CN114970103A - Instant delivery path optimization method considering dispenser experience and random travel time - Google Patents

Abstract

The invention discloses a real-time delivery route optimization method considering delivery staff experience and random travel time. S11, problem description; S12, problem assumption; S13, parameter and variable representation; S14, function representation of delivery staff experience; S15, single Stage mathematical model establishment; S16, multi-stage mathematical model establishment; S21, simulation heuristic method framework design; S22, Monte Carlo simulation design; S23, improved adaptive large neighborhood search algorithm design. The method of the invention solves the real-time distribution route problem by combining the simulation method and the heuristic algorithm.

Description

A real-time delivery route optimization method considering delivery staff experience and random travel time

technical field

The invention belongs to the technical field of logistics distribution path optimization, and relates to a real-time distribution path optimization method that considers the experience of the distribution staff and random travel time.

Background technique

In recent years, with the rising tide of online shopping, instant delivery has gradually become an important part of urban logistics. In real-time distribution logistics activities, enterprises receive real-time distribution needs from customers and complete distribution services to customers in real time. Its application areas include takeaway, fresh food, medicine, and supermarkets. As a new type of logistics distribution mode, instant distribution has the characteristics of multiple frequencies, small batches, and limited vehicle resources. In addition, customers often need to get delivery services within an hour or two after placing an order, which makes instant delivery highly time-sensitive. Therefore, when making an instant delivery plan, enterprises not only need to reduce logistics costs as much as possible to obtain higher economic benefits, but also need to ensure the on-time delivery rate of goods to improve customer satisfaction.

In the actual logistics and distribution process, the travel time of vehicles is affected by many factors. On the one hand, external environments such as traffic jams and bad weather lead to randomness of travel time. If the randomness of travel time is ignored, companies may develop inefficient logistics and distribution schemes. On the other hand, when repeatedly providing delivery services to customers in a certain area, the delivery staff will learn the road conditions in the delivery area, and the resulting experience can further shorten the travel time. For example, when the delivery staff knows the shortcuts in the delivery area, the interval of traffic lights, the traffic flow on the road and other traffic information, the delivery time will be significantly shortened. According to estimates by relevant experts, the driving time can be shortened by up to 40% under the influence of the experience of the delivery staff. Therefore, how to make a more accurate assessment and plan a better distribution path in combination with the actual logistics distribution activities is a major problem faced by enterprises in providing instant distribution services.

SUMMARY OF THE INVENTION

Aiming at the deficiencies of the prior art, the present invention solves the real-time distribution path problem by combining the simulation method and the heuristic algorithm, and the proposed method is called the simulation heuristic method, and specifically proposes a real-time distribution that considers the experience of the delivery staff and the random travel time. Path optimization method. Include the following steps:

Include the following steps:

S10, establishing an instant distribution route optimization model;

S20, the solution method of the design model;

Wherein, S20 specifically includes the following steps:

S21, simulation heuristic method framework design;

S22, Monte Carlo simulation design;

S23, improving the design of an adaptive large neighborhood search algorithm.

Preferably, the S10, establishing an instant distribution path optimization model, specifically includes the following steps:

S11, problem description;

S12, problem hypothesis;

S13, parameter and variable representation;

S14, the function representation of the experience of the delivery staff;

S15, single-stage mathematical model establishment;

S16, establishing a multi-stage mathematical model.

Preferably, the S12, the problem assumption, includes the setting for the vehicle, the setting for the customer and the setting for the enterprise.

Preferably, in S14, the function of the experience of the delivery staff is expressed as:

Among them, T ₀ is the travel time of the vehicle when the delivery person has no experience at all, x _i and x _j represent the number of visits, and l is the learning factor, representing the growth rate of experience; when the vehicle travels between nodes i and j, if Both i and j represent customer points, and the travel time depends on the average experience of the delivery staff on the two customers; if a node in i or j is a distribution center, the travel time only depends on the experience value of the delivery staff on the customers among them; Under the influence of the experience of the delivery staff, the longest travel time can be shortened as αT ₀ , where α represents the longest shortening ratio of the travel time; from this function expression, it can be seen that the travel time of the vehicle is actually affected by the number of customer visits.

Preferably, in S16, the establishment of a multi-stage mathematical model includes establishing a multi-stage stochastic vehicle path optimization model, the objectives of which are:

表示第r阶段车辆k是否被使用，若是，则

否则

V_c ^r为第r阶段的顾客集合；K为企业拥有的车辆集合,K＝{1,2,…,m}，共m辆；V^r为阶段r决策时的节点集合，V^r＝{0}∪V_c ^r；E(·)表示随机变量的期望值；

为阶段r派出的车辆从节点i到节点j的行驶时间；

为在阶段r的决策中若车辆k从节点i行驶到节点j，则为1，否则为0；c₁为每单位行驶时间成本；c₂为每单位延迟配送时间修正成本；c₃为每单位超出最长在途时间的时间修正成本；DT_i为顾客i的订单延迟送达时间；ZT_k为车辆k超出最长在途时间的时间。where f is the fixed cost of vehicle startup;

Indicates whether the vehicle k is used in the rth stage, if so, then

otherwise

_Vc ^r is the set of customers in the rth stage; K is the set of vehicles owned by the enterprise, K={1,2,...,m}, a total of m vehicles; V ^r is the set of nodes in the decision-making stage r, V ^r ={ 0} _∪V cr ^; E(·) represents the expected value of the random variable;

travel time of the vehicle dispatched for phase r from node i to node j;

In the decision of stage r, if vehicle k travels from node i to node j, it is 1, otherwise it is 0; c ₁ is the cost per unit of travel time; c ₂ is the correction cost per unit of delayed delivery time; c ₃ is the cost per unit of delayed delivery time. Unit time correction cost exceeding the maximum transit time; DT _i is the delayed delivery time of customer i's order; ZT _k is the time when vehicle k exceeds the maximum transit time.

Preferably, the S22, Monte Carlo simulation design, includes the following steps:

S221, randomly generate the specific value of each random variable according to the probability distribution;

S222, calculate the objective function value of the solution;

S223 , repeating S221 and S222 N _sim times to calculate the expected target value of the solution, where N _sim is the number of simulations.

