摘要
布局问题属于具有很强应用背景的组合优化问题 ,除其内在的 NP完全的计算复杂性 ,布局还包括约束复杂性问题和布局物体与空间的形状复杂性问题 .针对布局求解中存在的问题 ,该文进行了基于全局优化的布局求解方法研究 .布局问题中有一类关于复杂分片光滑连续函数全局优化求解的问题 .传统的优化算法对此无能为力 ,遗传算法是一种有前途的全局优化算法 ,但目前的各种遗传算法的效率和精度不能令人满意 .文中从生物可以从环境中学习生存技巧、自主的趋利避害的思路出发 ,增加了学习算子 ,引用函数的局部信息 ,构造拟牛顿方向 ,令每个个体在当前状态下有目的地搜索 ,最有效的向局部最优点趋进 .通过典型测试函数与传统遗传算法 ,模拟退火算法 ,复合形法进行比较验算 ,表明该算法具有优良的求解质量和较好的求解效率 ;并以旋转卫星舱布局的简化模型为背景 ,建立多目标优化数学模型 ,与传统遗传算法和乘子法的计算结果比较 ,该算法求解的质量和效率更优 .该文研究表明 ,基于学习的遗传算法在布局优化中具有应用潜力 ;启发式随机搜索策略和局部优化算法相结合的求解方案是解决复杂函数优化的有效途径 .
Packing problems are categorized as combinatorial optimization problems with strong application background. Except for their intrinsic NP-hard computational complexities, packing problems also involve many constraints and the shape complexity of packing objects and packing space. This paper is concerned with the research on global optimization algorithms based solution for packing problems.One category of packing problems involves global optimization with complex functions of piece by piece smooth continuation. The traditional optimization methods hardly deal with such problems effectively due to the nature of ill-conditioned functions. Recently, genetic algorithms have shown some promising for global optimization, but their efficiency to locate a precise result has not been quite satisfied. This paper, borrowing some idea from natural creatures with capability to learn skills of survival (avoiding dangers and achieving better states) from the environment, has proposed and developed an algorithm, named Learning-based Genetic Algorithm (LGA), to overcome the difficulties the other GA faced. The LGA has made use of the local analytic information of the functions through a Learning Operator to form the Quazi-Newton directions, then let every individual to be able to search for a local optimum efficiently. By comparison with traditional GA, Simulated Annealing Algorithm and Complex Method on typical testing problems, the LGA has shown very good global results in terms of high precision and efficiency. A multi-object optimization model is formulated on simplified satellite cabin packing problem. By comparison on an case of such packing problem constructed with known optimal solution, and another produced with random data and unknown optimal solution, LGA is superior to the Multiplier Algorithm and an Improved GA in term of solution quality and efficiency. In conclusion, the proposed LGA has shown some potential to deal with packing problems with good expectation. Combining a heuristic random searching strategy with local optimal algorithms is effective solution for complex optimization problem.
出处
《计算机学报》
EI
CSCD
北大核心
2001年第12期1242-1249,共8页
Chinese Journal of Computers
基金
国家自然科学基金 ( 6 99740 0 2 )资助
