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Mixed Discrete Non-Linear Near-Optimization

IP.com Disclosure Number: IPCOM000103867D
Original Publication Date: 1993-Feb-01
Included in the Prior Art Database: 2005-Mar-18
Document File: 2 page(s) / 46K

Publishing Venue

IBM

Related People

Okano, A: AUTHOR

Abstract

This article describes an algorithm for a mixed discrete non-linear near-optimization. Generally, a mixed discrete non-linear optimization problem can be described as follows:

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Mixed Discrete Non-Linear Near-Optimization

      This article describes an algorithm for a mixed discrete
non-linear near-optimization.  Generally, a mixed discrete non-linear
optimization problem can be described as follows:

      minimize f(X) subject to G(X) <= 0.

      Uppercase letters indicate vectors.  X is a vector of
variables.  f(X) is called an objective function.  G(X) is called a
constraint, and may be non-linear.  Some Xs can have only discrete
values, while others can have continuous values.  It is usually
difficult to obtain an optimal solution because there are many local
optimums.  If f(X) and G(X) are algebraic expressions, the following
algorithm for this problem can provide a nearly optimal solution.
This algorithm uses a genetic algorithm and Lagrange's multiplier
method.

      0.  Let Xi (1<=i<=n) be members of X, n be the size of X, and m
be the number of discrete variables.  Let Xi (1<=i<=m) be discrete
variables and Xi (m+1<=i<=n) be continuous variables.  Let Di be a
set of possible values of Xi (1<=i<=m).

      1.  Generate a predefined number of Xs.  Xi (1<=i<=m) are
selected randomly from Di.

      2.  Perform steps 8 to 14 for all Xs.

      3.  Select two Xs corresponding to the fitness described in
step 13.

      4.  Generate a new X by crossover of the two Xs.

      5.  Mutate the new X probabilisticaly.

      6.  Perform steps 8 to 14 for the new X.

      7.  Go to ste...