Preferably, the S23, improving the design of an adaptive large neighborhood search algorithm, includes the following steps:

S231, the coding design of the solution;

S232, initialize the design;

S233, destroy the operator design;

S234, repair the operator design;

S235, local search design;

S236, design of the abandonment criterion of the solution;

S237, the operator selection mechanism design.

Preferably, the S232, initializing the design, includes the following steps:

S2321, generate an empty path sequence that only includes the starting point and the ending point of the vehicle;

S2322, randomly select a customer i, and determine whether the total demand on the route after customer i is inserted exceeds the vehicle capacity. If it exceeds, go to S2321, otherwise go to S2323;

S2323, determine the latest service time of two consecutive customers j, j+1 and customer i on the route, if LTj<LT _i <LT _j+1 , insert customer i into customer j and customer j Between +1, LT _i is the latest delivery time promised by customer i's order;

S2324, determine whether all customers are inserted into the path, if so, go to S2325, otherwise go to S2322;

S2325, merge all sequences into the same sequence, and remove one of two adjacent 0 values in the sequence;

S2326, determine whether the number of paths in the sequence reaches the number of vehicles, if so, stop, otherwise add a 0 value in the sequence until the number of paths and the number of vehicles are equal.

Preferably, the S233, destroying the operator design, includes the following steps:

S2331, random removal: randomly select N _remove customer points from the current solution to remove;

S2332, path removal: randomly select a sub-path in the solution, and remove all customer points in the sub-path;

S2333, worst removal: define the cost of customer point i in the current solution as cost(s,i)=Z(s)-Z- _i (s), where Z(s) is the target value of the current solution, and Z _-i (s) is the target value after removing customer point i. The worst removal operator first calculates the target value of the current solution, and then calculates the target value after each customer point is removed, so as to obtain each customer The cost of the point, and finally select the customer point with the highest cost from the current solution to remove, and repeat this step until N _remove customer points are removed;

S2334, the worst distance removal: define the distance cost of customer point i in the current solution as the sum of the distance from customer i to its previous customer point and the distance to its next customer point, namely cost(s,i)= d _i-1,i +d _i,i+1 , each time the customer points with the largest distance cost are selected and removed until N _remove customer points are removed;

S2335, worst time removal: define the time cost of customer point i in the current solution as the difference between the latest delivery time and the arrival time, that is, timecost(s,i)=|LT _i -s _i |, each time Select the customer point with the largest time cost to remove until N _remove customer points are removed;

S2336, similarity removal: define the similarity between two customer points as R _ij =φ ₁ d _ij +φ ₂ |LT _i -LT _j |+φ ₃ r _ij +φ ₄ |q _i -q _j |, where d _ij is the distance between two customers, LT _i is the latest delivery time, qi is the customer demand, and r _ij represents whether customer _i and customer j are in the same sub-path, if so, r _ij =1, otherwise r _ij =-1. φ ₁ -φ ₄ are their respective weights; the similar removal operator randomly selects a customer point to remove from the current solution, and stores the removed customer point in the sequence C _remove ; calculates the relationship between each customer point in the solution and The similarity of the last customer point in the sequence C _remove and select the customer point with the largest similarity to remove and store it in the sequence C _remove , repeat this step until N _remove customer points are removed;

S2337, adjacent similarity removal: this operator is a special case of the similarity removal operator, where φ ₁ =φ ₂ =φ ₃ =0, φ ₄ =1, this operator removes customer points with similar distances.

Preferably, the S234, repairing the operator design, includes the following steps:

S2341, greedy insertion: randomly select a customer from the sequence C _remove , calculate the target increase value caused by inserting the customer into each position in the solution S _remove , select the position with the smallest increase value to insert the customer into the solution, and repeat this step Until all customer points in C _remove are inserted into the solution.

其中

为顾客i插入后引起的最小目标增加值，

表示顾客i插入后引起的第二小目标增加值。选择后悔值最大的顾客并将该顾客插入到增加值最小的位置上，重复这一步骤直到C_remove中所有顾客点全部插入解中。S2342, regret value insertion: Calculate the target increase value caused by each customer inserting each position in the solution, and define the regret value as

in

the minimum target increment after insertion for customer i,

Represents the second smallest target increase after insertion by customer i. Select the customer with the largest regret value and insert the customer into the position with the smallest increase value. Repeat this step until all customer points in C _remove are inserted into the solution.

S2343, distance greedy insertion: randomly select a customer from the sequence C _remove , calculate the distance increment caused by inserting the customer into each position in the solution S _remove , the formula is d _i =d _hi +d _ij -d _hj . Select the position with the smallest distance increment to insert the customer, and repeat this step until all customer points in C _remove are inserted into the solution.

S2344, Cost greedy insertion with noise disturbance: The greedy insertion operator selects the optimal position when selecting the insertion position of each customer. This lack of randomness easily makes the algorithm fall into a local optimum. The cost greedy insertion with noise perturbation is based on the greedy insertion operator, adding noise to perturb the target increase value. The calculation formula of the target increase value after noise perturbation is: insertcost _-i =insertcost _i +u*r*insertcost _max , where insertcost _i is the target increase value before noise disturbance, insertcost _max is the maximum target increase value inserted in all positions, u is the noise parameter, and r is a random number in [-1,1].

S2345, distance greedy insertion with noise perturbation: This operator is an extended form of the distance greedy insertion operator. It also adds noise perturbation when calculating the distance increment. The calculation formula is similar to the cost greedy insertion with noise perturbation.

The beneficial effects of the present invention are as follows:

Compared with the prior art, the present invention innovatively considers the change in the expected value of the random travel time caused by the experience of the dispatcher, and defines a travel time function based on the experience of the dispatcher to measure this important change for the instant distribution route problem. , a single-stage and multi-stage distribution route optimization model is constructed with the goal of minimizing the total distribution cost. In addition, the present invention focuses on improving the adaptive large-neighborhood search algorithm, and designs a simulation heuristic solving framework combined with Monte Carlo simulation.

