Research on optimization of manned robot swarm scheduling based on ant-sparrow algorithm

Considering the optimization problem of manned robot swarm scheduling in public environment, we constructed a demand-time-space-energy consumption scheduling model taking passenger waiting time and robot swarm energy consumption as optimization goals. This paper proposes an ant-sparrow algorithm based on the same number constraints colonies of ant and sparrow, which combines the advantages of ant colony algorithm great initial solution and the fast convergence speed of the sparrow search algorithm. After a limited number of initial iterations, the ant colony algorithm is transferred to the sparrow search algorithm. In order to increase the diversity of feasible solutions in the later stage of the ant-sparrow algorithm iteration, a divide-and-conquer strategy is introduced to divide the feasible solution sequence into the same small modules and solve them step by step. Applying it to the manned robot swarm scheduling service in the public environment, experiments show that the ant-sparrow algorithm introduced with a divide-and-conquer strategy can effectively improve the quality and convergence speed of feasible solutions.


Introduction
In recent years, the networked leasing business represented by shared transportation has been developing rapidly and has attracted widespread attention [1]. This has initiated the exploration of robotic swarm manned services in public environments. The coordinated operation of robot swarm deployed in public environment should meet the rapid response to the needs of passengers and minimize the energy consumption of the robot swarm. How to construct a collaborative robot swarm scheduling model and design a globally optimal and fast convergence algorithm is crucial for robotic swarm manned services scheduling problem [2].
At present, scholars have few researches on robotic manned services, and most of them are coordinated scheduling of cargo transportation [3][4][5]. The overall efficiency of cargo transportation is required to be high, while the individual response time of collaborative scheduling method does not need to be concerned. Aiming at the lack of parking space, traffic congestion, high energy consumption and high cost problems, Jelokhani [6] builds a spatiotemporal temporal matching model and proposes a new method based on GIS and ant colony, so as to find the best shared path and reduce traffic congestion better. In order to improve the flexibility and responsiveness of the flexible manufacturing system to customer needs, Maryam Mousavi et al. [7] adopt a hybrid GA-PSO method to evaluate the objective function value with the goal of optimizing the manufacturing time and the number of AGVs. The scheduling of numerical examples is evaluated before and after optimization, and the hybrid GA-PSO algorithm is superior to the other two algorithms. The multi-objective particle swarm algorithm, which is improved by Sasan Barak  manufacturing systems, has improved the efficiency of the system [8]. For the flexible job shop scheduling problem with energy consumption constraint, Lei D et al. [9] propose the imperialist competitive algorithm (ICA) to reduce the delay time and the total energy consumption with the goal of Makespan, total delay time and total energy consumption, which reduce delay time and energy consumption. At present, genetic algorithm, particle swarm algorithm, ant colony algorithm, empire competition algorithm have made great progress in solving cooperative scheduling problems with complex constraints [10][11]. Inspired by the sparrow foraging and anti-predation mode, Xue J proposes the sparrow search algorithm with the characteristics of high solution efficiency and wide search range to solve the continuous function optimization problem. However, due to the lack of effective operators for discrete scheduling problems, there are still problems such as slow convergence, insufficient search range or easy to get stuck at locally optimal value.
The robot serves passengers, and the service environment is a dense crowd environment. The optimization goal must not only consider traditional scheduling constraints, but also take into account factors such as passenger tolerance, emotion, and patience. Inspired by the above research ideas of domestic and foreign scholars, the algorithm for the optimization of the robot carrier service scheduling problem should meet the short response time and the lowest global energy consumption. For this purpose, a new type of robot swarm scheduling method is explored, demand-time-spaceenergy consumption scheduling model is designed to solve the problem by the combination of ant colony algorithm and improved sparrow search algorithm, namely ant-sparrow algorithm.

Description of the load task
The robots are denoted by the set , the total number is M, and the number of robots available for scheduling at the current moment is m. The passengers who need to carry the service are denoted by the set Robots are distributed in certain locations in the terminal building. In order to make the robot resources reasonably utilized, in the ( ) t t   time period, the passengers who need to be served and idle robots are placed in the scheduling pool for dispatch. Then in the scheduling pool, there is a limited set c N of manned mission plans, and each passenger needs to be bound to a robot. According to the robot and passenger's location and robot status information, robots are assigned by the system to serve the passengers. Assuming that j r is assigned to i p , the scheme of manned mission is defined as S . Among them, current position of the robot are denoted by ( , )

Robot population scheduling model
, ij z as 0, 1 variables, the i-th passenger carried by the j-th robot is denoted by =1 , voltage and current of the j-th robot are respectively denoted by ij u and ij i . The following demand-time-space-energy scheduling model is constructed by this paper, which includes the objective function and constraints.
Among them, the weight factors of robot moving distance, driving energy consumption, and service time in equation (1) are represented by 1 2 3 , , w w w respectively. Equation (2) x net represents the set of path networks built under the precondition of avoiding collision between the robot and the obstacle. Equation (3) represents the number of robots available for scheduling according to the current robot status information. Equation (4) represents the Manhattan distance between the robot and the passenger, and the length cost of the robot moving one grid is denoted by parameter C. Equation (5)- (8) indicates that a task can be implemented by only one manned robot at the same moment. Equation (9)-(12) represents the constraints on the range of motion of the robot and the passenger.

