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

Abstract

The invention discloses an instant delivery path optimization method considering the experience of a deliverer and random travel time, S11, describing problems; 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; 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. The method of the invention combines a simulation method and a heuristic algorithm to solve the problem of the instant distribution path.

Description

Instant delivery path optimization method considering dispenser experience and random travel time

Technical Field

The invention belongs to the technical field of logistics distribution path optimization, and relates to an instant distribution path optimization method considering distributor experience and random running time.

Background

In recent years, with the rising trend of online shopping, instant distribution is becoming an important part of urban logistics. In the instant distribution logistics activity, enterprises receive distribution demands put forward by customers in real time and complete distribution services to the customers in real time, and the application fields of the enterprises comprise take-out, fresh food, medicine, business and super-business and the like. As a novel logistics distribution mode, the instant distribution has the characteristics of multiple frequencies, small batch, limited vehicle resources and the like. In addition, customers often need to be served within one or two hours after placing an order, which makes the instant delivery very time-efficient. Therefore, when an enterprise makes an instant distribution scheme, not only the logistics cost needs to be reduced as much as possible to obtain higher economic benefits, but also the on-time delivery rate of commodities needs to be ensured to improve the satisfaction degree of customers.

In the actual logistics distribution process, the travel time of the vehicle is affected by many factors. On one hand, external environments such as traffic jam and severe weather cause the driving time to be random. If the randomness of travel time is neglected, the enterprise may develop inefficient logistics distribution schemes. On the other hand, when the delivery service is repeatedly provided to the customers in a certain area, the deliverer learns the road condition in the delivery area, and the experience of this can further shorten the travel time. For example, when a distributor knows traffic information such as shortcuts, intervals between traffic lights, and traffic flow on roads in a distribution area, the distribution time is significantly shortened. According to the estimation of relevant experts, the travel time can be shortened by 40% at most under the influence of the experience of the distributor. Therefore, how to combine the actual logistics distribution activities to make more accurate evaluation and plan a better distribution path is a significant problem for enterprises to provide instant distribution services.

Disclosure of Invention

Aiming at the defects of the prior art, the invention combines a simulation method and a heuristic algorithm to solve the problem of the instant distribution route, the proposed method is called as a simulation heuristic method, and particularly provides an instant distribution route optimization method considering the experience of distributors and random running time. The method comprises the following steps:

the method comprises the following steps:

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.

Preferably, the step S10 of establishing an instant delivery path optimization model specifically includes the following steps:

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.

Preferably, the question hypothesis includes a setting for the vehicle, a setting for the customer, and a setting for the business S12.

Preferably, at S14, the function of the experience of the distributor 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 the i or the j is a distribution center, the running time only depends on the experience value of a distributor to customers in the i or the j; under the influence of the experience of the dispatcher, the maximum running time is shortened to alpha T 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.

Preferably, the S16, the multi-stage mathematical model building, includes building a multi-stage random vehicle path optimization model with the goal of:

wherein f is the fixed cost of vehicle starting;

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

Otherwise

V _c ^r Is the customer set of the r stage; k is a set of vehicles owned by the enterprise, K ═ 1,2, …, m }, for m vehicles; v ^r Set of nodes at decision time for stage r, V ^r ＝{0}∪V _c ^r (ii) a 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.

Preferably, the S22, monte carlo simulation design, includes the following steps:

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 number of simulations.

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

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.

Preferably, the S232, initializing the design, includes 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, the latest service time of two consecutive customers j, j +1 and customer i on the path is judged, if LTj<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 yes, 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.

Preferably, the S233, the method for designing the destruction operator, includes the following steps:

s2331, random removal: randomly selecting N from the current solution _remove A customer pointRemoving;

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

s2333, worst removal: defining cost of customer point i in current solution as cost (s, i) ═ Z(s) -Z _-i (s), wherein Z(s) is a target value for 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 up to N customer points with the greatest cost per selection distance _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 of the calculation solutionsCustomer point and 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 in distance, 1.

Preferably, the S234 repairing operator design includes 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 in the solution are inserted.

