Oppositional concepts in population-based problem solving

遗传算法、差异进化和蚁群等基于种群的优化技术有着广泛的应用。这些优化方法已被证明在许多情况下是有用的，在许多情况下，传统的优化方法遇到它们的适用范围。然而，基于人口的计划有其自身的局限性。具体地说，它们可能通常需要相当长的计算时间才能找到解决方案。当我们处理高维和/或复杂的优化问题时，这种缺点变得越明显，这(几乎)总是这样。因此，提高这些技术速度的方法已经被研究了很长一段时间。这项研究的主要焦点将集中在开发方法，以提高差异进化和蚁群的速度。将使用相反的概念来加速方法的收敛，同时保持必要的解的准确性。基于对立的优化方法通常包括同时考虑解和相反的解(染色体和反染色体、路径和相反的路径)。最近在成功设计和使用基于对立的差异进化方面的成就鼓励我们为这些技术寻求一些关于数学形式主义的基本答案，并为所有基于种群的算法开发对立方案的潜力。将使用标准基准函数和衡量标准来验证正在调查的方法基于对立的扩展的更好性能。作为真实世界的测试案例，还将进行医学图像的分割，特别是乳腺和前列腺超声图像。基于群体的方法已经被用来以不同的方式从数字图像中提取对象。正如文献报道的那样，他们的结果在某些情况下是令人印象深刻的。然而，用这些方法处理图像是极其昂贵的。这限制了它们在实际案例中的使用。在这里，任何级别的加速都是可取的。图像数据集以及放射科医生的地面真实数据可用于实验性能验证。

Population-based optimization techniques such as genetic algorithms, differential evolution and ant colonies have diverse applications. These optimization methods have proven to be useful in many cases where conventional optimization methods encounter their applicability limits. However, population-based schemes have their own limitations. Specifically, they may often need considerable computational time to find a solution. This disadvantage becomes more visible the larger the population is, which is (almost) always the case when we deal with high-dimensional and/or complex optimization problems. Hence, methods by which to increase the speed of these techniques have been under investigation for quite some time. The main focus of this research will centre on development of methods to increase the speed of differential evolution and ant colonies. Oppositional concepts will be employed to accelerate the convergence of the methods while maintaining the necessary level of solution accuracy. Opposition-based approaches to optimization generally incorporate the simultaneous consideration of the solution and the opposite solution (chromosome and anti-chromosome, path and opposite path). Recent achievements in the successful design and use of opposition-based differential evolution encourage us to seek some fundamental answers with respect to a mathematical formalism for these techniques and to exploit the potentials of oppositional schemes for all population-based algorithms. Standard benchmark functions and metrics will be used to verify the better performance of opposition-based extensions of methods under investigation. As a real-world test case, segmentation of medical images, specifically breast and prostate ultrasound images, will be undertaken as well. Population-based methods have been used to extract objects from digital images in different ways. Their results, as reported in literature, are in some cases impressive. However, processing images with these methods are extremely expensive. This has restricted their use in practical cases. Any level of speedup is desirable here. Image data sets along with radiologist's ground-truth are available for experimental performance verification.