Optimum: Global vs Local X2 Why the problem Objective . Nonconvex contours objective or constraints G constraint (wiggly contours) X1 resonance Spring k N/cm .Disjoint design mass space P= p cos(ot) Local information, e.g., derivatives, does not distinguish local from global optima-the grand Unsolved Problem in Analysis
Optimum: Global vs. Local X2 Why the problem: Objective •Nonconvex contours objective or constraints constraint (wiggly contours) X1 L G resonance d Spring k N/cm •Disjoint design mass space d P P = p cos ( ωt) k • Local information, e.g., derivatives, does not distinguish local from global optima - the Grand Unsolved Problem in Analysis
What to do about it A"shotgun" approach Tunnel Start \ yopt M1 M2<M1 Tunneling algorithm finds a better minimum
• Use a multiprocessor computer • Start from many initial designs • Execute multipath optimization • Increase probability of locating global minimum • Probability, no certainty • Multiprocessor computing = analyze many in time of one = new situation = can do what could not be done before. What to do about it A —shotgun“ approach: F Start M1 Opt. Tunnel M2<M1 X •—Tunneling“ algorithm finds a better minimum
What to do about it Tunnel shotgun Start、!Oprt Multiprocessor computer M1 M2<M1 Tunneling algorithm finds a better minimum
A —shotgun“ approach: • Use a multiprocessor computer • Start from many initial designs • Execute multipath optimization • Increase probability of locating global minimum • Probability, no certainty • Multiprocessor computing = analyze many in time of one = new situation = can do what could not be done before. What to do about it F Start M1 Opt. Tunnel shotgun Multiprocessor computer M2<M1 X •—Tunneling“ algorithm finds a better minimum
What to do about it A“ shotgun" approach: Tunnel Start、!Oprt Use a multiprocessor computer Start from many initial designs M1 M2<M1 · EXecute multipath optimization Increase probability of locating Tunneling algorithm global minimum finds a better minimum Probability, no certainty Multiprocessor computing analyze many in time of one new situation can do what could not be done before
What to do about it F Start M1 Opt. Tunnel A —shotgun“ approach: • Use a multiprocessor computer • Start from many initial designs • Execute multipath M2<M1 optimization X • Increase probability of locating global minimum •—Tunneling“ algorithm • Probability, no certainty finds a better minimum • Multiprocessor computing = analyze many in time of one = new situation = can do what could not be done before
Using optimization to Impart Desired Attributes
Using Optimization to Impart Desired Attributes