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 in the solution are inserted.

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 . Selecting the position with the smallest distance increment for insertionThe customer, repeat this step until C _remove All customer points in the solution are inserted.

S2344, greedy insertion of cost with noise disturbance: the greedy insertion operator selects the optimal position when selecting the insertion position of each customer, and the insertion mode with the lack of randomness easily causes the algorithm to be trapped in local optimization. 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 increment inserted in all positions, u is the noise parameter and r is [ -1,1]The random number in (c).

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.

The invention has the following beneficial effects:

compared with the prior art, the method and the system have the advantages that aiming at the problem of the instant delivery path, the expected value change of random travel time caused by the experience of a dispenser is innovatively considered, the travel time function based on the experience of the dispenser is defined to measure the important change, and the single-stage and multi-stage delivery path optimization model is constructed with the aim of minimizing the total delivery cost. In addition, the invention aims to improve the self-adaptive large neighborhood search algorithm and designs a simulation heuristic solving framework by combining Monte Carlo simulation.

For enterprises, the method is beneficial to reasonably planning the vehicle path and reducing the logistics distribution cost; the logistics distribution efficiency is improved, and the competitiveness of enterprises in the market is kept; for the delivery personnel, the invention is beneficial to the delivery personnel to accumulate the delivery experience and improve the delivery capability; the method is favorable for improving the balance of the workload of the distributor and ensuring the fairness of the income. For customers, the invention is beneficial to the customers to obtain better logistics service experience and improve the customer satisfaction.

Drawings

FIG. 1 is a block diagram of a method for optimizing an immediate delivery route in consideration of the experience of the delivery personnel and the random travel time according to an embodiment of the present invention;

FIG. 2 is a schematic diagram illustrating the encoding method of the solution of the instant distribution route optimization method considering the experience of the distributor and the random travel time according to the embodiment of the present invention;

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

FIG. 4 is a graph comparing convergence rates of an instant delivery path optimization method considering the dispenser experience and random travel time in accordance with an embodiment of the present invention;

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

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

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

On the contrary, the invention is intended to cover alternatives, modifications, equivalents and alternatives which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. It will be apparent to one skilled in the art that the present invention may be practiced without these specific details.

S10, establishing an instant distribution path optimization model;

s11, problem description;

an enterprise sells goods on an online platform while providing instant distribution services to each customer. The method comprises the steps that a customer places an order in real time in business hours, order information after the order is placed is displayed on an enterprise system, then an enterprise makes a decision according to a certain rule, the order is distributed to vehicles and a driving path is planned for the vehicles, and finally the vehicles need to return to an enterprise distribution center to receive subsequent distribution tasks after the vehicles complete the tasks. Due to the heterogeneity of the goods purchased by customers, vehicles cannot carry the goods of new orders in advance. Generally, for optimization of such dynamic problems, an enterprise may divide business hours into a plurality of time periods from a time axis, and make decisions for newly appearing customer orders at the time node of the end of each phase. Therefore, this type of problem is also referred to as a multi-stage optimization problem.

Due to the influence of factors such as traffic jam and severe weather, the driving time is random. The randomness of the travel time has a significant effect on the performance of the entire distribution system, and particularly in a multi-stage decision problem, the randomness of the travel time may cause an enterprise to not predict the available time of a vehicle in advance during decision making, thereby greatly increasing the complexity of the problem. Further, with multiple deliveries in a particular area, the deliverer may gradually build up experience with a particular road, which in turn may affect the actual travel time of the vehicle.

S12, problem hypothesis;

assume 1 (setting regarding vehicle): the vehicles correspond to the distributors one by one, wherein the distribution vehicles are vehicles of the same type. Each vehicle has a capacity limit so that the sum of the customer demands served by each vehicle cannot exceed the maximum capacity of the vehicle. The vehicle has a maximum time-in-transit limit and must return to the distribution center after all distribution tasks are completed.

Assume 2 (settings for the customer): customer orders cannot be split, each customer can only be serviced by one vehicle and only once. Each customer order requires picking at a distribution center before distribution and the order distribution has a commitment to latest delivery time limit. The default service time of the present invention is not significant compared to the delivery time, and therefore customer service time is not considered.

