A local linear embedding module for evolutionary computation optimization

Abstract

A Local Linear Embedding (LLE) module enhances the performance of two Evolutionary Computation (EC) algorithms employed as search tools in global optimization problems. The LLE employs the stochastic sampling of the data space inherent in Evolutionary Computation in order to reconstruct an approximate mapping from the data space back into the parameter space. This allows to map the target data vector directly into the parameter space in order to obtain a rough estimate of the global optimum, which is then added to the EC generation. This process is iterated and considerably improves the EC convergence. Thirteen standard test functions and two real-world optimization problems serve to benchmark the performance of the method. In most of our tests, optimization aided by the LLE mapping outperforms standard implementations of a genetic algorithm and a particle swarm optimization. The number and ranges of functions we tested suggest that the proposed algorithm can be considered as a valid alternative to traditional EC tools in more general applications. The performance improvement in the early stage of the convergence also suggests that this hybrid implementation could be successful as an initial global search to select candidates for subsequent local optimization.Evolutionary Computation (EC) is often used as a global search method in real world optimization problems. This is due to the fact that many real world optimization problems are nonlinear and result in multimodal objective functions. In such applications, local optimization methods, (e.g., matrix inversion, steepest descent, conjugate gradients) which are prone to trapping in local minima, have limited success.Given some (usually measured) target data, an optimization problem seeks to reconstruct the unknown parameters that, via the use of an appropriate function, can F. Boschetti ( ) CSIRO-EM,

Dimensionality Reduction Optimization

“…Similar, Bremer et al [15] use kernel functions with support vector description to search for feasible scheduling solutions in the energy domain. To some extend related is the approach by Boschetti [16], who employs LLE to support the evolutionary search with candidate solutions.…”