Abstract: For solving the optimization problems with large scale constraints，an adaptive penalty strategy handling with constraints，which converts the optimization problem with both equality constraints and inequality constraints to one only with upper and low constraints of decision variables，is presented.The ideas of feasible measure and feasible degree for the constraints are introduced to describe the degree to which the decision variables meet the constraints，and according to which the adaptive penalty function is constructed.For examining the validity of the penalty strategy，the traffic signal timings optimization problem of a single intersection is computed by three kinds of algorithm and the results of large amounts of simulation show that the adaptive penalty strategy designed in this paper can effectively handle with the constraints of the traffic signal timings optimization problem with large scale constraints.

Key words: penalty strategy, genetic algorithm, hybrid optimization

摘要： 针对约束优化问题的求解，设计了一种处理约束条件的自适应惩罚策略，用于将具有不等式约束和等式约束的优化问题转变为仅包含决策变量上、下限约束的优化问题。该策略通过引入约束可行测度、可行度的概念来描述决策变量服从于不等式约束和等式约束的程度，并以此构造处理约束条件的自适应惩罚函数，惩罚值随着约束可行度的变化而动态自适应地改变。为了检验该惩罚策略的有效性，针对单路口交通信号优化问题进行了应用研究，并用三种不同算法进行了大量的仿真计算，结果表明所设计的自适应策略在具有高度约束条件的城市交通信号优化问题中具有良好的效果。

关键词: 惩罚策略, 遗传算法, 混合优化