Assume 3 (settings for business): the business online business has working time limitation, and only the order is received and the vehicle is dispatched for distribution in the working time. The number of vehicles and distributors owned by a business is limited.

S13, representing parameters and variables;

the parameters and variable specifications used for the model are shown in table 1.

TABLE 1 model-related parameters and variable description

S14, function representation of the distributor experience;

in an actual logistics distribution process, many environmental conditions affect the travel time of a vehicle, and the accumulated experience of the distributor learning can shorten the travel time to some extent. Therefore, based on the existing research, the invention provides a functional relation formula again to represent the variation trend of the travel time under the influence of the experience of the distributor, and the formula is shown as a formula (18).

Wherein, T ₀ For the time of travel of the vehicle when the dispenser is completely inexperienced, x _i And x _j Indicating the number of visits, l being a learning factor, indicating the rate of growth of the experience. When the vehicle is traveling between nodes i and j, if both i and j represent customer points, the travel time is dependent on the average of the dealer's experience with both customers. If one node in i or j is taken as a distribution center, the running time is onlyDepending on the dispenser's experience with the customer therein. In addition, the maximum travel time is shortened to α T under the influence of the experience of the dispenser ₀ . 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.

Meanwhile, the running time of the vehicle is random. The present invention assumes that it follows a normal distribution, i.e. TT _ij ～N(u _ij ,σ ² ). In a prior literature study, expected value u _ij General default equals T ₀ . However, considering the influence of the experience of the dispenser, the travel time is normally distributed, but the expected value u is _ij It is calculated by equation (18). Therefore, the expected value of the travel time on the same route is different for different distributors. The experience of the same dispenser may also have different effects on different routes.

S15, establishing a single-stage mathematical model;

in a single delivery phase, the number of available vehicles and the customer order information are known and all vehicles are located at the delivery center. Due to travel time ZT _ij Has randomness, so that the delivery time AT of the customer order _i Delayed delivery time DT of customer order _i And time of vehicle exceeding maximum time in transit ZT _k Also random. Thus, the problem can be viewed as a random static vehicle path problem. Meanwhile, the simplest penalty correction strategy is adopted for the situation that the latest arrival time of the customer and the longest transit time of the vehicle are violated possibly. Based on the above description, a single-stage stochastic vehicle path optimization model is constructed with the objective of minimizing the distribution cost of the enterprise as follows.

The objective function equation (1) represents the minimum delivery cost, which is divided into four parts: vehicle fixed costs, vehicle travel costs, delayed delivery of customer orders, and revised costs beyond the maximum time in transit of the vehicle. Equation (2) (3) is a flow balance constraint that means that the vehicle must visit a customer if it is to be serviced, and must leave the customer after the service is over. Equation (4) indicates that each customer can only be serviced by one vehicle. The formula (5) indicates that all dispatched vehicles are from the distribution center and must return to the distribution center after completing the distribution task. The expression (6) indicates that the number of vehicles is limited and the number of vehicles dispatched cannot exceed the number of vehicles owned by the company. Equation (7) indicates that the capacity of all customer orders on each delivery path cannot exceed the maximum capacity of the vehicle. Equation (8) is to eliminate the constraint of the vehicle path sub-loop. Expressions (9) and (10) are respectively calculation expressions for calculating the time for which the order is delayed to arrive and the vehicle exceeds the maximum time. And (3) the equation (11) is a decision variable value constraint.

S16, establishing a multi-stage mathematical model.

In the instant delivery problem, the arrival of customer orders is dynamic, requiring the enterprise to make multiple stages of decision optimization. In addition, the current decision of the enterprise affects the time for the vehicle to return to the distribution center, and further affects the decision of the next stage. For example, sending out more vehicles may improve the on-time delivery rate of orders, but may reduce the number of available vehicles at a later stage. Thus, when an enterprise makes a decision, it is likely that such a situation will arise: if a large number of customers place orders at this stage, more vehicles still remain to return to the distribution center without completing the last distribution task. At this time, the distribution center has too few available vehicles to meet the distribution requirements of too many customer orders. Therefore, the invention takes the vehicles which are carrying out the distribution tasks and do not return to the distribution center as potential available resources, and carries out order distribution and path planning on the premise of the available time of all vehicles.

