困难最优化问题基准的证明全局极小值
Certified Global Minima for a Benchmark of Difficult Optimization Problems
摘要：
我们为全局优化社区提供了六个欺骗性基准函数（五个有界约束函数和一个非线性约束问题）的新的最优性证明。这些高度多峰的非线性测试问题是全局优化求解器最具挑战性的基准函数之一;有些甚至没有用近似方法解决。我们报告的全局最优值已经使用Charibde（Vanaret et al.，2013），一种结合了进化算法和基于区间的方法的混合算法。虽然元分析通常解决大的问题，并提供足够好的解决方案，有限的计算能力，精确的方法被认为是不适合困难的多峰最优化问题。Charibde新的最优性结果的实现表明，调和随机算法和数值分析方法是向前迈进了一步，处理问题，到目前为止被认为是无法解决的。我们还提供了一个比较与国家的最先进的求解器的基础上的数学规划方法和人口为基础的metabolistics，并显示Charibde，除了是可靠的，是非常有竞争力的最好的求解器上给定的检验函数。
英文摘要：
We provide the global optimization community with new optimality proofs for six deceptive benchmark functions (five bound-constrained functions and one nonlinearly constrained problem). These highly multimodal nonlinear test problems are among the most challenging benchmark functions for global optimization solvers; some have not been solved even with approximate methods. The global optima that we report have been numerically certified using Charibde (Vanaret et al., 2013), a hybrid algorithm that combines an evolutionary algorithm and interval-based methods. While metaheuristics generally solve large problems and provide sufficiently good solutions with limited computation capacity, exact methods are deemed unsuitable for difficult multimodal optimization problems. The achievement of new optimality results by Charibde demonstrates that reconciling stochastic algorithms and numerical analysis methods is a step forward into handling problems that were up to now considered unsolvable. We also provide a comparison with state-of-the-art solvers based on mathematical programming methods and population-based metaheuristics, and show that Charibde, in addition to being reliable, is highly competitive with the best solvers on the given test functions.
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