17-03-2014, 05:33 PM
Abstract—Differential Evolution (DE) is featured by its simple
parameter control; genetic operation and fine robustness.
However, DE yet still has difficulty with complex functions in
continuous space due to its searching blindness and
inefficiency from time to time. An adaptive DE algorithm
based on LS-SVM (Least Square Support Vector Machine) is
proposed in this paper. The key genetic operators such as
differential mutation and crossover are modified; Adaptive
population evolution guiding strategy based on LS-SVM n-best
training set approximation and optimization is designed; With
applying condition analyzed, the procedure and complexity of
the LS-SVM based evolution guiding strategy is summarized.?
The comparative results of the proposed DE with traditional
one based on various standard test functions effectively
demonstrate the high accuracy and efficiency of the proposed
approach for continuous multi-modal optimization.
Keywords-differential evolution; global optimization; least
square SVM; n-best training set; approximation function
I. INTRODUCTION
Differential Evolution (DE) algorithm is a kind of realencoded,
population evolution based meta-heuristic global
optimization method. DE has relative higher ability of global
optimization than those conventional deterministic methods
such as steepest descent, BFGS for simple uni-modal
functions [1, 2], or even some relative more complex
continuous space problems, for instance, the optimization of
some special non-linear, non-differentiable, or even nondescribable
functions, which may sometimes make the
conventional methods be prematurely trapped into local
optima. However, as stochastic searching strategy, DE
algorithm is still affected by high randomness despite its
better global searching and converging ability relative to
other meta-heuristic techniques, like genetic algorithm,
particle swarm optimization (PSO), ant colony optimization
(ACO), simulated annealing (SA) and taboo searching, etc.
Therefore, DE’s efficiency of global searching is restricted
by its high blindness when optimizing complex, continuous,
and multi-modal problems [3-6].
The previous research with regard to searching efficiency
improvement for DE algorithm has primarily focused on the
following two aspects: 1) Adaptive optimization of the
control parameters (differential factor F and crossover
probability CR ) with meta-heuristic methods (SA, PSO and
ACO) to adjust the probability and scale of genetic
operations [6-8]. Although this kind of methods may
improve the population diversity and converging efficiency
to certain extent for some special problems, the feasibility
and flexibility of DE algorithm are negatively affected by the
deteriorative complexity brought in by extra routine in the
meanwhile; 2) Modification of some offspring born in each
iterative generation to make them appropriately approach to
the current optimum by introducing customized operators
(local enhanced operators, or second time-crossover, etc)
[9,10]. Methods of this kind may indeed accelerate the
converging process when approaching the global optimum
for certain multi-modal functions (with large curvature and
smooth area around the global optimum) by enhancing the
greediness of the modified individuals. However, population
diversity would suffer great loss, and DE would probably run
more risk of premature convergence.
This paper proposes an alternative way to improve the
converging efficiency of DE algorithm mainly based on least
square SVM function approximation. The main contents are
organized in the following manner. First, the enhanced
differential mutation and simplified crossover operations are
introduced. Then, a method for adaptively improving the
quality of global searching based on LS-SVM regression
function approximation and optimization is designed and
analyzed. In the next section, the effectiveness and efficiency
of the presented DE algorithm are demonstrated by
comparative tests of several standard functions. We draw our
conclusion and discuss about future work in the end.
parameter control; genetic operation and fine robustness.
However, DE yet still has difficulty with complex functions in
continuous space due to its searching blindness and
inefficiency from time to time. An adaptive DE algorithm
based on LS-SVM (Least Square Support Vector Machine) is
proposed in this paper. The key genetic operators such as
differential mutation and crossover are modified; Adaptive
population evolution guiding strategy based on LS-SVM n-best
training set approximation and optimization is designed; With
applying condition analyzed, the procedure and complexity of
the LS-SVM based evolution guiding strategy is summarized.?
The comparative results of the proposed DE with traditional
one based on various standard test functions effectively
demonstrate the high accuracy and efficiency of the proposed
approach for continuous multi-modal optimization.
Keywords-differential evolution; global optimization; least
square SVM; n-best training set; approximation function
I. INTRODUCTION
Differential Evolution (DE) algorithm is a kind of realencoded,
population evolution based meta-heuristic global
optimization method. DE has relative higher ability of global
optimization than those conventional deterministic methods
such as steepest descent, BFGS for simple uni-modal
functions [1, 2], or even some relative more complex
continuous space problems, for instance, the optimization of
some special non-linear, non-differentiable, or even nondescribable
functions, which may sometimes make the
conventional methods be prematurely trapped into local
optima. However, as stochastic searching strategy, DE
algorithm is still affected by high randomness despite its
better global searching and converging ability relative to
other meta-heuristic techniques, like genetic algorithm,
particle swarm optimization (PSO), ant colony optimization
(ACO), simulated annealing (SA) and taboo searching, etc.
Therefore, DE’s efficiency of global searching is restricted
by its high blindness when optimizing complex, continuous,
and multi-modal problems [3-6].
The previous research with regard to searching efficiency
improvement for DE algorithm has primarily focused on the
following two aspects: 1) Adaptive optimization of the
control parameters (differential factor F and crossover
probability CR ) with meta-heuristic methods (SA, PSO and
ACO) to adjust the probability and scale of genetic
operations [6-8]. Although this kind of methods may
improve the population diversity and converging efficiency
to certain extent for some special problems, the feasibility
and flexibility of DE algorithm are negatively affected by the
deteriorative complexity brought in by extra routine in the
meanwhile; 2) Modification of some offspring born in each
iterative generation to make them appropriately approach to
the current optimum by introducing customized operators
(local enhanced operators, or second time-crossover, etc)
[9,10]. Methods of this kind may indeed accelerate the
converging process when approaching the global optimum
for certain multi-modal functions (with large curvature and
smooth area around the global optimum) by enhancing the
greediness of the modified individuals. However, population
diversity would suffer great loss, and DE would probably run
more risk of premature convergence.
This paper proposes an alternative way to improve the
converging efficiency of DE algorithm mainly based on least
square SVM function approximation. The main contents are
organized in the following manner. First, the enhanced
differential mutation and simplified crossover operations are
introduced. Then, a method for adaptively improving the
quality of global searching based on LS-SVM regression
function approximation and optimization is designed and
analyzed. In the next section, the effectiveness and efficiency
of the presented DE algorithm are demonstrated by
comparative tests of several standard functions. We draw our
conclusion and discuss about future work in the end.