,F,Z)
• ri in 60180,
• ro in 901110 mm
• t in 10.53 mm,
• F in 600101000 N
• Z in 2110

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Innovized Principles

• t 1.5 mm
• F 1,000 N
• ro-ri20mm
• Z 3 till 9 (monotonic)
• Starts with small ri and smallest ro
• Both increases with brake mass
• ri reaches max limit, ro increases

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Innovized Principles (cont.)

• Surface area, S?(ro2-ri2)n
• T 8 1/S
• May be intuitive, but comes out as an optimal
  property
• r_i,max reduces the gap, but same T-S relationship

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Mechanical Spring Design

• Minimize material volume
• Minimize developed stress
• Three variables (d, D, N) discrete, real,
  integer
• Eight non-linear constraints
• Solid length restriction
• Maximum allowable deflection (P/k6in)
• Dynamic deflection (Pm-P)/k1.25in
• Volume and stress limitations

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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
• (k560 lb/in)
• 559.005, 559.877, 559.998 lb/in

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Optimal Springs, Optimal Recipe
d0.283 in
k559.9 lb/in
k559.0 lb/in
d0.331 in
k559.5 lb/in
d0.394 in
Increased stress
Increased volume
d0.4375 in
k559.6 lb/in
k560.0 lb/in
d0.5 in
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Innovized Principles (cont.)

• Investigation reveals S81/(kV0.5)
• Two constraints reveal 50k560 lb/in
• Largest allowable k attains optimal solution
• Dynamic deflection constraint active

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Higher-Level Innovizations

• All optimal solutions have identical spring
  constant
• Constraint g_6 is active
• (P_max-P)/k dw
• k(p_max-P)/dw
• k(1000-300)/1.25 or 560 lb/in
• Change dw
• k values change

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Welded-Beam Design

• Minimize cost and deflection
• Four variables and four constraints
• Shear stress
• Bending stress
• bh
• Buckling load

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Innovizations

• Two properties
• Very small cost solutions behave differently than
  rest optimal solutions

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Innovizations (cont.)

• All solutions make shear stress constraint active

• Minimum deflection at t10, b5 (upper bounds)
• Transition when buckling constraint is active
• Minimum cost when all four are active

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Variations in Variables

• Small-cost t reduces, b, l, h increases
• Otherwise t constant, b reduces,
• l increases, h reduces

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Reliability of this procedure

• Confidence in the obtained Pareto front
• Bensons method, Normal Constraint method, KKT
  conditions.
• Confidence in the obtained principles.
• KKT Analysis
• Big proof and Benchmark results.

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Higher Level Innovization

• Innovization principles for
• Robust Optimization
• Reliability Based Optimization
• Innovization principles considering
• Different pairs of objectives.

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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

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• Thank You
• Questions and suggestions are welcome