Classification-assisted memetic algorithms for solving optimization problems with restricted equality constraint function mapping

The success of Memetic Algorithms (MAs) has driven many researchers to be more focused on the efficiency aspect of the algorithms such that it would be possible to effectively employ MAs to solve computationally expensive optimization problems where single evaluation of the objective and constraint functions may require minutes to hours of CPU time. One of the important design issues in MAs is the choice of the individuals upon which local search procedure should be applied. Selecting only some potential individuals lessens the demand for functional evaluations hence accelerates convergence to the global optimum. In recent years, advances have been made targeting optimization problems with single equality constraint h(x) = 0. The presence of previously evaluated candidate solutions with different signs of constraint values within some localities thus allows the estimation of the constraint boundary. An individual will undergo local search only if it is sufficiently close to the approximated boundary. Elegant as it may seem, the approach had unfortunately assumed that every constraint function maps the design variables to optimize into unbounded real values. This, however, may not always be the case in practice. In this paper, we present a strategy to efficiently solve constrained problems with a single equality constraint; the function of which maps the design variables into restricted (either strictly non-negative or strictly non-positive) real values only.