Innovization Finding Patterns in Pareto Optimal Solutions and

Innovization: Finding Patterns in Pareto Optimal Solutions and their Applications by Prof. Kalyanmoy Deb Electrical & Computer Engineering Department Michigan State University kdeb@egr. msu. edu www. coin-laboratory. com

MOO & Pareto Optimality Many BEST Solutions in Multi-Objective Optimization • Innovization / Knowledge : What is common among PO Solutions ? ? • Equivalent of Fritz-John conditions ? www. coin-laboratory. com

Example : Design of Electric Induction Motor [Deb K. et. al. 2006] Objectives • S : Size • P : Power Variables • d: Wire Dia • r : Armature Radius • n : # of Turns Knowledge • d = const (Identical Wire Dia) • P α r (Armature Radius vs Power) Knowledge for Designer : Inno-vization Innovation through Optimization www. coin-laboratory. com

Innovization Overview DM Start MOP • Problem Info • Lower Level Pref Initialize t=0 Pt , At EMO Operators t=t+1 Pt+1 , At+1 Learn from Non. Dom set? No No At+1 Yes RONLINE Terminate ? Yes Rule 1, 80% Rule 2, 75% …… No Learn from PO Solns ? Stop ROFFLINE Yes Offline Innovization www. coin-laboratory. com Online Innovization Rule 1, 98% Rule 2, 96% ……. • Knowledge from current KDO run yes DM Satisfied ? No

No Learning Case DM Start MOP • Problem Info • Lower Level Pref Initialize t=0 Pt , At EMO Operators t=t+1 Pt+1 , At+1 Learn from Non. Dom Set? No No At+1 Yes RONLINE Terminate ? Yes Rule 1, 80% Rule 2, 75% …… No Learn from PO Solns ? Stop ROFFLINE Yes Offline Innovization www. coin-laboratory. com Online Innovization yes Rule 1, 98% Rule 2, 96% ……. DM Satisfied ? • Knowledge from current run No

No Learning Case : Example [Deb K. et. al. 2006] PO Front • No Learning • Pareto-Optimal Front obtained www. coin-laboratory. com

Offline Learning Only DM Start MOP • Problem Info • Lower Level Pref Initialize t=0 Pt , At EMO Operators t=t+1 Pt+1 , At+1 Learn from Non. Dom set? Yes No RONLINE No At+1 Terminate ? Yes Rule 1, 80% Rule 2, 75% …… No Learn from PO Solns ? Stop ROFFLINE Yes Offline Innovization www. coin-laboratory. com Online Innovization yes Rule 1, 98% Rule 2, 96% ……. DM Satisfied ? • Knowledge from current run No

Offline Learning Only : Example PO front + • • www. coin-laboratory. com Dominant rules in PO Solutions obtained Recipe for future designs Rules

Online Learning Only DM Start MOP • Problem Info • Lower Level Pref Initialize t=0 Pt , At EMO Operators t=t+1 Pt+1 , At+1 Learn from Non. Dom Set? No No At+1 Yes RONLINE Online Innovization Rule 1, 80% Rule 2, 75% …… Terminate ? Yes No Learn from PO Solns ? Stop ROFFLINE Yes Offline Innovization www. coin-laboratory. com Rule 1, 98% Rule 2, 96% ……. • Knowledge from current run yes DM Satisfied ? No

Online Learning Only : Example PO front + Rules + Faster Convergence www. coin-laboratory. com • • Dominant rules in PO Solutions obtained Faster Convergence

Types of Innovized Knowledge Problem Specific Lower Level Knee region SV = 400 Temporal Higher Level Gen. . . Gen-98 Gen-99 Gen-100 F k. N SV = 4*F www. coin-laboratory. com Bandaru, S. 2013] Hierarchy of Design Rules • First, y=2 • Then x 2/x 1 = 2

Summary • PO solutions carry important design information (Knowledge) • Such design knowledge can be extracted in “Offline” or “Online” or “both” ways • Applications of such knowledge • Improve understanding of physical system and design process • Reduce convergence time for optimization run • Provide good initialization heuristics for similar class problem • Different types of Design Knowledge • Problem specific • Higher Level : Parametric Study • Lower Level : Decision Maker preferred region • Temporal : Hierarchal Design www. coin-laboratory. com

References Deb, K. , & Srinivasan, A. (2006, July). Innovization: Innovating design principles through optimization. In Proceedings of the 8 th annual conference on Genetic and evolutionary computation (pp. 1629 -1636). ACM. Bandaru, S. (2013). Automated innovization: Knowledge discovery through multiobjective optimization (Doctoral dissertation, Ph. D. thesis, Indian Institute of Technology Kanpur). www. coin-laboratory. com