代码 | 自适应大邻域搜索系列之(3) - Destroy和Repair方法代码实现解析

本文详细解析ALNS算法中Destroy和Repair方法的具体实现,包括AOperator、ADestroyOperator、ARepairOperator三个类的介绍,以及OperatorManager如何管理这些方法的权重和选择策略。通过OperatorManager的recomputeWeight、selectOperator和updateScores方法,阐述了如何动态调整权重、选择操作及更新成绩。

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前言

上一篇文章中我们具体解剖了ALNS类的具体代码实现过程,不过也留下了很多大坑。接下来的文章基本都是“填坑”了,把各个模块一一展现解析给大家。不过碍于文章篇幅等原因呢,也不会每一行代码都进行讲解,那些简单的代码就跳过了,相信大家也能一眼就看懂。好了,废话不多说,开始干活吧。

01 照旧总体概述

前面我们提到,ALNS中的重中之重就是Destroy和Repair方法了,在整一个ALNS框架中呢,涉及这俩货的有Destroy和Repair方法的具体实现、Destroy和Repair方法管理(包括各个Destroy和Repair方法权重分配、成绩打分、按权重选择哪个Destroy和Repair方法等操作)。所以在这次的ALNS代码中呢,这俩货的代码实现呢也分为两个模块:

  • Destroy和Repair方法具体实现模块
  • Destroy和Repair方法管理模块

下面我们将对其进行一一讲解,不知道大家小板凳准备好了没有。

02 Destroy和Repair方法具体实现

关于Destroy和Repair方法,由三个类组成,分别是AOperator、ADestroyOperator、ARepairOperator。它们之间的继承派生关系如下:

下面对其一一讲解。

2.1 AOperator

这是一个基础父类,它抽象了Destroy和Repair方法共有的一些方法和特征(成绩、权重、名称等等),然后Destroy和Repair方法再各自继承于它,实现自己的功能模块。成员变量已经注释清楚了,关于protected的一个成员noise噪声模式会在后面讲到。其他的方法也很简单就不做多解释了。

class AOperator
{
private:
	//! Total number of calls during the process.
	size_t totalNumberOfCalls;

	//! Number of calls since the last evaluation.
	size_t nbCallsSinceLastEval;

	//! score of the operator.
	double score;

	//! weight of the operator.
	double weight;

	//! designation of the operator.
	std::string operatorName;

protected:
	//! Indicate if the operator is used in noise mode or not.
	bool noise;
public:

	//! Constructor.
	AOperator(std::string name){
		operatorName = name;
		init();
	}

	//! Destructor.
	virtual ~AOperator(){};

	//! Initialize the values of the numbers of calls.
	void init()
	{
		totalNumberOfCalls = 0;
		nbCallsSinceLastEval = 0;
		score = 0;
		weight = 1;
	}

	//! reset the number of calls since last eval.
	void resetNumberOfCalls()
	{
		nbCallsSinceLastEval = 0;
	}

	//! Simple getter.
	//! \return the total number of calls to the operator since
	//! the beginning of the optimization process.
	size_t getTotalNumberOfCalls(){return totalNumberOfCalls;};

	//! Simple getter.
	//! \return the number of calls to this operator since the last
	//! evaluation.
	size_t getNumberOfCallsSinceLastEvaluation(){return nbCallsSinceLastEval;};

	void increaseNumberOfCalls()
	{
		totalNumberOfCalls++;
		nbCallsSinceLastEval++;
	}

	//! Simple getter.
	double getScore() const
    {
        return score;
    }

	//! Simple getter.
    double getWeight() const
    {
        return weight;
    }

