Classification-assisted Memetic Algorithms for Equality-constrained Optimization Problems with Restricted Constraint Function Mapping

Solving constrained optimization problems using Memetic Algorithms (MAs) has become an important alternative that overcomes the following limitations: the adversary of a global search method to locate the global optimum with sufficient precision and the inability of a local search method to escape from some local optimum. With the success of MAs, researchers in the field are now focused more than ever on the aspect of efficiency of the algorithms such that it would be possible to effectively employ MAs in the context of computationally expensive optimization problems where single evaluation of the objective and constraint functions may require minutes to hours of CPU time or even more. One of the important design issues of MAs is the choice of individuals produced by the global search method upon which the 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 either inequality constraints g(x) ≤ 0 or single equality constraint h(x) = 0. The earlier utilized the feasibility class (feasible or infeasible) of previously evaluated candidate solutions while the latter made use of their raw constraint values. In the latter case, the feasible candidate solutions lie on the constraint boundary defined by the equality 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 equality-constrained problems; the constraint function of which maps the design variables into restricted (either strictly nonnegative or strictly non-positive) real values only. Keywords-Evolutionary Computation; Memetic Algorithms; Genetic Algorithms; Sequential Quadratic Programing; Equalityconstrained Optimization; Computationally-expensive Problems; Classification; Support Vector Machine