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Evolutionary multi-criterion optimization (EMO) algorithms emphasize non-dominated and less crowded solutions in a population iteratively until the population converges close to the Pareto optimal set. During the search process, non-dominated solutions are differentiated only by their local crowding or contribution to hypervolume or using a similar other metric. Thus, during evolution and even at the final iteration, the true convergence behavior of each non-dominated solutions from the Pareto optimal set is unknown. Recent studies have used Karush Kuhn Tucker (KKT) optimality conditions to develop a KKT Proximity Measure (KKTPM) for estimating proximity of a solution from Pareto optimal set for a multi-objective optimization problem. In this paper, we integrate KKTPM with a recently proposed EMO algorithm to enhance its convergence properties towards the true Pareto optimal front. Specifically, we use KKTPM to identify poorly converged non-dominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Assisted by the KKTPM, the modified algorithm is designed in a way that maintains the total number of function evaluations as low as possible while making use of local search where it is most needed. Simulations on both constrained and unconstrained multi- and many objectives optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms. 相似文献
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为提高发动机燃油经济性,首先通过部分负荷试验,验证了滚流比对燃油经济性的影响;再通过气道稳流试验,验证了所建立的三维稳态计算模型的准确性以及气道评价参数之间的关系.基于计算机液体动力学(CFD)分析影响气道流通特性的几何参数,采用最优拉丁超立方抽样和响应面法(RSM)拟合出发动机进气道的近似模型,应用第二代非劣排序遗传算法(NSGA-Ⅱ)对气道中心线倾斜角和喉口下压角进行优化,通过比较流量系数、滚流比等参数确定优化设计方案.研究结果表明:优化后的进气道模型能够在保证流量系数不变的情况下一定程度上提高滚流比,最终获得了提升气道滚流比的优化设计结果. 相似文献
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在进化多目标优化研究领域,多目标优化是指对含有2个及以上目标的多目标问题的同时优化,其在近些年来受到越来越多的关注。随着MOEA/D的提出,基于聚合的多目标进化算法得到越来越多的研究,对MOEA/D算法的改进已有较多成果,但是很少有成果研究MOEA/D中权重的产生方法。提出一种使用多目标进化算法产生任意多个均匀分布的权重向量的方法,将其应用到MOEA/D,MSOPS和NSGA-III中,对这3个经典的基于聚合的多目标进化算法进行系统的比较研究。通过该类算法在DTLZ测试集、多目标旅行商问题MOTSP上的优化结果来分别研究该类算法在连续性问题、组合优化问题上的优化能力,以及使用矩形测试问题使得多目标进化算法的优化结果在决策空间可视化。实验结果表明,没有一个算法能适用于所有特性的问题。然而,MOEA/D采用不同聚合函数的两个算法MOEA/D_Tchebycheff和MOEA/D_PBI在多数情况下的性能比MSOPS和NSGA-III更好。 相似文献
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Standard binary crossover operators (e.g., one-point, two-point, and uniform) tend to decrease the diversity of solutions
while they improve the convergence to the Pareto front. This is because standard binary crossover operators, which are called
geometric crossovers, always generate an offspring in the line segment between its parents under the Hamming distance in the
genotype space. In our former study, we have already proposed a nongeometric binary crossover operator to generate an offspring
outside the line segment between its parents. In this article, we examine the effect of our crossover operator on the performance
of evolutionary multiobjective optimization (EMO) algorithms through computational experiments on various multiobjective knapsack
problems. Experimental results show that our crossover operator improves the search ability of EMO algorithms for a wide range
of test problems.
This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January
31–February 2, 2008 相似文献
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Multiobjective Evolutionary Algorithms (MOEAs) are increasingly being used for effectively solving many real-world problems, and many empirical results are available. However, theoretical analysis is limited to a few simple toy functions. In this work, we select the well-known knapsack problem for the analysis. The multiobjective knapsack problem in its general form is NP-complete. Moreover, the size of the set of Pareto-optimal solutions can grow exponentially with the number of items in the knapsack. Thus, we formalize a (1+ε)-approximate set of the knapsack problem and attempt to present a rigorous running time analysis of a MOEA to obtain the formalized set. The algorithm used in the paper is based on a restricted mating pool with a separate archive to store the remaining population; we call the algorithm a Restricted Evolutionary Multiobjective Optimizer (REMO). We also analyze the running time of REMO on a special bi-objective linear function, known as LOTZ (Leading Ones : Trailing Zeros), whose Pareto set is shown to be a subset of the knapsack. An extension of the analysis to the Simple Evolutionary Multiobjective Optimizer (SEMO) is also presented. A strategy based on partitioning of the decision space into fitness layers is used for the analysis. 相似文献
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