    //! resetter.
    void resetScore()
    {
        this->score = 0;
    }

    //! Simple setter.
	void setScore(double s)
	{
		this->score = s;
	}

   
### 自适应大邻域搜索 (ALNS) 解决车辆路径问题 (VRP) 自适应大邻域搜索 (Adaptive Large Neighborhood Search, ALNS) 是一种高效的元启发式算法,广泛应用于解决复杂的组合优化问题,特别是车辆路径问题 (Vehicle Routing Problem, VRP)[^1]。以下是基于 Python 的 ALNS 实现来解决 VRP 问题的核心逻辑。 #### 1. ALNS 算法概述 ALNS 结合了破坏操作 (Destroy Operator) 修复操作 (Repair Operator),通过动态调整这些操作的选择概率强度,在解空间中探索更优的解决方案[^2]。具体来说: - **破坏操作**:移除部分客户节点以创建不完整的解。 - **修复操作**:重新插入被移除的客户节点以恢复完整解。 #### 2. Python 实现核心结构 以下是一个简化版的 ALNS 框架用于求解 VRP 问题: ```python import random from copy import deepcopy class ALNS_VRP: def __init__(self, customers, distances, capacity): self.customers = customers # 客户列表 self.distances = distances # 距离矩阵 self.capacity = capacity # 车辆容量 # 初始化操作集 self.destroy_operators = [self.random_removal] self.repair_operators = [self.greedy_insertion] def random_removal(self, solution, removal_rate=0.2): """随机删除一定比例的客户""" removed_customers = [] remaining_solution = [] for route in solution: to_remove = int(len(route) * removal_rate) indices_to_remove = random.sample(range(len(route)), to_remove) new_route = [customer for i, customer in enumerate(route) if i not in indices_to_remove] removed_customers.extend([route[i] for i in indices_to_remove]) remaining_solution.append(new_route) return remaining_solution, removed_customers def greedy_insertion(self, partial_solution, unassigned_customers): """贪婪地将未分配客户插入现有路线""" complete_solution = deepcopy(partial_solution) while unassigned_customers: best_customer = None best_position = None min_cost_increase = float(&#39;inf&#39;) for customer in unassigned_customers: for r_idx, route in enumerate(complete_solution): for pos in range(len(route) + 1): # 插入位置 cost_increase = self.calculate_cost_increase(customer, route, pos) if cost_increase < min_cost_increase and self.is_feasible(route + [customer], self.capacity): min_cost_increase = cost_increase best_customer = customer best_position = (r_idx, pos) if best_customer is not None: r_idx, pos = best_position complete_solution[r_idx].insert(pos, best_customer) unassigned_customers.remove(best_customer) else: break # 如果无法找到可行的位置,则停止 return complete_solution def calculate_cost_increase(self, customer, route, position): """计算插入客户的成本增加量""" prev_node = 0 if position == 0 else route[position - 1] next_node = 0 if position >= len(route) else route[position] cost_increase = ( self.distances[prev_node][customer] + self.distances[customer][next_node] - self.distances[prev_node][next_node] ) return cost_increase def is_feasible(self, route, capacity): """检查路线是否满足容量约束""" total_demand = sum(self.customers[c][&#39;demand&#39;] for c in route) return total_demand <= capacity def solve_vrp(self, initial_solution, max_iterations=100): current_solution = initial_solution best_solution = deepcopy(current_solution) best_cost = self.evaluate_solution(current_solution) for _ in range(max_iterations): destroy_operator = random.choice(self.destroy_operators) repair_operator = random.choice(self.repair_operators) destroyed_solution, removed_customers = destroy_operator(current_solution) repaired_solution = repair_operator(destroyed_solution, removed_customers) current_cost = self.evaluate_solution(repaired_solution) if current_cost < best_cost: best_solution = deepcopy(repaired_solution) best_cost = current_cost current_solution = repaired_solution return best_solution def evaluate_solution(self, solution): """评估当前解的成本""" total_cost = 0 for route in solution: route_cost = 0 previous_node = 0 for node in route: route_cost += self.distances[previous_node][node] previous_node = node route_cost += self.distances[previous_node][0] # 返回起点 total_cost += route_cost return total_cost ``` #### 3. 使用说明 上述代码提供了一个基础框架,可以扩展更多功能,例如引入自适应机制调节不同操作的概率[^3]。主要步骤如下: - 输入距离矩阵 `distances` 客户需求字典 `customers`。 - 提供初始解 `initial_solution`(可以通过其他简单启发式方法生成)。 - 运行 `solve_vrp()` 方法获取最终最优解。 #### 4. 扩展方向 为了进一步提升性能,可考虑以下改进措施: - 添加更多的破坏修复算子。 - 引入强化学习或机器学习模型预测最佳操作序列。 - 利用并行化技术加速迭代过程[^2]。 --- ###
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