2017 Volume 8 Issue 2 Pages 23-35
In this paper we focus on the linearly constrained continuous optimization. A one of the state-of-the-art stochastic algorithms for ill-conditioned and nonseparable unconstrained problems, namely the covariance matrix adaptation evolution strategy (CMA-ES) is applied to solve linearly constrained continuous optimization problems. We extend the box constraint handling technique that turns a box constrained optimization problem into an unconstrained optimization problem by introducing an artificial fitness landscape, where a penalty function is added to the function value at the nearest feasible solution. The penalty function is adapted during search so as to create an artificial landscape outside the feasible domain that makes the function as easily solvable by the CMA-ES as possible. Treating a box constraint as a special case of linear constraints, we generalize the box constraint handling to apply the same technique to an arbitrary linear constrained problem. Moreover, the adaptation of the penalty coefficient is accelerated. The resulting linear constraint handling technique exhibits an invariant performance on problems with linear constraints under a linear transformation of the coordinate system, showing that a linearly constrained problem can be essentially as efficiently solvable by the CMA-ES as a box constrained problem.
