Dual Evolutionary Optimization

The most general strategy for handling constraints in evolutionary optimization is through penalty functions. The choice of the penalty function is critical to both success and eciency of the optimization. Many strategies have been proposed for formulating penalty functions, most of which rely on arbitrary tuning of parameters. An new insight on function penalization is proposed in this paper that relies on the dual optimization problem. Use of duality is particularly relevant to evolutionary optimization since it applies to any type of variable and function spaces (continuous or discrete, linear or not, with one or many extrema) as evolutionary algorithms do. An evolutionary algorithm for approximately solving dual optimization problems is rst presented. It calculates Lagrange multipliers at the optimum, which have great practical importance for cost sensitivity analysis. Next, an exact penalty function without extra parameter to be tuned is proposed. Among a Lagrangian based class of penalty functions, it applies a minimal penalty, which contributes to keeping the evolutionary search ecient. Numerical tests are provided for continuous variables and inequality constraints