Multiobjective evacuation routes optimization problem is defined to find out optimal evacuation routes for a group of evacuees under multiple evacuation objectives. For improving the evacuation efficiency, we abstracted the evacuation zone as a superposed potential field network (SPFN), and we presented SPFNbased ACO algorithm (SPFNACO) to solve this problem based on the proposed model. In Wuhan Sports Center case, we compared SPFNACO algorithm with HMERPACO algorithm and traditional ACO algorithm under three evacuation objectives, namely, total evacuation time, total evacuation route length, and cumulative congestion degree. The experimental results show that SPFNACO algorithm has a better performance while comparing with HMERPACO algorithm and traditional ACO algorithm for solving multiobjective evacuation routes optimization problem.
The evacuation planning in largescale public area usually possesses two difficult points:
large scale: the largescale public area has a complex flat structure. And it can hold thousands of people.
multisource and multisink: in evacuation process, the evacuees often start at different places in public area and run away from different exits.
In a word, the evacuation planning in largescale public area is a challenging problem. For solving this problem, researchers have put forward some effective methods. Shi et al. [
The remainder of this paper is organized as follows. Section
People in largescale public areas are in danger because of a lot of manmade or natural accidents, such as fire, hurricane, and bomb [
Besides, evacuation routes optimization problem usually needs to consider multiple objectives, such as total clearance time [
In this paper, the evacuation zone is divided into many subzones. Each evacuation plan is composed of each evacuee’s route. So each evacuation plan
Thus, the multiobjective evacuation routes optimization problem in this paper could be formulated as in Algorithm
Finding the pareto optimal set [
plans, make
Subject to
where,
time step,
The evacuation routes optimization problem involves three objectives that need to be achieved simultaneously, namely, minimization of total evacuation time, minimization of total evacuation route length, and minimization of cumulative congestion degree.
Total evacuation time (TET) is given by
Total evacuation route length (TERL) is given by
Cumulative congestion degree (CCD) is given by
The electric potential field of the point charge is shown in Figure
Potential field of point charge.
Positive point charge
Negative point charge
The center point of the stadium could be seen as a positive point charge, and each exit could be seen as a negative point charge. The Wuhan Sports Center (Figure
Wuhan Sports Center (
Based on the superposed potential, we proposed the superposed potential field network (SPFN) to abstract the stadium. This model is partly based on the point model used in [
The stadium is divided into 157 subzones. Each subzone is abstracted as a node in SPFN. Each link between two nodes represents a connection relationship between two subzones. The potential of each node is the potential of the center point of the corresponding subzone. The capacity of each node is the capacity of the corresponding subzone. The coordinate of each node is the coordinate of the center point of the corresponding subzone. If an evacuee or a group of evacuees is seen as a positive test charge, it would always move from high potential node to low potential node. There are 216 links and 157 nodes in the SPFN of the Wuhan Sports Center stadium, including 10 exits nodes and 42 bleachers nodes. Figure
Potential distribution of SPFN of Wuhan Sports Center stadium.
For solving the multiobjective evacuation routes optimization problem mentioned in Section
The main procedure of SPFNACO algorithm is listed in Algorithm
The
construct new population
The main procedure of Superposed Potential Field Based Wheel Method is listed in Algorithm
For each PV, there is a corresponding evacuation plan generated as follows:
The capacity constraint is given by
The potential constraint is given by
The procedure of superposed potential field based roulette wheel method is shown in Algorithm
The distance
where,
The allowed visit neighbor node
where,
The transition probability
where,
under
vector, at
the pheromone and the heuristic information.
The heuristic information
where,
According to roulette wheel selection, the node
probability, which is given by:
Besides, we rule that
An example to show the superposed potential field based roulette wheel method.
When the interim destination node is selected, the ant
We define a concept called remaining distance to interim destination node to measure whether the ant
The pheromone on each link between nodes is updated by
In this paper, we took a 20000 evacuees’ drill in Wuhan Sports Center Stadium as an example to do simulation experiment. This stadium has 42 bleachers subzones and 10 exits subzones. Ants are randomly allocated to 42 bleachers subzones, and each ant represents 100 evacuees. The maximum speed of each ant is 2 m/s [
Parameter values in SPFNACO, HMERPACO, and ACO.










200  10  2 m/s  25 s  1  3  0.5  200  100 
Figure
Figure
Evacuation curves of the three algorithms.
Figure
Timevarying congestion degrees in three algorithms.
SPFNACO
HMERPACO
ACO
Figure
The natural logarithm of hypervolume for three algorithms.
SPFNACO
HMERPACO
ACO
Figure
The proportion of nondominated plans derived from three algorithms.
We proposed a multiobjective optimization algorithm of the evacuation routes SPFNACO, which is based on the organization of the evacuees’ spacetime paths within a superposed potential field network (SPFN). The ACO algorithm organizes evacuees’ spacetime paths without any domain knowledge that can help improve evacuation efficiency; the HMERPACO algorithm merely employs one promotive factor for improving evacuation efficiency; the SPFN efficiently combines two factors together, which can facilitate the raise of evacuation efficiency by reasonably organizing the evacuees’ spacetime paths. By validation of simulation experiment, compared with HMERPACO and ACO algorithms, the SPFNACO algorithm is more suitable to solve the multiobjective optimization problem of the evacuation routes.
It is planned to do further researches on the basis of SPFNACO, such as defining more realistic evacuation scenarios, studying the effects of grouping size of evacuees and the total number of evacuees on evacuation efficiency, and discussing the influences of the population size of pheromone vectors and the number of evolution generations on algorithm performance.
This work was supported in part by the National Science Foundation of China under Grant nos. 61170202, 40971233, and 61202287.