For enterprises, the present invention is conducive to rationally planning vehicle paths and reducing logistics distribution costs; it is beneficial to improve logistics distribution efficiency and maintain the competitiveness of enterprises in the market; for delivery staff, the present invention is beneficial to delivery staff to accumulate delivery experience , improve the distribution capacity; it is beneficial to improve the balance of the workload of the distribution staff and ensure the fairness of the income. For customers, the present invention is beneficial for customers to obtain better logistics service experience and improve customer satisfaction.

Description of drawings

1 is a schematic diagram of a framework of an instant delivery route optimization method considering delivery staff experience and random travel time according to an embodiment of the present invention;

2 is a schematic diagram of a coding scheme of a solution of an instant delivery route optimization method considering delivery staff experience and random travel time according to an embodiment of the present invention;

3 is a schematic diagram of a cross-exchange operator of an instant delivery route optimization method considering delivery staff experience and random travel time according to an embodiment of the present invention;

4 is a comparison diagram of the convergence speed of an instant delivery route optimization method considering delivery staff experience and random travel time according to an embodiment of the present invention;

5 is a comparison diagram of experimental results of an instant delivery route optimization method considering delivery staff experience and random travel time according to an embodiment of the present invention;

FIG. 6 is a comparison diagram of vehicle travel paths of an instant delivery path optimization method considering delivery staff experience and random travel time according to an embodiment of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

On the contrary, the present invention covers any alternatives, modifications, equivalents and arrangements within the spirit and scope of the present invention as defined by the appended claims. Further, in order to give the public a better understanding of the present invention, some specific details are described in detail in the following detailed description of the present invention. The present invention can be fully understood by those skilled in the art without the description of these detailed parts.

S10, establishing an instant distribution route optimization model;

S11, problem description;

A business sells goods on an online platform while offering instant delivery to every customer. Customers place orders in real time during business hours, and the order information after placing the order will be displayed on the enterprise system, and then the enterprise makes decisions based on a certain rule, assigns the order to the vehicle and plans the driving path for it, and finally the vehicle must return after completing the task. Go to the enterprise distribution center to accept subsequent distribution tasks. Due to the heterogeneity of products purchased by customers, vehicles cannot carry new orders in advance. Generally speaking, for the optimization of such dynamic problems, enterprises can divide the business hours into multiple time periods from the time axis, and make decisions for the new customer orders that appear in this period at the time node at the end of each period. Therefore, this type of problem is also called a multi-stage optimization problem.

The driving time is random due to factors such as traffic congestion and bad weather. The randomness of travel time has a significant impact on the performance of the entire distribution system, especially in multi-stage decision-making problems, the randomness of travel time will cause companies to fail to predict the availability of vehicles in advance when making decisions, which greatly increases the complexity of the problem. sex. In addition, with multiple deliveries in a specific area, the delivery staff will gradually accumulate experience on specific roads, and the delivery staff experience will also affect the actual driving time of the vehicle.

S12, problem hypothesis;

Assumption 1 (setting about vehicles): vehicles and delivery staff correspond one-to-one, and delivery vehicles are all vehicles of the same type. Each vehicle has a certain capacity limit, so the sum of customer demands served by each vehicle cannot exceed the maximum capacity of the vehicle. Vehicles have a maximum transit time limit and must return to the distribution center after completing all delivery tasks.

Assumption 2 (setting about customers): customer orders cannot be split, each customer can only be served by one vehicle and only once. Each customer order needs to be picked up at the distribution center before it is shipped, and there is a promised latest delivery time limit for order delivery. The default service time of the present invention is not significant compared to the delivery time, so the customer service time is not considered.

Assumption 3 (about the setting of the enterprise): The online business of the enterprise is limited by working hours, and it only accepts orders and sends vehicles for delivery during working hours. Businesses have a limited number of vehicles and delivery staff.

S13, parameter and variable representation;

The parameters and variables used in the model are described in Table 1.

Table 1. Description of parameters and variables related to the model

S14, the function representation of the experience of the delivery staff;

In the actual logistics distribution process, many environmental conditions will affect the driving time of the vehicle, and the experience accumulated by the delivery staff can shorten the driving time to a certain extent. Therefore, on the basis of the existing research, the present invention proposes a new functional relationship to represent the change trend of the travel time under the influence of the experience of the delivery staff. The formula is shown in formula (18).

Among them, T ₀ is the travel time of the vehicle when the delivery person has no experience at all, x _i and x _j represent the number of visits, and l is the learning factor, which represents the growth rate of experience. When the vehicle travels between nodes i and j, if i and j both represent customer points, the travel time depends on the average experience of the delivery person for the two customers. If a node in i or j is a distribution center, the travel time only depends on the experience value of the delivery staff to the customers in it. In addition, under the influence of the experience of the courier, the travel time can be shortened to αT ₀ at the longest. From this function expression, it can be known that the travel time of the vehicle is actually affected by the number of customer visits.

At the same time, the driving time of the vehicle is random. The present invention assumes that it obeys a normal distribution, that is, TT _ij ~N(u _ij ,σ ² ). In previous literature studies, the expected value u _ij is generally equal to T ₀ by default. However, since the influence of the experience of the delivery staff is considered, although the travel time obeys the normal distribution, its expected value u _ij needs to be calculated by formula (18). Therefore, for different couriers, the expected value of travel time on the same route is not the same. For the same courier, the influence of his experience on different routes is also different.

S15, single-stage mathematical model establishment;

In a single delivery phase, the number of vehicles available and information on customer orders are known, and all vehicles are located in the distribution center. Since the travel time ZT _ij is random, the delivery time AT _i of the customer order, the delayed delivery time DT _i of the customer order and the time ZT _k when the vehicle exceeds the longest transit time are also random. Therefore, the problem can be regarded as a stochastic static vehicle routing problem. At the same time, the simplest punishment correction strategy is adopted for the situation that may violate the latest delivery time of customers and the longest transit time of vehicles. Based on the above description, a single-stage stochastic vehicle routing optimization model is constructed with the goal of minimizing the distribution cost of the enterprise as shown below.

