Reducing casualties and property losses through effective evacuation route planning has been a key focus for researchers in recent years. As part of this effort, an enhanced sparrow search algorithm (MSSA) was proposed. Firstly, the Golden Sine algorithm and a nonlinear weight factor optimization strategy were added in the discoverer position update stage of the SSA algorithm. Secondly, the Cauchy-Gaussian perturbation was applied to the optimal position of the SSA algorithm to improve its ability to jump out of local optima. Finally, the local search mechanism based on the mountain climbing method was incorporated into the local search stage of the SSA algorithm, improving its local search ability. To evaluate the effectiveness of the proposed algorithm, the Whale Algorithm, Gray Wolf Algorithm, Improved Gray Wolf Algorithm, Sparrow Search Algorithm, and MSSA Algorithm were employed to solve various test functions. The accuracy and convergence speed of each algorithm were then compared and analyzed. The results indicate that the MSSA algorithm has superior solving ability and stability compared to other algorithms. To further validate the enhanced algorithm’s capabilities for path planning, evacuation experiments were conducted using different maps featuring various obstacle types. Additionally, a multi-exit evacuation scenario was constructed according to the actual building environment of a teaching building. Both the sparrow search algorithm and MSSA algorithm were employed in the simulation experiment for multi-exit evacuation path planning. The findings demonstrate that the MSSA algorithm outperforms the comparison algorithm, showcasing its greater advantages and higher application potential.

With the rapid urbanization of China and the emergence of densely populated places, the large-scale crowd gathering activities such as cultural tourism, conference forums, and sports events are constantly increasing. However, the frequency of safety accidents associated with these gatherings has surged significantly. For instance, a serious stampede accident occurred during the Halloween activities of the Itaewon in Seoul on October 29th, 2022, and the high-density crowd could not be effectively and timely evacuated, resulting in 156 deaths. In the early morning of March 1st, 2022, a fire broke out at the Ramad Shopping Center in the Syrian capital Damascus, causing 14 fatalities and 4 injuries. Consequently, the planning and design of evacuation routes for crowds in such emergencies has become a major focus of research [

One key component in the field of evacuation path research is the path planning algorithm. Based on their characteristics, these algorithms can be categorized into classical intelligent optimization algorithms and heuristic intelligent optimization algorithms [

Inspired by the foraging and anti-predatory behavior of sparrows, Xue et al. designed the sparrow search algorithm (SSA) in 2020 [

Given the widespread application of the sparrow search algorithm in unmanned aerial vehicle trajectory planning, we aim to utilize this algorithm for personnel evacuation path planning. However, due to the different goals and application scenarios between the two types of application areas, the factors that the path algorithm needs to consider are also different. Drone trajectory planning [

The sparrow search algorithm can plan routes based on the current location, target location, obstacles and other information. It then optimizes decisions within the stochastic process using available information. However, the sparrow algorithm also possesses certain flaws and shortcomings. In the early stages of algorithm iteration, the search range is limited, and cannot perform effective global searches. And there is a risk of falling into local optimal solutions in the later stage of iteration. Therefore, there is scope for targeted optimization [

(1) The Golden Sine Cosine Algorithm and a nonlinear weight factor are introduced into the Sparrow Algorithm Producer Update Equation, thereby enhancing the global and local search capabilities of the discoverers.

(2) The Gaussian Cauchy perturbation strategy is added to the proposed algorithm, which is to improve its ability to escape local optima.

(3) The strategy of mountain climbing is presented to improve the local search ability of the SSA algorithm.

To evaluate the effectiveness of the improved algorithm, we conducted comparative experiments using five different algorithms, including the SSA algorithm, MSSA algorithm, WOA algorithm, GWO algorithm, and IGWO algorithm, to solve the standard test functions, aiming to verify and assess the effectiveness of the improved algorithm. Ultimately, the comparative experiments with the evacuation simulation model built by the grid method were carried out to prove the proposed algorithm’s potential for practical engineering applications.

