### 带有约束条件的遗传算法 Python 实现 遗传算法是一种基于自然选择和遗传学机制的全局搜索概率算法，适用于解决复杂的组合优化问题。当涉及到带有约束条件的情况时，在设计适应度函数以及执行遗传操作的过程中需要特别考虑这些约束。 #### 设计适应度函数 为了处理约束条件，通常会在计算个体适应度的时候加入惩罚项来反映违反约束的程度。如果某个解不满足给定的约束，则其对应的适应度会被降低甚至置零，从而减少该不良解被选中的可能性[^1]。 ```python def fitness_function(individual, constraints): """评估单个染色体（即候选解）的适应度""" # 计算目标函数值 objective_value = calculate_objective(individual) penalty = 0 # 对于每一个约束条件进行判断并累加罚分 for constraint in constraints: if not eval(constraint): penalty += abs(eval(f"{constraint} - penalty ``` #### 初始化种群与定义边界范围 初始化阶段要确保所有的初始解都位于可行域内，并且对于连续变量还需要指定合理的上下限作为取样区间[^2]。 ```python import numpy as np bounds = [(lower_bound_i, upper_bound_i) for i in range(dimension)] population_size = 100 initial_population = [ tuple(np.random.uniform(low=bound[0], high=bound[1]) for bound in bounds) for _ in range(population_size)] ``` #### 遗传操作：选择、交叉、变异 在实施上述三种基本遗传操作之前，应该先筛选掉那些明显不符合约束条件的个体；而在生成新后代之后也要再次验证它们是否仍然保持有效。此外，还可以采用特殊的策略比如修复法或局部调整等方式使得不可行解变得合法化。 ```python from random import randint, uniform def crossover(parents, cross_rate): offspring = [] while len(offspring)<len(parents)-1 : parent_1,parent_2 = parents[randint(0,len(parents)-1)],parents[randint(0,len(parents)-1)] child = list(parent_1[:]) if uniform(0, 1) < cross_rate and check_constraints(child): pos = randint(0, dimension-1) child[pos:] = parent_2[pos:] offspring.append(tuple(child)) return offspring def mutate(individual, mutation_rate,bounds): mutated_individual=list(individual) for idx,val in enumerate(mutated_individual): if uniform(0, 1) < mutation_rate: lower,upper=bounds[idx] mutated_individual[idx]=uniform(lower,upper) return tuple(check_constraints(mutated_individual)) def select_parents(population,fitnesses,k=3): selected_indices=np.argpartition(-np.array(fitnesses),k)[:k] return [population[i]for i in selected_indices] def evolve(population,constraints,cross_rate=.8,mutation_rate=.1): next_generation=[] population_with_fitness=[*zip([fitness_function(i,constraints)for i in population],population)] sorted_pop=sorted(population_with_fitness,key=lambda x:x[0],reverse=True)[:(len(population)//2)+1] best_half=[i[-1]for i in sorted_pop] children=crossover(best_half,cross_rate) mutants=[mutate(c,mutation_rate,bounds)for c in children] next_generation.extend(best_half) next_generation.extend(children) next_generation.extend(mutants) return next_generation[:len(population)] ```