The objective function formula (1) represents the minimization of the delivery cost, where the delivery cost is divided into four parts: the fixed cost of the vehicle, the cost of the vehicle, the delayed delivery of the customer order, and the correction cost exceeding the maximum travel time of the vehicle. Equations (2) and (3) are flow balance constraints, which means that if a vehicle serves a customer, it must visit the customer, and must leave the customer after the service is over. Equation (4) indicates that each customer can only be served by one vehicle. Equation (5) indicates that all dispatched vehicles start from the distribution center and must return to the distribution center after completing the distribution task. Equation (6) indicates that the number of vehicles is limited, and the number of vehicles dispatched cannot exceed the number of vehicles owned by the enterprise. Equation (7) indicates that the capacity of all customer orders on each delivery route cannot exceed the maximum capacity of the vehicle. Equation (8) is to eliminate the constraints of the vehicle path sub-loop. Equations (9) and (10) are the expressions for calculating the delay in order delivery and the time when the vehicle exceeds the maximum time. Equation (11) is the value constraint of decision variable.

S16, establishing a multi-stage mathematical model.

In the just-in-time delivery problem, the arrival of customer orders is dynamic, which requires companies to perform multi-stage decision optimization. In addition, the company's current decision-making affects the time when the vehicle returns to the distribution center, which in turn affects the next stage of decision-making. For example, dispatching more vehicles can increase the on-time delivery rate of an order, but reduce the number of vehicles available in the next phase. Therefore, when a company makes a decision, it may happen that if a large number of customers place orders at this stage, there are still many vehicles that have not completed the last delivery task and returned to the distribution center. At this time, there are too few available vehicles in the distribution center to meet the delivery requirements of excessive customer orders. To this end, the present invention regards vehicles that are in the process of delivery tasks but have not returned to the distribution center as potentially available resources, and performs order allocation and route planning on the premise of the availability of all vehicles.

和潜在可用车辆

对于可用车辆

其最早可用时间就等于决策的时间节点。对于潜在可用车辆

其最早可用时间等于它们回到配送中心的时间。然而，行驶时间的随机性导致了潜在可用车辆回到配送中心的时间也具有随机性。因此对于企业的决策来说，潜在可用车辆的可用时间信息是不确定的。It can be seen from the above description that the vehicles dispatched by the enterprise in the logistics plan after the decision in stage r may be divided into two types: the existing vehicles available in the distribution center

and potentially available vehicles

for available vehicles

The earliest available time is equal to the time node of the decision. For potentially available vehicles

Their earliest available time is equal to their return to the distribution center. However, the randomness of travel times results in randomness in the time when potentially available vehicles return to the distribution center. Therefore, the availability time information of potentially available vehicles is uncertain for enterprise decision-making.

Aiming at the real-time distribution routing problem studied, a multi-stage stochastic vehicle routing optimization model is established, and its objectives are as follows:

From the point of view of a single stage, this objective formula is equivalent to formula (1). In addition, in a multi-stage problem, not only each stage needs to meet the constraints specified by the single-stage model, but also the following constraints:

Equation (13) indicates that the enterprise will only make decisions during business hours. Equation (14) indicates that each decision is only for customer orders that appear in this stage. Equation (15) indicates that the delivery time of the customer order is not earlier than the departure time of the vehicle. Equation (16) indicates that the departure time of the dispatched vehicle should be after its available time. Equation (17) is the value constraint of decision variable.

S20, the solution method of the design model.

S21, simulation heuristic method framework design;

The simulation heuristic method combines the meta-heuristic algorithm and the simulation method to solve the stochastic combinatorial optimization problem. It has the advantages of flexibility and easy implementation, and has been successfully applied to solve the random vehicle routing problem. In the simulation heuristic method framework, the meta-heuristic algorithm is responsible for the search and update of the solution, and the simulation method is responsible for evaluating the solution obtained by the meta-heuristic algorithm. The framework of the simulation heuristic method designed by the present invention is shown in FIG. 1 .

Solving stochastic combinatorial optimization problems based on simulation heuristics has a premise: an efficient meta-heuristic algorithm can obtain high-quality solutions to deterministic problems corresponding to stochastic combinatorial optimization problems, and the high-quality solutions of deterministic problems are likely to be It is also a high-quality solution for random problems. In the instant delivery routing problem, the travel time is random and obeys a normal distribution. Therefore, in the designed simulation heuristics framework, the expected value of travel time is used in place of random travel time to transform a stochastic model with random travel time into a deterministic model.

Then, the present invention designs an improved adaptive large neighborhood search algorithm (Improved Adaptive Large Neighborhood Search, IANLS) based on the adaptive large neighborhood search algorithm (Adaptive Large Neighborhood Search, ALNS) to solve the determination model. During each iteration, the updated solution obtained by IALNS needs to be simulated in a stochastic environment to evaluate the quality of the solution. The simulation method adopted in the present invention is Monte Carlo simulation. Considering the solution efficiency of the simulation heuristic method, only the updated solution accepted by IALNS will undergo a fast simulation process to calculate the expected target value of the solution, and the number of simulations N _fs in this stage is small. In addition, the simulation heuristics framework defines a solution sequence of size N _l for storing updated solutions after fast simulations. When the number of solutions in the solution sequence is less than N _l , the updated solutions are directly stored in it and sorted according to the expected target value. Otherwise, the updated solution needs to be compared with the solution at the end of the solution sequence, and the solution with the lower expected value of the two is kept in the solution sequence.

Finally, when the IALNS iteration ends, the solution sequence has stored N _l possible solutions as the optimal solution of the stochastic model. At this point, the solution sequence goes through a second simulation run to calculate the desired target value for each solution. It is worth noting that the number of simulations N _s in this round is much larger than N _fs in order to more accurately evaluate each solution compared to the first round of simulations.

S22, Monte Carlo simulation design;

In the established problem model, the travel time is random. Therefore, the present invention adopts the Monte Carlo simulation method to calculate the expected target value of the solution, which can be mainly divided into the following three steps: S221, randomly generating the specific value of each random variable according to the probability distribution; S222, calculating the objective function value of the solution; S223, repeating S221 and S222N _sim times to calculate the expected target value of the solution. The detailed calculation steps are shown in Table 2.

