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中文摘要：
提出一种基于实数编码处理约束优化问题的线性算法，并对其复杂度和收敛性进行分析．该算法将约束优化问题的高维搜索空间通过线性变换映射到二维空间，在二维空间中探索原优化问题的解，从数学分析的角度给出一种线性适应度函数．算法中融人一种基于密度函数的交叉算子和变异算法，采用基于分级聚类的平均联接方式以维持Pareto最优解集个体数目．3组典型优化问题的测试表明，该算法是可行和有效的，解集分布的均匀性与多样性均较理想．
英文摘要：
A linear evolutionary algorithm for solving constrained optimization problems （LEACOP） based on real-coded method is proposed, and its complexity and convergence are also analyzed. One of the main advantages of the proposed algorithm is that the search space of constrained dominance problems with high dimensions is compressed into two dimensions. A linear fitness function based on mathematic analysis is deduced in two dimension space to fast evaluate fitness value of each individual in population. A crossover operator based on density function and a new mutation operator are developed to extend the search space and extract better solution. In addition, an average linkage based on hierarchical clustering method is introduced into the LEACOP to maintain the number of individuals on Pareto set. A few benchmark multi-objective optimization problem which is di this algorithm. The numerical experiments show that proposed provides good performance in terms of uniformity and diversity ed into three groups is introduced to test algorithm is feasible and effective, and it of solutions.
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