From the above description, the logistics scenario after the decision of stage r may be divided into two types: existing available vehicles for distribution centers

And potentially available vehicles

For available vehicles

Its earliest time of availability is equal to the time node of the decision. For potentially usable vehicles

Their earliest time of availability equals the time they return to the distribution center. However, the randomness of the travel time results in randomness in the time the potentially available vehicles return to the distribution center. The available time information for potentially available vehicles is therefore uncertain for the decision of the enterprise.

Aiming at the researched instant delivery path problem, a multi-stage random vehicle path optimization model is established, and the target is as follows:

from a single stage point of view, the target formula is equivalent to formula (1). In addition, the multi-stage problem is required to satisfy not only the constraint conditions specified by the single-stage model but also the following constraints for each stage:

equation (13) indicates that the business will make decisions only during business hours. Equation (14) represents that each decision is only for customer orders that occur within this phase. 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 for the dispatched vehicle should be after its available time. And (17) is decision variable value constraint.

And S20, designing a solving method of the model.

S21, simulating heuristic method frame design;

the simulation heuristic method combines the meta heuristic algorithm and the simulation method to solve the random combinatorial optimization problem, has the advantages of flexibility and easy realization, and has been successfully applied to solving the random vehicle path problem. In the simulation heuristic method framework, the meta-heuristic algorithm is responsible for searching and updating the solution, and the simulation method is responsible for evaluating the solution obtained by the meta-heuristic algorithm. The simulation heuristic method framework designed by the invention is shown in figure 1.

The method for solving the random combinatorial optimization problem based on the simulation heuristic method has the following premise: an efficient meta-heuristic can solve a high-quality solution to the deterministic problem for the stochastic combinatorial optimization problem, and the high-quality solution to the deterministic problem is likely to be a high-quality solution to the stochastic problem as well. In the instant delivery path problem, the travel time is random and follows a normal distribution. Thus, in the design's simulation heuristic framework, the expected value of travel time is used instead of the random travel time to transform a random model with random travel time into a deterministic model.

Then, the invention designs an Improved Adaptive Large Neighborhood Search algorithm (IANLS) to solve the determined model on the basis of the Adaptive Large neighbor Search Algorithm (ALNS). During each iteration, the updated solution obtained by the IALNS needs to be simulated in a random environment to evaluate the quality of the solution. The simulation method adopted by the invention is Monte Carlo simulation. Considering the solving efficiency of the simulation heuristic method, only the updated solution accepted by the IALNS can be subjected to the rapid simulation process to calculateDesired target value of solution, and simulation number of times N of the stage _fs Less. In addition, the simulation heuristic method framework defines a size N _l The update sequence of (1) is used for storing the updated solution after the rapid simulation. When the number of solutions in the solution sequence is less than N _l And directly storing the updated solution into the database, and sequencing according to the expected target value. Otherwise, the updated solution needs to be compared with the last solution in the solution sequence, and the solution with the smaller desired value in the two solutions is retained in the solution sequence.

Finally, when the IALNS iteration is over, N is already stored in the solution sequence _l And the solution is possible to be the optimal solution of the stochastic model. At this point, the solution sequence undergoes a second round of simulation to calculate the desired target value for each solution. It is noted that compared to the first round of simulation, the number of simulation times N of the present round is _s Is far greater than N _fs To more accurately evaluate each solution.

S22, carrying out Monte Carlo simulation design;

in the problem model established, the travel time is random. Therefore, the method for calculating the expected target value of the solution by adopting the Monte Carlo simulation method mainly comprises the following three steps: 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, a desired target value of the solution is calculated. The detailed calculation steps are shown in table 2.

