Multiobjective Optimization of Evacuation Routes in Stadium Using Superposed Potential Field Network Based ACO

Algorithm 2

Procedure of SPFN-ACO.

S1. Initializes initial PVs population 𝑃₀ as all-zero vectors. The population size of 𝑃₀ is 2∗𝑁_𝑝. The number of ants is 𝑁_𝐴. 𝑚=1.

S2. For each PV, do:

 S2.1. Each ants simultaneously finds its evacuation route under current PV by Simulation of Evacuation Process;

 S2.2. All ants’ routes construct the corresponding evacuation plan under current PV and the objectives’ values

 of this plan are calculated.

S3. Non-dominated sort 2∗𝑁_𝑝PVs according to corresponding route plan’s objectives. And, select the top 𝑁_𝑝PVs.

S4. Update top 𝑁_𝑝PVs. The updated top 𝑁_𝑝PVs construct PVs population 𝑃_𝑚

S5. 𝑚=𝑚+1.

S6. For each PV in 𝑃_𝑚−1, do:

 S6.1. Each ants simultaneously finds its evacuation route under current PV by Simulation of Evacuation Process;

 S6.2. All ants’ routes construct the corresponding evacuation plan under current PV and the objectives’ values of this plan are

 calculated.

S7. Update 𝑁_𝑝 pheromone vectors in 𝑃_𝑚−1. The updated top 𝑁_𝑝 pheromone vectors construct pheromone vectors population 𝑄_𝑚.

The 𝑃_𝑚−1 and 𝑄_𝑚 construct 𝑅_𝑚, namely 𝑅_𝑚=𝑃_𝑚−1∪𝑄_𝑚. The population size of 𝑅_𝑚 is 2∗𝑁_𝑝.

S8. Non-dominated sort 𝑅_𝑚 according to corresponding route plan’s objectives. And, select the top 𝑁_𝑝 pheromone vectors to

construct new population 𝑃_𝑚.

S9. If 𝑚⩽𝑚_Max, go to S5. Or else, terminate the algorithm and output final Pareto optimal set of evacuation plans.

Note: 𝑚 is the number of generations; 𝑚_Max is the maximum number of generations.