Table 2 Monte Carlo simulation calculation process

S23, improving the design of an adaptive large neighborhood search algorithm.

The present invention designs an improved adaptive large neighborhood search algorithm. First, the destruction and repair operators are designed or improved according to the characteristics of the problem. Second, a local search process is added to IALNS for the purpose of enhancing the local search capability of the algorithm. Finally, the abandonment criterion of the solution in Artificial Bee Colony Algorithm (ABC) replaces the simulated annealing criterion in traditional ALNS. The basic flow of IALNS is shown in Table 3.

Table 3 The basic process of IALNS

S231, Coding Design of Solutions

First, the solution of the problem is encoded by natural numbers, see Figure 2. If the problem contains 6 customers and 3 cars, the solution to the problem in this case can be represented by the sequence shown in Figure 2. The sequence between two values 0 represents the driving path of a vehicle. The first 0 value represents the starting point of the path, the latter 0 value represents the end point of the path, and the non-zero value represents the visited customer number. The driving path of all vehicles constitutes a problem a solution of .

S232, initialize the design;

Due to its regular destruction and repair operators, ALNS can easily iterate from poor quality solutions to high quality solutions. Therefore, the quality of the initial solution is not so important, and a high-quality initial solution can easily cause the algorithm to converge prematurely and fall into a local optimum. On the premise of ensuring the feasibility of the vehicle capacity, the present invention adopts a simple insertion heuristic method to generate the initial solution, and the specific process is as follows: (1) generate an empty path sequence that only includes the starting point and the ending point of the vehicle; (2) randomly select one For customer i, determine whether the total demand on this route exceeds the vehicle capacity after inserting customer i. If it exceeds, go to step (1), otherwise go to step (3); (3) judge the latest service time of two consecutive customers j, j+1 and customer i on the route, if LT _j < LT _i <LT _j+1 , insert customer i between customer j and customer j+1; (4) judge whether all customers are inserted into the path, if so, go to step (5), otherwise go to step (2) ); (5) merge all sequences into the same sequence, and remove one of the two adjacent 0 values in the sequence; (6) judge whether the number of paths in the sequence reaches the number of vehicles, if so, stop, otherwise Add 0 values to the sequence until the number of paths equals the number of vehicles.

S233, destroy the operator design;

The destruction operators used by IALNS include random removal operator, path removal operator, worst removal operator, worst distance removal operator, worst time removal operator, similarity removal operator and adjacent similarity Remove operator. During the destruction phase, IALNS will choose one of these operators to destroy the solution. The destruction operator will remove a certain number of customers from the current solution S _current , and at the same time store the removed customers in the sequence C _remove and get the solution S _remove after removing the customers. Among them, the number of removed customers N _remove has an important influence on the solution performance of the algorithm. If the N _remove value is too large, the solution speed of the algorithm will be slowed down, and if it is too small, it is not conducive for the algorithm to jump out of the local optimum. In the present invention, N _remove is related to the number n of customers.

S2331, random removal: randomly select N _remove customer points from the current solution to remove. Although this operator is simple to operate, the randomness of customer point removal can greatly expand the search space of the solution and increase the search efficiency of the algorithm. Diversity.

S2332, path removal: randomly select a sub-path in the solution, and remove all customer points in the sub-path, which is beneficial to obtain a solution with the least number of vehicles.

S2333, worst removal: define the cost of customer point i in the current solution as cost(s,i)=Z(s)-Z- _i (s), where Z(s) is the target value of the current solution, and Z _-i (s) is the target value after removing customer point i. The worst removal operator needs to first calculate the target value of the current solution, and then calculate the target value after each customer point is removed, so as to obtain the cost of each customer point, and finally select the customer point with the highest cost from the current solution. Remove, repeat this step until N _remove customer points are removed.

S2334, the worst distance removal: define the distance cost of customer point i in the current solution as the sum of the distance from customer i to its previous customer point and the distance to its next customer point, namely cost(s,i)= d _i-1,i +d _i,i+1 , each time the customer points with the largest distance cost are selected and removed until N _remove customer points are removed.

S2335, worst time removal: define the time cost of customer point i in the current solution as the difference between the latest delivery time and the arrival time, that is, timecost(s,i)=|LT _i -s _i |, each time Select the customer point with the largest time cost to remove until N _remove customer points are removed.

S2336, similarity removal: define the similarity between two customer points as R _ij =φ ₁ d _ij +φ ₂ |LT _i -LT _j |+φ ₃ r _ij +φ ₆ |q _i -q _j |, where d _ij is the distance between two customers, LT _i is the latest delivery time, qi is the customer demand, and r _ij represents whether customer _i and customer j are in the same sub-path, if so, r _ij =1, otherwise r _ij =-1. φ ₁ -φ ₄ are the respective weights. The similarity removal operator randomly selects a customer point to remove from the current solution, and stores the removed customer point in the sequence C _remove . Calculate the similarity between each customer point in the solution and the last customer point in the sequence C _remove , and select the customer point with the largest similarity to remove and store it in the sequence C _remove . Repeat this step until N _remove customer points are removed. remove.

S2337, adjacent similarity removal: this operator is a special case of the similarity removal operator, where φ ₁ =φ ₂ = _φ 3=0, φ ₄ =1, this operator removes some customer points with similar distances.

S234, repair the operator design;

In the repair phase, IALNS will select a customer sequence C _remove to be removed from many repair operators and re-insert it into S _remove , thereby generating an updated solution S _upd8te corresponding to the current solution S _current . In the repair phase, IALNS uses five repair operators, namely greedy insertion, regret insertion, distance greedy insertion, cost greedy insertion with noise perturbation, and distance greedy insertion with noise perturbation.

S2341, greedy insertion: randomly select a customer from the sequence C _remove , calculate the target increase value caused by inserting the customer into each position in the solution S _remove , select the position with the smallest increase value to insert the customer into the solution, and repeat this step Until all customer points in C _remove are inserted into the solution.

