将优化问题抽象成目标函数后,目标函数和启发式优化算法的匹配程度决定了优化求解的效率.为反映目标函数的优化特征并指导优化算法及其参数的选择,本文模拟绝热量子计算中的多基态演化,提出了一种适应度地形探索算法.根据基态波函数倾向于向势能较小处收敛且收敛程度受量子效应强度影响的特性,用目标函数编码势能场后算法引入了一个量子效应递减的多基态演化过程,用其持续收敛的基态波函数簇反映目标函数的适应度地形.根据量子路径积分,算法由尺度递减的扩散蒙特卡罗(diffusion Monte Carlo,DMC)实现.实验表明算法综合直观地反映了适应度地形的众多特征,所得信息能直接指导后续优化,其计算模式和启发式优化相似,无需引入其他计算,这为适应度地形研究引入了新的视角.
A Fitness Landscape Exploration Algorithm Simulating Adiabatic Quantum Computation
After transforming an optimization problem into an objective function,the degree of matching between the objective function and the chosen heuristic optimization algorithm determines the efficiency of the following optimization.By simulating multi-ground states evolution in adiabatic quantum computation,a fitness landscape exploration algorithm is proposed to reflect the optimization characteristics of the objective function and guide the selection of optimization algo-rithms and their parameters.In quantum ground state evolution,the ground state wave function of a particle tends to con-verge towards regions with lower potential energy,and the extent of convergence is influenced by the quantum effect strength.Using these features,we encode the potential energy field by the objective function in a multi-ground states evolu-tion with diminishing quantum effect,and consequently the fitness landscape of the objective function is reflected by the dis-tributions of a set of converging ground state wave function in this adiabatic evolution.Based on the quantum path integral,the algorithm is implemented using a downscaling diffusion Monte Carlo(DMC).Experiments illustrated that the algorithm comprehensively and intuitively reflected numerous features of the fitness landscape,and the obtained information could di-rectly guide optimization thereafter.Its computational mode resembles that of heuristic optimization,as it does not introduce other computations during optimization.These features introduce a novel perspective to the study of fitness landscape.
fitness landscapeheuristic optimizationadiabatic quantum computationground state evolutiondiffu-sion Monte Carloquantum annealing
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