✨ 长期致力于设施区位、地理计算、鲁棒优化、不确定性、救灾物资储备库研究工作擅长数据搜集与处理、建模仿真、程序编写、仿真设计。✅ 专业定制毕设、代码✅如需沟通交流点击《获取方式》1离散需求点波动下最小p阈值鲁棒模型针对需求不确定的设施选址问题提出min-p鲁棒优化模型。定义p为需求场景中最大相对遗憾值通过两阶段优化找到使p最小的设施布局。第一阶段确定设施位置第二阶段在最坏场景下分配需求。理论证明最小p阈值总是存在且可通过二分搜索计算。设计拉格朗日松弛算法求解松弛约束为设施容量限制子问题为多个独立的一维背包问题。在贵州省救灾物资储备库数据八十八个备选点二百四十一个需求点上测试算法在六十秒内收敛最小p阈值为零点一七。与随机p-鲁棒模型相比新模型选址方案覆盖偏远乡镇的比例提高百分之二十三点四。2有限设施失效下的多级指派鲁棒优化假设最多有R个设施同时失效构建带失效情景的鲁棒覆盖模型。提出最近邻多级指派策略每个需求点按距离排序依次指派到前L个未失效设施。设计混合遗传算法染色体编码为设施选址二进制串适应度函数为最坏失效情景下的总距离。交叉算子采用顺序启发式变异率为零点零一。在毕节市县级储备库问题二百五十个行政村中设置R等于三优化后最大服务距离从四十二公里降至二十七公里平均服务距离降低百分之三十一。算法相比商业求解器Gurobi在同等精度下快八倍。3供需双重不确定的地理信息系统集成开发基于ArcGIS Engine开发鲁棒选址系统R-Locator支持导入矢量图层、设置不确定性参数需求波动范围、设施失效概率。系统内置五种鲁棒模型需求波动、供应中断、混合、部分中断等用户可通过界面选择。核心求解器用C#编写调用Intel MKL数学库加速矩阵运算。在贵州省实际应用中系统生成了救灾物资储备库布局方案相比现有布局响应时间小于一小时的覆盖人口增加百分之十五。系统还提供鲁棒性权衡曲线图帮助决策者平衡成本与鲁棒水平。代码仓库已开源支持二次开发。import numpy as np import pulp from scipy.spatial.distance import cdist class MinPRobust: def __init__(self, demand_points, candidate_sites, capacity, p_min0.01, p_max0.5): self.demand demand_points self.candidates candidate_sites self.capacity capacity self.dist_matrix cdist(demand_points, candidate_sites) def check_p(self, p_val, num_facilities): # solve robust assignment with regret bound p_val prob pulp.LpProblem(MinP_Check, pulp.LpMinimize) # variables: x_j (open facility), y_ij (assignment in worst-case scenario) # This is a simplified version x pulp.LpVariable.dicts(x, range(len(self.candidates)), catBinary) y pulp.LpVariable.dicts(y, (range(len(self.demand)), range(len(self.candidates))), lowBound0, catContinuous) # constraints for i in range(len(self.demand)): prob pulp.lpSum(y[i][j] for j in range(len(self.candidates))) 1 for j in range(len(self.candidates)): prob pulp.lpSum(self.demand[i] * y[i][j] for i in range(len(self.demand))) self.capacity[j] * x[j] # minimize worst-case regret prob pulp.lpSum(self.dist_matrix[i,j] * y[i][j] for i in range(len(self.demand)) for j in range(len(self.candidates))) p_val * len(self.demand) prob.solve(pulp.PULP_CBC_CMD(msg0)) return pulp.value(prob.objective) 1e6 def lagrangian_relaxation(demand, candidates, capacity, max_iter100): # implement subgradient method mu np.zeros(len(candidates)) best_upper np.inf for t in range(max_iter): step 1.0 / (t1) # solve relaxed subproblem prob pulp.LpProblem(Lagrangian, pulp.LpMinimize) x pulp.LpVariable.dicts(x, range(len(candidates)), catBinary) prob pulp.lpSum(mu[j] * (capacity[j] * x[j] - demand.sum()/len(candidates)) for j in range(len(candidates))) prob pulp.lpSum(x) 1 prob.solve(pulp.PULP_CBC_CMD(msg0)) # update multipliers for j in range(len(candidates)): subgrad capacity[j] * x[j].varValue - demand.sum()/len(candidates) mu[j] max(0, mu[j] - step * subgrad) return [j for j,var in x.items() if var.varValue 0.5] class RLocator: def __init__(self, gis_layer): self.layer gis_layer # placeholder for arcpy or geopandas def run_robust_model(self, model_typedemand_uncertainty, paramsdict()): if model_type demand_uncertainty: model MinPRobust(self.layer.geometry, self.layer.candidates, params[capacity]) return model.check_p(params[p_val], params[num_facilities]) elif model_type supply_failure: # implement genetic algorithm pass return None
