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optimization
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Radford, A D and Gero J S (1988). Design by Optimization in Architecture, Building, and Construction,
Van Nostrand Reinhold, New York
optimization techniques
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● which technique depends on● nature of problem● nature of information required
● historically● mathematical problem – single optimal value● not interested in suboptimal values
● design● both decisions and suboptimal solutions important● suboptimal solutions options● may be more acceptable in terms of unstated objectives
optimization techniques
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● nature of problem / information● design variables discrete &/or discontinuous &/or non-contiguous● steel beams in discrete sizes● no. of lifts discontinuous,● materials non-contiguous● nonlinear relationships heat loss
types of techniques
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● calculus● continuous and differentiable
● linear programming (LP)● well developed method● linear relationship among variables
● nonlinear programming (NLP)● nonlinear relationships
● dynamic programming (DP)● discrete, nonlinear, handles constraints
● evolutionary computation● population
general strategies
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● exhaustive enumeration● all possible solutions
● implicit enumeration● e.g. branch & bound, DP
● hill-climbing● moving from existing solution to an improved solution
linear programming● best developed technique
● most frequently used● guarantees optimum solution
● 3 conditions● variables must be continuous, >= 0● O.F. must be linear, OF=20x1 +12x2
● constraints must be linear, 4x1 + 3x2 > 18
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linear programming● convex spaces
● feasible solution space
● O.F. moves away from origin● optimum solution at vertex
7/33x1
x2
dynamic programming● design problems
● not continuous or linear
● definition (Richard Bellman)● an optimal set of decisions has the property that whatever the first decision is, the remaining decisions must be optimal with respect to the outcome which results from the first decision
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if you don’t’ do the best with what you have,you will never do the best with what you
should have had
dynamic programming● stage-state formulation
● implicit enumeration of all paths
● guarantees global optimum● non-serial DP doesn’t guarantee● but pretty good
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Stage 1 2 3
es
4 5State
evolutionary computation● hill-climbing
● one solution at a time● in direction of steepest slope
● local optima● variables &/or constants● equations – y = mx + c
● EC in parallel● populations● survival of the fittest – probability● random generation 10/33
LO
GO
evolutionary computation
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evolutionary computation
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evolutionary computation
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evolutionary computation
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evolutionary computation
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evolutionary computation
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evolutionary computation
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evolutionary computation
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evolutionary computation
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evolutionary computation
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evolutionary computation
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artificial life
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multicriteria optimization
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● single objective● e.g. cost
● several conflicting objectives● max light – min heat● best looking, min cost car
● Pareto solutions● best compromise
● tradeoffs
c1
c2