其中

为顾客i插入后引起的最小目标增加值，

表示顾客i插入后引起的第二小目标增加值。选择后悔值最大的顾客并将该顾客插入到增加值最小的位置上，重复这一步骤直到C_remove中所有顾客点全部插入解中。S2342, regret value insertion: Calculate the target increase value caused by each customer inserting each position in the solution, and define the regret value as

in

the minimum target increment after insertion for customer i,

Represents the second smallest target increase after insertion by customer i. Select the customer with the largest regret value and insert the customer into the position with the smallest increase value. Repeat this step until all customer points in C _remove are inserted into the solution.

S2343, distance greedy insertion: randomly select a customer from the sequence C _remove , calculate the distance increment caused by inserting the customer into each position in the solution S _remove , the formula is d _i =d _hi +d _ij -d _hj . Select the position with the smallest distance increment to insert the customer, and repeat this step until all customer points in C _remove are inserted into the solution.

S2344, Cost greedy insertion with noise disturbance: The greedy insertion operator selects the optimal position when selecting the insertion position of each customer. This lack of randomness easily makes the algorithm fall into a local optimum. The cost greedy insertion with noise perturbation is based on the greedy insertion operator, adding noise to perturb the target increase value. The calculation formula of the target increase value after noise perturbation is: insertcost _-i =insertcost _i +u*r*insertcost _max , where insertcost _i is the target increase value before noise disturbance, insertcost _max is the maximum target increase value inserted in all positions, u is the noise parameter, and r is a random number in [-1,1].

S2345, distance greedy insertion with noise perturbation: This operator is an extended form of the distance greedy insertion operator. It also adds noise perturbation when calculating the distance increment. The calculation formula is similar to the cost greedy insertion with noise perturbation.

S235, local search design;

After the destruction and repair phase, IALNS adds a local search phase, which is mainly to enhance the local search ability of the algorithm. At this stage, the algorithm chooses to use 2-opt* or 3-opt* for local search according to the length of the subpath, that is, exchange two customer points or three customer points for each subpath in the solution to optimize the current solution. Essentially, IALNS performs iterative update of the solution by selecting one of many operators in the destruction and repair phase. Although this expands the search space of understanding, it also means that it brings more randomness, while local search The addition of operators can make up for this defect to a certain extent, and balance the breadth and depth of the algorithm in search.

S236, design of the abandonment criterion of the solution;

In traditional ALNS, the judgment criterion of simulated annealing is added to accept the non-improved solution, that is, when the updated solution generated in the iterative process is not better than the current solution, the algorithm has a certain probability to accept the updated solution. However, although the simulated annealing criterion helps the algorithm to search for a better solution in the global scope in the early iteration, it is obviously not conducive to the algorithm to find a better solution in a local area. Therefore, the present invention draws on the idea of abandoning the solution of ABC, and replaces the simulated annealing criterion with an abandonment criterion, so as to expect IALNS to obtain a better balance in terms of search depth and breadth.

The specific method of abandoning the criterion is to generate an updated solution in each iteration process. If the updated solution is not better than the current solution, the number of consecutive unimproved is increased by one, otherwise the number of consecutive unimproved is reset to zero. When the number of consecutive unimproved times reaches the threshold _Nt , a cross-exchange operator is used to perturb the current solution. The cross-exchange operator randomly selects two sub-paths in the solution, then selects a segment of continuous customer points from the two sub-paths, and finally exchanges the selected customer points on the two sub-paths. The schematic diagram of the operator is shown in Figure 3.

S237, the operator selection mechanism design.

表示第i个算子在第r个N_s次迭代的权重。通过这一公式，算子权重与其历史表现挂钩，达到算子权重自适应调整的目的。For the second destruction operator and all repair operators, the present invention adopts an adaptive operator selection strategy. At the very beginning of the algorithm, all operators have the same initial weight and initial score, the initial weight is set to 1, the initial score is 0, and the weight and score are updated every N _s iterations. Each iteration algorithm selects a destruction operator and a repair operator to update the solution according to the roulette rule, and records the number of times u _i that operator i is selected, and the operator with a larger weight is easier to be selected. The operator is then given different scores according to the quality of the updated solution obtained after each iteration. When the updated solution is better than the global optimal solution, the damage and repair operator scores σ ₁ are assigned. When the updated solution is worse than the global optimal solution but better than the current solution, a score σ ₂ is assigned. When the updated solution is worse than the current solution, no score is assigned. When one N _s iterations ends, the weight of the operator is updated using the formula as the initial weight of the next N _s iteration operator. At the same time, the total score s _i and the selected times u _i obtained in the N _s iterations are reset to zero. The formula is shown in (19), where ρ is the weight adjustment coefficient, indicating the importance of the historical weight and the operator performance when the operator weight is updated,

Represents the weight of the ith operator in the rth _Ns iterations. Through this formula, the operator weight is linked to its historical performance to achieve the purpose of adaptive adjustment of the operator weight.

Experimental results and analysis:

The experimental content of the present invention is mainly divided into two parts: the performance verification of the simulation heuristic method and the calculation and analysis of the real-time distribution route optimization model. These two parts correspond to the first embodiment and the second embodiment respectively.

Embodiment 1;

The solution performance of the simulation heuristic method based on IALNS and Monte Carlo simulation is largely affected by the above-defined various parameters, and the parameters set in the present invention are shown in Table 4.

Table 4 Parameter settings

In the framework of the simulation heuristic method designed by the present invention, Monte Carlo simulation is not an optimization method, and the solution performance of the simulation heuristic method mainly depends on IALNS. Therefore, this section first conducts experiments on the deterministic problem of the single delivery stage of the research problem, without considering the randomness of the vehicle travel time, to verify the solution effect of the IALNS algorithm. At the same time, we use the well-known Solomon dataset for experiments and choose to compare with the results obtained by the solver Gurobi. The Solomon dataset is mainly generated for the vehicle routing problem with time windows, and can be divided into three categories according to the geographical distribution characteristics of customer points: cluster distribution (labeled C), random distribution (labeled R), clustering and Random mixed distribution (labeled RC). In addition, considering the solution efficiency of Gurobi, suitable data are selected from the Solomon dataset for experiments, while the maximum solution time of Gurobi is limited to 1800 seconds.

