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مقاله IEEE با عنوان Locating Multiple Optimal Solutions of Nonlinear Equation
Systems Based on Multiobjective Optimization
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هدفه یا Multiobjective Optimization پیاده سازی میکند.
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چکیده لاتین مقاله به صورت ذیل میباشد :
Nonlinear equation systems may have multiple optimal solutions.
The main task of solving nonlinear equation
systems is to simultaneously locate these optimal solutions in a single run. When solving nonlinear equation systems by
evolutionary algorithms, usually a nonlinear
equation system should be transformed into a kind of
optimization problem. At present, various
transformation techniques have been proposed. This paper
presents a simple and generic transformation technique based
on multiobjective optimization for nonlinear equation
systems. Unlike the previous work, our transformation technique transforms a nonlinear equation system into a
biobjective optimization problem that can be
decomposed into two parts. The advantages of our
transformation technique are twofold:
1)
all the optimal solutions of a nonlinear equation system are
the Pareto optimal solutions of the transformed problem,
which are mapped into diverse points in the objective space, and
2) multiobjective evolutionary algorithms can
be directly applied to handle the transformed
problem. In order to verify
the effectiveness of our transformation technique, it has been integrated with nondominated sorting genetic algorithm
II to solve nonlinear equation systems. The experimental
results have demonstrated that, overall, our
transformation technique outperforms another
state-of-the-art multiobjective optimization based transformation
technique and four single-objective optimization based
approaches on a set of test instances. The influence of the types
of Pareto front on the performance of our transformation technique
has been investigated empirically. Moreover, the limitation of
our transformation technique has also been identified and
discussed in this paper.