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灾情巡视问题的蚁群两目标优化算法研究
引用本文:厍向阳.灾情巡视问题的蚁群两目标优化算法研究[J].数学的实践与认识,2010,40(20).
作者姓名:厍向阳
基金项目:陕西省自然科学基金,陕西省教育厅专项科研计划项目
摘    要:分析目前灾情巡视问题求解方法存在的缺陷,归纳出灾情巡视问题两目标优化模型.针对灾情巡视问题模型特点,引入蚁群算法和多目标优化理论,提出两个灾情巡视问题的蚁群两目标优化算法:算法1将灾情巡视问题的道路网络转化为完全图,增加m-1个(m为巡视组数)虚拟巡视起点,将灾情巡视两目标优化问题转化为单旅行商两目标优化问题,然后使用蚁群算法和多目标优化理论进行迭代求解.算法2使用一只蚂蚁寻找一个子回路,m个子回路构成一个灾情巡视可行方案,采用罚函数法和多目标优化理论构建增广两目标优化评价函数,使用g组,共g×m只蚂蚁共同协作来发现灾情巡视问题的最优解.算法特点:①算法1将灾情巡视两目标优化问题转化为单旅行商两目标优化问题,可以充分利用已有蚁群算法求解单旅行商问题的研究成果;②两个算法引入蚁群算法,提高了算法效率;③两个算法克服目前灾情巡视问题的求解方法不严密性缺陷;④两目标优化算法可以为用户提供多个满足约束条件的Pareto组合解,扩大了用户选择范围,增强了算法的适用性.算法测试表明:灾情巡视问题的蚁群两目标优化算法是完全可行和有效的.

关 键 词:灾情巡视问题  蚁群算法  多目标优化  Pareto解

The Two-Objective Optimization Algorithm about the Problem of Inspecting Disaster Situation Based on the Ant Colony Algorithm
SHE Xiang-yang.The Two-Objective Optimization Algorithm about the Problem of Inspecting Disaster Situation Based on the Ant Colony Algorithm[J].Mathematics in Practice and Theory,2010,40(20).
Authors:SHE Xiang-yang
Abstract:ItIt is analysied that the limitations of the now way solving the problem of inspecting disaster situation,the two-objective optimization model is generalized about the problem. Two algorithms are put forward,facing the characteristics of inspecting disaster situation,importing the ant colony algorithm and multi-objective optimization throry:The first algorithm solves the problem of inspecting disaster by iterative approach,being based on the ant colony algorithm and multi-objective optimization throry,after transfroming roadway network to complete graph(network),adding(m-1) dummy start node being visted,and transfroming the problem of inspecting disaster situation to multi-tsp problem with two optimization aims function.The second algorithm emploies one ant to search a sub-loop,m ants in cooperation to search m sub-loop which compose a feasible visting scheme,the generalized objective function are set up with penalty function and multi-objective optimization theory,making use of g groups,earch group being composed of m ants to together search the optimization visting scheme about the problem of inspecting disaster situation.Two algorithms advantages:①first algorithm,transfroming the problem of inspecting disaster situation to multi-tsp problem with two aims,sufficiently makes use of now researching production solving one-TSP problem based on the ant colony algorithm.②two algorithms improve their executing efficiency, importing the ant colony algorithm.③two algorithms get over the disadvantage of approximately solveing the problem of inspecting disaster situation at present.④the two-objective optimization algorithm about the problem of inspecting disaster situation can supply numerous Pareto combination solutions for users,which satisfy restriction conditions,enlarges the scope of users selection,improves applicability of the algorithm solving the inspecting disaster situation problem.Algorithms testing show:The two-objective optimization algorithms about the problem of inspecting disaster situation based on the ant colony algorithm are completely feasible and availability.
Keywords:problem of inspecting disaster situation  ant colony algorithm  multi-objective optimization  pareto solution
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