The experimental results are shown in Table 5. Compared with Gurobi, IALNS has obvious advantages in operation time and is comparable to Gurobi in solution accuracy. Among them, IALNS is better than Gurobi in the performance of examples R103, C106 and C109. This fully shows that IALNS can get a better solution in a short time, showing good performance.

In order to further prove the performance of IALAS, the same local search operation as IALNS is also added to the standard ALNS. At the same time, for the fairness of the comparison, both IALNS and ALNS use the same destruction and repair operator, and other parameter settings are also the same. The two algorithms first calculate the solomon_100_C101 data set with different iteration times, and then calculate the final results of the C101, C102, C103, R101, R102, R103, RC101, RC102, RC103 cases with 100 customer points respectively. The experimental results As shown in Figure 4 and Figure 5. The main functions of the ABC abandonment criterion and the simulated annealing criterion are to improve the optimization ability of the algorithm and avoid the algorithm falling into local optimum quickly. However, it can be seen from the results in the figure that the ABC abandonment criterion makes IALNS have a higher solution accuracy, and the effect is obviously better than that of IALNS.

Table 5 Comparison of calculation results between IALNS and Gurobi

Embodiment 2

The present invention transforms data with 100 customer points in the Solomon data set. First, the entire business hours of the business are divided into 10 stages, each with a duration of 1 hour. Then, for each stage, 15 to 25 customers are randomly selected from 100 customer points as customers who place orders in this stage, and their order time is randomly generated within the time period of this stage. Finally, we only keep the customer point coordinates, demand, and vehicle capacity data in the study. The latest delivery time for customers is randomly generated by comprehensively considering the time when customers place an order and the distance from the merchant to the customer. Finally, we take C101, R101 and RC101 as the benchmark examples, and generate 4 different multi-stage example sets for each example, a total of 12 sets of data sets are used for this experiment.

For 12 sets of examples, we use the designed simulation heuristic method to carry out numerical experiments in three scenarios: travel time determination, random travel time without considering the influence of the experience of the courier, random travel time and the influence of the experience of the courier are considered. Corresponding to scene 1, scene 2 and scene 3 respectively.

Taking the first stage data of the C101_1 dataset as an example, the driving paths in three experimental scenarios are calculated respectively. It is worth noting that the experience of the delivery staff is obtained after all 10 stages of delivery tasks in this group of examples. As shown in Figure 6, the driving paths in the three experimental scenarios are quite different. When travel times are random, customers who could otherwise be served by the latest time may be delayed. Delayed delivery will increase the penalty cost, which will lead to the change of the optimal driving path of the delivery staff. When further considering the influence of the experience of the delivery staff, the optimal delivery plan will be more inclined to assign customer orders to more experienced delivery staff for delivery, which will further lead to changes in the optimal delivery route. Therefore, it is necessary to consider the randomness of the travel time and the experience of the delivery staff when planning the vehicle path.

Table 6 The calculation results of the calculation example

Table 6 shows the total cost of 12 groups of examples in three different experimental scenarios and their change ratios. Compared with scenario one, the total cost of scenario two is reduced by 8.68% on average. The main reason for this is that when the number of dispatched vehicles is comparable, the correction cost considering random travel time will be significantly lower, resulting in a lower total delivery cost. At the same time, the lower revision cost side reflects the higher on-time delivery rate of goods. Compared with scenario two, the total cost of scenario three is reduced by an average of 10.65%. From this result, it can be seen that when formulating the logistics distribution plan, considering the influence of random travel time and the experience of the delivery staff, it is beneficial to reduce the delivery cost, improve the on-time delivery rate of the goods and the delivery efficiency of the delivery staff.

The above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

Claims (10)

1. An instant delivery route optimization method considering dispenser experience and random travel time, comprising the steps of:

s10, establishing an instant distribution path optimization model;

s20, designing a solving method of the model;

wherein, S20 specifically includes the following steps:

s21, simulating heuristic method frame design;

s22, carrying out Monte Carlo simulation design;

and S23, improving the design of the self-adaptive large neighborhood search algorithm.

2. The method according to claim 1, wherein the step S10 of establishing the immediate delivery route optimization model specifically includes the steps of:

s11, problem description;

s12, problem hypothesis;

s13, representing parameters and variables;

s14, function representation of the distributor experience;

s15, establishing a single-stage mathematical model;

s16, establishing a multi-stage mathematical model.

3. The method of claim 2, wherein the question hypothesis, S12, includes a setting for a vehicle, a setting for a customer, and a setting for a business.

4. The method of claim 2, wherein said S14, the function of the distributor' S experience is expressed as:

wherein, T ₀ For the time of travel of the vehicle when the dispenser is completely inexperienced, x _i And x _j Expressing the number of visits, and l is a learning factor and expressing the growth speed of the experience; when the vehicle is traveling between nodes i and j, if both i and j represent customer points, the travel time depends on the average of the dealer's experience with both customers; if one node in i or j is a distribution center, the running time only depends on the experience value of a distributor to customers; under the influence of the experience of the distributor, the travel time is shortened to alpha T at the maximum ₀ Wherein α represents the longest reduction ratio of the travel time; from this functional expression, it is understood that the travel time of the vehicle is actually affected by the number of times of customer visits.

5. The method according to claim 2, wherein the S16, the multi-stage mathematical model building, comprises building a multi-stage stochastic vehicle path optimization model with the goal of:

wherein f is the fixed cost of vehicle starting;

indicating whether the vehicle k is used in the r stage, if yes, the vehicle k is used in the r stage

Otherwise

Is the set of customers of phase r; k is a set of vehicles owned by the enterprise, wherein K is {1,2, …, m }, and m vehicles; v ^r Set of nodes at decision time for stage r, V ^r ＝

E (-) represents the expected value of the random variable;

the travel time of the vehicle from node i to node j dispatched for stage r;

if the vehicle k runs from the node i to the node j in the decision of the stage r, the value is 1, otherwise, the value is 0; c. C ₁ Cost per unit travel time; c. C ₂ Correcting the cost for delivery time per unit delay; c. C ₃ Cost is corrected for time per unit exceeding the longest time in transit; DT _i Delay delivery time for an order for customer i; ZT _k The time that the vehicle k exceeds the longest time in transit.