TABLE 2 Monte Carlo simulation calculation procedure

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

The invention designs an improved self-adaptive large neighborhood search algorithm. Firstly, the damage and repair operators are designed or improved according to the characteristics of the problem. Second, a local search process is added to the IALNS for the purpose of enhancing the local search capability of the algorithm. Finally, the disclaimer criterion of the solution in the Artificial Bee Colony Algorithm (ABC) replaces the simulated annealing criterion in the conventional aln. The basic flow of the IALNS is shown in table 3.

TABLE 3 IALNS basic flow

S231, coding design of solution

The problem is first solved using natural number coding, see fig. 2. If the question contains 6 customers, 3 cars, the solution to the question in this case can be represented by a sequence as shown in figure 2. The sequence between two values 0 represents the travel path of a vehicle, the first 0 value representing the start of the path, the second 0 value representing the end of the path, the non-0 values representing the customer number of the visit, the travel paths of all vehicles constituting a solution to the problem.

S232, initializing design;

due to the regular destruction and repair operators, ALNS can easily iterate from poor quality solutions to high quality solutions. Thus, the quality of the initial solution is not that important, which instead tends to cause the algorithm to converge prematurely and fall into local optimality. On the premise of ensuring the feasibility of the vehicle capacity, the invention adopts a simple insertion heuristic method to generate an initial solution, and the specific process is as follows: (1) generating an empty path sequence only comprising a vehicle starting point and a vehicle finishing point; (2) 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 result exceeds the preset value, turning to the step (1), otherwise, turning to the step (3); (3) judging the latest service time of two consecutive customers j, j +1 and customer i on the path, if LT _j <LT _i <LT _j+1 Then insert customer i between customer j and customer j + 1; (4) judging whether all customers are inserted into the path, if so, turning to the step (5), otherwise, turning to the step (2); (5) combining all sequences into the same sequence, and removing one of two adjacent 0 values in the sequence; (6) and 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.

S233, operator design is destroyed;

the damage operators used by the IALNS include a random removal operator, a path removal operator, a worst distance removal operator, a worst time removal operator, a similar removal operator, and a neighboring similar removal operator. In the destroy phase, the IALNS selects one of these operators to destroy the solution. The destroy operator will solve S from the current one _current In which a certain number of customers are removed and the removed customers are simultaneously deposited in the sequence C _remove Get the solution S after removing the customer _remove . Wherein the number of removed customers N _remove Has important influence on the solving performance of the algorithm. N is a radical of _remove Too large a value will slow the algorithm's solving speed, while too small a value will not help the algorithm jump out of local optimum. In the present invention, N _remove Associated with the number of customers n.

S2331, random removal: randomly selecting N from the current solution _remove Although the operator is simple to operate, the randomness of the removal of the customer points can greatly expand the search space of the solution, and the diversity of algorithm search is increased.

S2332, route removal: a sub-path of the solutions is randomly selected and all customer points in the sub-path are removed, which is advantageous for obtaining a solution with the least number of vehicles.

S2333, worst removal: defining cost of customer point i in current solution as cost (s, i) ═ Z(s) -Z _-i (s), wherein Z(s) is a target value for the current solution, and Z _-i (s) is the target value after removing customer point i. The worst removal operator requires first calculating the target value of the current solution and then calculating each customer pointThe removed target value is used for obtaining the cost of each customer point, finally, the customer point with the highest cost is selected from the current solution for removal, and the steps are repeated until N _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 ₆ |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 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 In (1). 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 1, this operator removes customers that are close in distanceAnd (4) point.

S234, repairing operator design;

repair phase IALNS selects a customer sequence C to be removed from a plurality of repair operators _remove Reinsertion into S _remove Thereby generating a current solution S _current Corresponding update solution S _upd8te . In the repair stage, the IALNS uses five repair operators, namely greedy insertion, regret insertion, distance greedy insertion, cost greedy insertion with noise disturbance and distance greedy insertion with noise disturbance.

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 in the solution are inserted.

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 in the solution are inserted.

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 . Selecting the position with the minimum distance increment to insert the customer, and repeating the steps until C _remove All customer points in the solution are inserted.

