Many artificial benchmark problems have been proposed for different kinds of continuous optimization, e.g., global optimization, multimodal optimization, multiobjective optimization, dynamic optimization, and constrained optimization. However, there is no unified framework for constructing these types of problems and possible properties of many problems are not fully tunable. This will cause difficulties for researchers to analyze strengths and weaknesses of an algorithm. To address these issues, this paper proposes a simple and intuitive framework, which is able to construct different kinds of problems for continuous optimization. The framework utilizes the ${k}$ -d tree to partition the search space and sets a certain number of simple functions in each subspace. The framework is implemented into global/multimodal optimization, dynamic single objective optimization, multiobjective optimization, and dynamic multiobjective optimization, respectively. Properties of the proposed framework are discussed and verified with traditional evolutionary algorithms.

中文翻译：

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一个构造连续优化问题的开放框架

对于各种不同的连续优化，已经提出了许多人工基准问题，例如，全局优化，多峰优化，多目标优化，动态优化和约束优化。但是，没有统一的框架来构造这些类型的问题，并且许多问题的可能特性也不是完全可调的。这将使研究人员难以分析算法的优缺点。为了解决这些问题，本文提出了一个简单直观的框架，该框架能够构造各种问题以进行持续优化。该框架利用$ {k} $ -d树划分搜索空间，并在每个子空间中设置一定数量的简单函数。该框架已实施为全局/多峰优化，动态单目标优化，多目标优化和动态多目标优化。讨论了所提出框架的性质，并通过传统的进化算法进行了验证。