Novel derivative of harmony search algorithm for discrete design variables

Calculus has widespread applications in science and engineering. Optimization is one of its major subjects, where a problem can be mathematically formulated and its optimal solution is determined by using derivatives. However, this calculus-based derivative technique can only be applied to real-valu...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 199; no. 1; pp. 223 - 230
Main Author Geem, Zong Woo
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 15.05.2008
Elsevier
Subjects
Calculus of variations and optimal control
Combinatorial optimization
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Discrete variable
Evolutionary algorithm
Exact sciences and technology
Harmony search
Mathematical analysis
Mathematics
Meta-heuristics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Real functions
Sciences and techniques of general use
Soft computing
Stochastic derivative
Harmony search
Discrete variable
Evolutionary algorithm
Soft computing
Combinatorial optimization
Stochastic derivative
Meta-heuristics
Optimization method
Continuous function
Search algorithm
Numerical analysis
Real function
Applied mathematics
Optimal solution
Mathematical programming
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Summary:Calculus has widespread applications in science and engineering. Optimization is one of its major subjects, where a problem can be mathematically formulated and its optimal solution is determined by using derivatives. However, this calculus-based derivative technique can only be applied to real-valued or continuous-valued functions rather than discrete-valued functions while there are many situations where design variables contain not continuous values but discrete values by nature. In order to consider these realistic design situations, this study proposes a novel derivative for discrete design variables based on a harmony search algorithm. Detailed analysis shows how this new stochastic derivative works in the bench-mark function and fluid-transport network design. Hopefully this new derivative, as a fundamental technology, will be utilized in various science and engineering problems.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2007.09.049