CEC2017优化问题的测试函数_cec2017测试函数太难了,cec2017函数 - CSDN文库

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ProblemDefinitionsandEvaluationCriteria

fortheCEC2017CompetitionandSpecial

SessiononConstrainedSingleObje....

TechnicalReport·October2016

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Introduction

In real-world applications, most optimization problems contain constraints (ranging from

physical, time, geometric, design etc.) which need to be satisfied while finding an optimal

solution. However, the presence of constraints alters the shape of the search space making it

difficult to solve. In the last few decades, stochastic search algorithms such as evolutionary

algorithms have gained popularity due to their effectiveness in solving optimization problems.

However, since evolutionary algorithms or most meta-heuristics naturally designed for

unconstrained optimization problems require additional mechanisms to solve constrained

optimization problems.

Initially, the effectiveness of different penalty functions (both in evolutionary algorithms and

in mathematical programming) has been investigated for several decades. However, the

penalty functions have, in general, several limitations.For instance, they are not suitable for

optimization problems where the optimum is on the boundary connecting the feasible and the

infeasible regions or when the feasible region is disjoint.In addition, penalty functions require

intensive fine-tuning to identify the most appropriate penaltyfactors to be employed. In the

last few decades, a variety approaches have been proposed in conjunction with evolutionary

algorithms to handle constraints. Most popular among them are self-adaptive penalty, epsilon

constraint handling, superiority of feasible and stochastic ranking. Recently, the idea of

ensemble of different constraint handling methods was proposed where each constraint

handling method is apt only for a group of problems [1].

For competition in CEC06 [2], 24 benchmark functions with dimensionality varying from 2-

20 have been developed. However, the CEC06 benchmark problems are not scalable. In the

modern era of Big Data, most optimization problems that are being considered contain few

hundreds of variables with a wide variety of constraints. Therefore, it necessary to test the

scalability of the optimization algorithms that are being developed on a set of scalable

constrained optimization problems. In [3], a test-case generator for constrained parameter

optimization problems was proposed. In [4], 18 benchmark functions which are scalable (10-

and 30-dimensional) were developed for the competition in CEC2010. However, the

optimization problems proposed for competitions in CEC06 and CEC2010 have been

successfully solved. In this report, we develop a set of 28 benchmark constrained

optimization problems with dimensions 10, 30, 50 and 100. The developed problems contain

a wide variety of constraints.

The mathematical formulas and properties of these functions are described in Section 1. In

Section 2, the evaluationcriteria are given. A suggested format to present the results is also

given in Section 3.

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