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 insertion mode with the lack of randomness easily causes the algorithm to be trapped in local optimization. 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 increment inserted in all positions, u is the noise parameter and r is [ -1,1]The random number in (c).

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.

S235, local search design;

after the damage and repair phase, the IALNS adds a local search phase, which is mainly to enhance the local search capability of the algorithm. At this stage, the algorithm chooses to use 2-opt or 3-opt for local search based on the length of the sub-paths, i.e., two customer points or three customer points are swapped for each sub-path in the solution to optimize the current solution. In essence, the IALNS selects one of a plurality of operators to perform iterative update of a solution in the damage and repair stage, so that although the known search space is enlarged, more randomness is brought, and the addition of a local search operator can make up for the defect to some extent, thereby balancing the search breadth and depth of the algorithm.

S236, designing a abandoning criterion of the solution;

a judgment criterion of simulated annealing is added in the traditional ALNS to accept a non-improved solution, namely when an updated solution generated in an iterative process is not superior to a current solution, an 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 stage of iteration, it is obviously not beneficial to the algorithm to search for a better solution in a local area. Therefore, the invention uses the idea of ABC abandoning solution to replace the simulated annealing criterion with a abandoning criterion in order to expect that the IALNS gets a better balance between the search depth and the search breadth.

The abandoning criterion is specifically that an updating solution is generated in each iteration process, if the updating solution is not superior to the current solution, the continuous times of non-improvement are increased by one, otherwise, the continuous times of non-improvement are returned to zero. When the number of continuous non-improvement times reaches the threshold value N _t The current solution is perturbed using a cross-exchange operator. The cross-exchange operator randomly selects two sub-paths in the solution, then respectively selects a section of continuous customer points from the two sub-paths, and finally exchanges the customer points selected on the two sub-paths. The operator diagram is shown in fig. 3.

And S237, designing an operator selection mechanism.

For the second damage operator and all the repair operators, the invention adopts a self-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 N is performed every time _s The weights and scores are updated once for each iteration. Each iteration algorithm selects a damage operator and a repair operator to update the solution according to the roulette rule, and records the number u of times of selecting the operator i _i The more heavily weighted operator is easier to select. And then giving different scores to the operators according to the quality of the updated solution obtained after each iteration. When the updated solution is superior to the global optimal solution, the score sigma is given to the damage and repair operator ₁ . Assigning a score σ when the updated solution is worse than the globally optimal solution but better than the current solution ₂ . When the updated solution is worse than the current solution, no score is assigned. When an N _s At the end of the sub-iteration, the weights of the operators are updated by using a formula as the next N _s Initial weight of the sub-iteration operator. While in the N _s Total score s obtained by sub-iteration operator _i And the number u of times of selection _i Return to zero. The formula is shown as (19), where ρ is a weight adjustment coefficient, which represents the importance degree of the historical weight and the operator expression when the operator weight is updated,

indicating the ith operator is at the r-th N _s The weight of the sub-iteration. By the formula, the operator weight is hooked with the historical expression of the operator weight, and the purpose of self-adaptive adjustment of the operator weight is achieved.

Experimental results and analysis:

the experimental contents of the invention are mainly divided into two parts: the two contents of the performance verification of the simulation heuristic method and the calculation and analysis of the instant distribution path optimization model respectively correspond to the following first embodiment and the second embodiment.

The first embodiment;

the solving performance of the simulation heuristic method based on the IALNS and the Monte Carlo simulation is greatly influenced by various parameters defined above, and the parameters set by the method are shown in Table 4.

TABLE 4 parameter settings

In the simulation heuristic method framework designed by the invention, Monte Carlo simulation is not an optimization method, and the solving performance of the simulation heuristic method mainly depends on IALNS. Therefore, this section first tests the deterministic problem of a single delivery phase of the problem under study, without considering the randomness of the vehicle travel time, to verify the solving effect of the IALNS algorithm. At the same time, we performed experiments using a well-known Solomon dataset and selected and compared the results obtained by the solver Gurobi. The Solomon data set is mainly generated aiming at the problem of vehicle paths 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), and a mixture of cluster and random distribution (labeled RC). In addition, in view of the solution efficiency of Gurobi, appropriate data is selected from the Solomon dataset to perform experiments while limiting the maximum solution time of Gurobi to 1800 seconds.