Solving algorithms
The ant colony algorithm is based on the probability function which is determined by the strength of the pheromone and the distance between different locations. As a result, the initial solution of the ant colony algorithm is better. However, the ant colony algorithm easily falls into local optimum and takes a long time for the algorithm to converge because of the large calculation of probability function. The sparrow search algorithm has a fast convergence and a wide search range, but the initial solution is highly randomized. In order to better solve the discrete scheduling optimization problem, it is difficult to break through with a single algorithm. Combining the advantages of the above two algorithms, an ant-sparrow algorithm is designed to solve the discrete scheduling optimization problem based on the constraint of the same number of ant colonies and sparrow colonies.

Convergence analysis of Ant-Sparrow optimization algorithm
The discrete optimization problem is described as , among them, x are denoted as n-dimensional vector of solutions in the feasible region S, ( ) g x is fitness functions in the feasible region S. * , min ( ) ( *) x g x g x    S , the optimal fitness value is denoted by The construction algorithm of the next generation of sparrow swarm is denoted by the following expression: ( 1) , among them , the k-th iteration of the sparrow swarm is denoted by ( ) X k , which is a M N  matrix. The size of the sparrow swarm is denoted by M , the length of the real encoding is denoted by N . The initial flock is denoted as (0) X . The state evolution matrix is denoted by D and is constructed in the following way. 11 12 1 , the next generation of sparrow swarm is selected from the pool of sparrow swarm formed by ( ) X k and ( 1) at the state of (k+1)-th generation '( 1) X k  is determined only by the state ( ) X k at the kth generation. Eventually, Definition 2 Given a Markov process  is denoted as the Markov process with the absorbing state property.
Proof 2 The next generation of sparrow swarm is selected by the ant-sparrow algorithm using a divide-and-conquer strategy to select the best individuals from the previous generation of sparrow swarm and the new sparrow swarm. Thus, the best feasible solution for each iteration will be selected and copied to the next generation. Hence, once the optimal solution * ( ) X k  x is searched by the antsparrow algorithm after the k-th iteration, then the optimal solution * x is also included in the sparrow swarm ' ( 1) X k  at the (k+1)-th iteration, * can be proved to satisfy the properties of absorbing state Markov process.
Definition 3 The ant-sparrow algorithm corresponds to the stochastic process , then the antsparrow algorithm converges with probability 1.
In summary, definition 3 is proven to be true and the ant-sparrow algorithm is convergent.

Introduction of divide-and-conquer strategy
Inspired by the partitioning idea of the quick sort algorithm, the divide-and-conquer strategy is introduced into the position transformation phase of the sparrow swarm, which is the partitioning of the feasible solution sequence into smaller scale identical modules and solving them step by step. "Conquering" is used in the quick sort algorithm to compare values within an array, while in this paper it is used to sparrow individual fitness function values. The schematic diagram of sequence ID swapping based on the divide-and-conquer strategy is shown in figure 1.   Figure 2 shows the steps of the ant-sparrow algorithm to solve the manned robotic swarm scheduling model.

Start
Initializing z ij ,w 1 ,w 2 ,w 3 Figure 2. Ant-sparrow algorithm flow chart.  The experiment takes a domestic airport terminal as an example. Figure 3 shows a domestic airport terminal floor plan drawn by MATLAB. In order to verify the performance when solving the robot collaborative scheduling problem, the experiment was conducted between the ant-sparrow algorithm and other six multi-objective optimization algorithms, such as GA, PSO, ACA and SSA. To ensure better fairness, the population size of each algorithm is set to 100, and the number of iterations is set to 300. Each algorithm is coded in the same way as the ant-sparrow algorithm.

Simulation experiments and results analysis
It is known that the annual throughput of an airport is about 100 million passengers, that is, the daily throughput is about 270,000 passengers. It can be seen that the daily throughput of a certain terminal is about 90,000, and the number of passengers arriving within 2 minutes at a certain time is about 50 to 75. The experiment is implemented in a certain terminal. At a certain moment, the demand for passenger flow in 2 minutes is assumed to be N1=20, and the number of idle robots is assumed to be M1=40 in experiment 1. The demand under the same conditions is assumed to be N2=20, and the number of idle robots is assumed to be M2=40 in experiment 2.

Experimental results and analysis
The following are the simulation conditions of this experiment. The traveling speed of the robot is 1~4 times the walking speed of the passenger, which is determined by It can be seen from Figure 4 that the ant-sparrow algorithm iterated 46 times to reach the optimum in experiment 1. The ant-sparrow algorithm converges to the optimum at a speed of 88 iterations in experiment 2. The convergence speed of the ant-sparrow algorithm and the quality of the solution are significantly better than other algorithms. Due to the divide-and-conquer strategy is used in the antsparrow algorithm to divide the feasible solution sequence into smaller-scale identical modules. This not only speeds up the convergence speed of the algorithm, but also improves the quality of feasible solutions.  Table 2 shows the energy consumption values required by different optimization algorithms to solve the scheduling model. Among them,  represents the ratio of the energy consumption value of the ant-sparrow algorithm solution model compared to the energy consumption value of other algorithms.