Metaheuristics and Heuristics for Global Optimization Problems
全局优化问题的元启发式和启发式
基本信息
- 批准号:RGPIN-2015-05522
- 负责人:
- 金额:$ 1.31万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2018
- 资助国家:加拿大
- 起止时间:2018-01-01 至 2019-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The quadratic assignment problem (QAP) was introduced in 1957 as a mathematical model for the location of a set of indivisible economical activities. Consider the problem of allocating a set of facilities to a set of locations, with the cost being a function of the distance and flow between the facilities, plus costs associated with a facility being placed at a certain location. The objective is to assign each facility to a location such that the total cost is minimized. It was shown that the QAP is NP-hard (Non-deterministic Polynomial-time hard), and that even finding an approximate solution within some constant factor from the optimal solution cannot be done in polynomial time unless P=NP. In fact the QAP, in contrast with its linear counterpart the linear assignment problem, remains one of the hardest optimization problems and no exact algorithm can solve problems of size n > 20. QAP is an example of a global combinatorial optimization, important in operations research and theoretical computer science. Global optimization problems fall within the broader class of nonlinear optimization. ******Numerical algorithms for nonlinear optimization can be categorized into gradient-based methods and direct search methods. Gradient-based methods use gradients or Hessians while direct search methods do not use derivative information. In this project, we are interested in solving problems when the derivatives of the underlying data are unavailable, unreliable, or impractical to obtain. These algorithms are known as derivative-free algorithms. In this project, we consider metaheuristics and heuristics algorithms as derivative-free algorithms. Heuristic methods are approximate algorithms in which we seek to obtain good, that is, near-optimal solutions at relatively low computational cost without being able to guarantee the optimality of*solutions. A disadvantage of heuristic methods is that they: Either generate only a very limited number of different solutions, or stop at poor quality local optima, which is the ***case for iterative improvement methods. Metaheuristics have been proposed which try to bypass these problems. A metaheuristic can be seen as a general purpose heuristic method toward promising regions of the search space containing high-quality solutions. ******Our objective from this project is to analyze, modify, and suggest some of the most common metaheuristics approaches, and show how these can be used to solve wireless sensor networks, output feedback pole assignment problems, CP/VIs/MPEC, minimax and integer programming problems. Finally, I am interested in combining metaheuristics algorithms with deterministic algorithms for the above problems. Finally, the proposed research program will enhance and promote the integration leading-edge research into interdisciplinary operations research and computer science education for Thompson Rivers University's diverse student population. *****
二次指派问题(QAP)于1957年被引入,作为一组不可分割的经济活动选址的数学模型。考虑将一组设施分配给一组地点的问题,其中成本是设施之间的距离和流量的函数,加上与将设施放置在特定位置相关的成本。目标是将每个设施分配到一个位置,从而使总成本最小化。证明了QAP是NP-难的(非确定性多项式时间难),并且除非P=NP,否则即使从最优解中找出某一常数因子内的近似解也不可能在多项式时间内完成。事实上,与其线性对应的线性分配问题相比,QAP仍然是最困难的优化问题之一,没有确切的算法可以解决n>;20的问题。QAP是全局组合优化的一个例子,在运筹学和理论计算机科学中很重要。全局优化问题属于更广泛的非线性优化类别。*非线性优化的数值算法可分为基于梯度的方法和直接搜索方法。基于梯度的方法使用梯度或海森,而直接搜索方法不使用导数信息。在这个项目中,我们感兴趣的是解决当基础数据的导数不可用、不可靠或不切实际时的问题。这些算法被称为无导数算法。在这个项目中,我们将元启发式算法和启发式算法视为无导数算法。启发式方法是一种近似算法,在这种算法中,我们寻求以相对较低的计算成本获得良好的、接近最优解的方法,而不能保证解的最优性。启发式方法的一个缺点是:它们要么只生成数量非常有限的不同解,要么止步于质量较差的局部最优,这就是迭代改进方法的*情况。已经提出了元启发式算法,试图绕过这些问题。元启发式可以被视为一种通用型启发式方法,用于搜索空间中包含高质量解的有希望的区域。*我们的目标是分析、修改和建议一些最常见的元启发式方法,并展示如何使用这些方法来解决无线传感器网络、输出反馈极点配置问题、CP/VIS/MPEC、极小极大和整数规划问题。最后,我感兴趣的是将元启发式算法与确定性算法相结合来解决上述问题。最后,拟议的研究计划将加强和促进前沿研究与跨学科运筹学和计算机科学教育的整合,面向汤普森·里弗斯大学的不同学生群体。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Tawhid, Mohamed其他文献
Tawhid, Mohamed的其他文献
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{{ truncateString('Tawhid, Mohamed', 18)}}的其他基金
Metaheuristics and Heuristics for Combinatorial and Discrete Optimization Problems
组合和离散优化问题的元启发式和启发式
- 批准号:
DDG-2021-00019 - 财政年份:2022
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Development Grant
Metaheuristics and Heuristics for Combinatorial and Discrete Optimization Problems
组合和离散优化问题的元启发式和启发式
- 批准号:
DDG-2021-00019 - 财政年份:2021
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Development Grant
Metaheuristics and Heuristics for Global Optimization Problems
全局优化问题的元启发式和启发式
- 批准号:
RGPIN-2015-05522 - 财政年份:2019
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Metaheuristics and Heuristics for Global Optimization Problems
全局优化问题的元启发式和启发式
- 批准号:
RGPIN-2015-05522 - 财政年份:2017
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Metaheuristics and Heuristics for Global Optimization Problems
全局优化问题的元启发式和启发式
- 批准号:
RGPIN-2015-05522 - 财政年份:2016
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Metaheuristics and Heuristics for Global Optimization Problems
全局优化问题的元启发式和启发式
- 批准号:
RGPIN-2015-05522 - 财政年份:2015
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Stochastic mathematical programs with equilibrium constraints
具有平衡约束的随机数学程序
- 批准号:
311631-2009 - 财政年份:2014
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Portfolio management investment system
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446501-2013 - 财政年份:2013
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Engage Grants Program
Stochastic mathematical programs with equilibrium constraints
具有平衡约束的随机数学程序
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$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
Stochastic mathematical programs with equilibrium constraints
具有平衡约束的随机数学程序
- 批准号:
311631-2009 - 财政年份:2011
- 资助金额:
$ 1.31万 - 项目类别:
Discovery Grants Program - Individual
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