The experimental results are shown in table 5, the IALNS has significant advantages in operation time compared with Gurobi, and is equivalent to Gurobi in terms of solution accuracy, wherein the IALNS is superior to Gurobi in performance of the examples R103, C106 and C109. This fully demonstrates that the IALNS can get a better solution in a short time, showing good performance.

To further demonstrate the performance of IALAS, the same local search operation as IALNS was also added to standard ALNS. Meanwhile, for the sake of fairness of comparison, the IALNS and the ALNS both use the same damage and repair operators, and other parameter setting values are the same. The two algorithms firstly perform calculation of different iteration numbers on the solomon _100_ C101 data set, and then respectively calculate the final results of the calculation examples of C101, C102, C103, R101, R102, R103, RC101, RC102 and RC103 with 100 customer points, and the experimental results are shown in fig. 4 and fig. 5. The ABC abandoning criterion and the simulated annealing criterion have the main functions of improving the optimizing capability of the algorithm and avoiding the algorithm from falling into local optimization quickly. However, as can be seen from the results in the figure, the ABC abandonment criterion enables the IALNS to have higher solution accuracy, and the effect is obviously better than that of the IALNS.

TABLE 5 IALNS vs Gurobi calculation comparison

Example two

The invention converts data with 100 customer points in the Solomon data set. First, the business hours of the enterprise are divided into 10 phases, and the time length of each phase is 1 hour. Then, for each stage, 15 to 25 customers are randomly selected from 100 customer points as the customers for placing orders in the stage, and the time for placing orders is randomly generated within the time of the stage. Finally, we only retain the customer point coordinates, demand and vehicle capacity data in the example. And the latest delivery time of the customer is randomly generated by comprehensively considering the order placing time of the customer and the distance from the merchant to the customer. Finally, using C101, R101, and RC101 as reference examples, 4 different sets of multi-stage example sets were generated for each example, and a total of 12 sets of data sets were used in the current experiment.

For 12 calculation examples, numerical experiments under three scenes, namely determining the running time, randomly running the vehicle and not considering the experience influence of a distributor, randomly running the vehicle and considering the experience influence of the distributor, are respectively carried out by adopting a designed simulation heuristic method, and the three scenes respectively correspond to a scene one, a scene two and a scene three.

Taking the first-stage data of the C101_1 data set as an example, the driving paths under three experimental scenes are respectively calculated. Notably, the experience of the distributor is obtained after the total 10 stages of distribution tasks in this set of examples. As shown in fig. 6, the travel paths in all three experimental scenarios have large differences. When the travel time is random, customers who could otherwise be served by the latest time may be delayed in delivery. And delayed delivery will additionally increase penalty cost, which in turn leads to change of the optimal driving path of the deliverer. When the empirical influence of the dispatchers is further considered, the optimal delivery plan may be more inclined to distribute the customer orders to the more experienced dispatchers for delivery, thereby further causing the optimal delivery path to change. Therefore, it is necessary to consider randomness of the travel time and the influence of experience of the dispenser when planning the vehicle route.

TABLE 6 calculation results

The total cost of the 12 sets of the calculation examples in three different experimental scenarios and the variation thereof are reduced by 8.68% on average compared with the total cost of the scenario two in the case of the scenario one shown in table 6. The main reason for this is that when a comparable number of vehicles are dispatched, the cost of correction for taking into account the random travel time will be significantly lower, resulting in a lower overall cost of the dispatch. Meanwhile, the lower correction cost side shows that the punctual delivery rate of the commodity is higher. And compared with the second scenario, the total cost of the third scenario is reduced by 10.65% on average. From this result, it is known that, when a logistics distribution plan is prepared, the influence of random travel time and the experience of the distributor is considered, which is beneficial to reducing distribution cost and improving the on-time delivery rate of the commodities and the distribution efficiency of the distributor.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

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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