6. The method of claim 1, wherein the S22, monte carlo simulation design, comprises the steps of:

s221, randomly generating a specific value of each random variable according to probability distribution;

s222, calculating an objective function value of the solution;

s223, repeating S221 and S222N _sim Next, calculating an expected target value of the solution, where N _sim Is the simulation times.

7. The method of claim 1, wherein the step of improving the adaptive large neighborhood search algorithm design S23 comprises the steps of:

s231, designing the decoding;

s232, initializing design;

s233, operator design is destroyed;

s234, repairing operator design;

s235, local search design;

s236, designing a abandoning criterion of the solution;

and S237, designing an operator selection mechanism.

8. The method according to claim 7, wherein the S232, initializing the design, comprises the following steps:

s2321, generating an empty path sequence only comprising a vehicle starting point and a vehicle finishing point;

s2322, randomly selecting a customer i, and judging whether the total demand on the path exceeds the vehicle capacity after the customer i is inserted. If the current value exceeds the preset value, turning to S2321, otherwise, turning to S2323;

s2323, judging the latest service time of two consecutive customers j, j +1 and customer i on the path, if LT is judged _j ＜LT _i ＜LT _j+1 Insert customer i between customer j and customer j +1, LT _i A latest delivery time promised for an order for customer i;

s2324, judging whether all customers are inserted into the path, if so, turning to S2325, and otherwise, turning to S2322;

s2325, merging all sequences into the same sequence, and removing one of two adjacent 0 values in the sequence;

s2326, judging whether the number of the paths in the sequence reaches the number of the vehicles, if so, stopping, and otherwise, adding a value of 0 in the sequence until the number of the paths is equal to the number of the vehicles.

9. The method of claim 8, wherein the step S233, destroying operator design, comprises the steps of:

s2331, random removal: randomly selecting N from the current solution _remove Removing each customer point;

s2332, route removal: randomly selecting a sub-path in the solution, and removing all customer points in the sub-path;

s2333, worst removal: defining the cost of customer point i in the current solution as cost (s, i) ═ Z(s) -Z _-i (s), wherein Z(s) is a target value of the current solution, and Z _-i (s) for the target value after removing customer point i, the worst removal operator calculates the target value of the current solution, then calculates the target value after each customer point is removed, thereby obtaining the cost of each customer point, finally selects the customer point with the highest cost from the current solution to remove, and repeats the steps until N is reached _remove Individual customer points are removed;

s2334, finally, removing: defining the distance cost of the customer point i in the current solution as the sum of the distance from the customer i to the previous customer point and the distance from the customer i to the next customer point, namely, discost (s, i) ═ d _i-1，i +d _i，i+1 Removing the customer points with the largest distance cost until N _remove Individual customer points are removed;

s2335, worst time removal: defining the time cost of customer point i in the current solution as the difference between the latest arrival time and the arrival time, i.e. timetop (s, i) ═ LT _i -s _i L, remove up to N each time the most time-costly customer site is selected _remove Individual customer points are removed;

s2336, similarly remove: defining the similarity between two customer points as R _ij ＝φ ₁ d _ij +φ ₂ |LT _i -LT _j |+φ ₃ r _ij +φ ₄ |q _i -q _j L where d _ij Distance between two customers, LT _i To the latest arrival time, q _i Is the customer demand, and r _ij Indicating whether customer i and customer j are in the same sub-path, if yes, then r _ij 1, otherwise r _ij ＝-1。φ ₁ -φ ₄ Are respective weights; the similarity removal operator randomly selects a customer point to remove from the current solution, and stores the removed customer point in the sequence C _remove Performing the following steps; each customer point in the computational solution and the sequence C _remove The similarity of the last customer point in the sequence C is removed and the customer point with the maximum similarity is selected and stored in the sequence C _remove Repeating this step until N _remove Individual customer points are removed;

s2337, proximity similarity removal: this operator is a special case of a similar removal operator, where φ ₁ ＝φ ₂ ＝φ ₃ ＝0，φ ₄ This operator removes customer points that are close together.

10. The method of claim 9, wherein the S234 repairing operator design comprises the following steps:

s2341, greedy insertion: from sequence C _remove Randomly selecting a customer, calculating the customer insertion solution S _remove The target increment value caused after each position is selected, the position with the minimum increment value is selected to insert the customer into the solution, and the steps are repeated until C _remove All customer points are inserted into the solution;

s2342, inserting the regret value: calculating the target added value caused by each customer inserting each position in the solution, and defining the regret value as

Wherein

The minimum target increment value caused after insertion for customer i,

indicating a second small target increment value caused by insertion of customer i; selecting the customer with the maximum regret value and inserting the customer into the position with the minimum increment value, and repeating the steps until C _remove All customer points are inserted into the solution;

s2343, greedy distance insertion: from sequence C _remove Randomly selecting a customer, calculating the customer insertion solution S _remove The distance increment caused after each position in the equation d _i ＝d _hi +d _ij -d _hj (ii) a Selecting the position with the minimum distance increment to insert the customer, and repeating the steps until C _remove All customer points are inserted into the solution;

s2344, cost greedy insertion with noise disturbance: the greedy insertion operator selects the optimal position when selecting the insertion position of each customer, and the algorithm is easy to fall into local optimization due to the insertion mode lacking randomness; the cost greedy insertion with noise disturbance is based on a greedy insertion operator, the noise is added to disturb the target added value, and the calculation formula of the target added value after the noise disturbance is as follows: insert cost _-i ＝insertcost _i +u*r*insertcost _max Wherein insert cost _i Adding value to the target before noise disturbance, insertcost _max For the maximum target add value inserted in all positions, u is the noise parameter and r is [ -1,1 [ ]]A random number within;

s2345, distance greedy insertion with noise disturbance: the operator is an extension form of a distance greedy insertion operator, noise disturbance is added in distance increment calculation, and a calculation formula is similar to cost greedy insertion with noise disturbance.

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