The sparrow search algorithm [

The sparrows follow the discoverers, and the number of discoverers accounts for 10%–20% of the total population. The equation for updating the position of the discoverers in the sparrow search algorithm is shown in

In

Within the iteration cycle, the discoverer is the sparrow with the best position among individuals in the sparrow population, while the other sparrows act as followers and scouts. The equation for updating the positions of the followers is shown in

In

In

Within the sparrow population, 10% to 20% of individuals are responsible for reconnaissance and warning. In each iteration, sparrow individuals are randomly selected from discoverers and followers to become scouts. The equation for updating the scout’s position is shown in

In

The Golden Sine Algorithm, proposed by Tanyildizi et al. in 2017, is based on scanning within the unit circle of the sine function, similar to the spatial search for target solving [

The algorithm first randomly generates S population individual positions, corresponding to the potential solutions of the target problem. The equation for updating the position of the i-th individual is shown in

In

In

Based on the description of the Golden Sine algorithm, it can be seen that during the iteration process, the individual optimal position

On the basis of adding the golden sine algorithm, the algorithm further optimizes the location update method of the discoverers by introducing a nonlinear weight factor

In

Code |
---|

if R_{2} < ST |

for i = 1:recover_Num |

X(Index(i),:) = ω_{2} * pbest(Index(i),:) * abs(sin(r_{1}))- |

r_{2} * sin(r_{1}) * abs(c_{1} * gbest-c_{2} * pbest(Index(i),:)); % Discoverer location update |

fit(Index(i)) = fun(X(Index(i),:),G); % Update of fitness value |

end |

else |

X(Index(i),:) = pbest(Index(i),:) + randn(1) * ones(1, dim); % Fly to other places |

end |

Heuristic algorithms can effectively reduce the solving time and improve the operational efficiency of the algorithm. In this article, we propose the MSSA algorithm introduces the mountain climbing method as a local search strategy. Then the search accuracy of the individual optimal position and optimal fitness value of the sparrow population could be improved. When compared with the simulated annealing algorithm and tabu search algorithm, the mountain climbing method has the advantage of reducing algorithm runtime and improving algorithm efficiency. Incorporating the mountain climbing method as an optimization strategy for the optimal position generated by the iterative cycle can quickly traverse the area near the optimal position searched by the algorithm. However, the mountain climbing method may become trapped in local optima. Therefore, it is necessary to increase the ability to jump out of the current position while traversing the surrounding positions. To address this, a Gaussian-Cauchy perturbation strategy is incorporated into the optimal position. The implementation logic of this strategy is to increase the perturbation coefficient to the search range of the current loop optimal position when the mountain climbing method greedily traverses it. This perturbation coefficient can offer a probability of escaping the current optimal position and enhancing the search ability of the global optimal position.

The MSSA algorithm proposed in this article adopts a Gaussian-Cauchy perturbation strategy, which can combine these two types of perturbations. Before calculating the perturbation of the optimal position, a random number is generated. If the random number is greater than 0.5, Gaussian perturbation will be used for calculation. Conversely, if the random number is less than 0.5, Cauchy perturbation will be used. The obtained perturbation probability will participate in the greedy traversal search for the optimal position of the mountain climbing method. Both distributions can improve and enhance the algorithm’s capability to escape local optima when utilized for algorithm optimization. The code snippet for the Gaussian-Cauchy perturbation strategy is shown in

Code |
---|

if rand > 0.5 |

bestX_rct = gbest.*(1 + gauss); % Gaussian perturbation strategy |

else |

bestX_rct = gbest.*(1 + cauchy); % Cauchy perturbation strategy |

end |

This section combines the above four improvements with traditional SSA algorithms, including the Golden Sine Cosine Algorithm optimization strategy, nonlinear weight factor optimization strategy, mountain climbing local search strategy, and Gaussian Cauchy perturbation strategy. Then, an improved Sparrow Optimization Algorithm (MSSA) was proposed. Referring to the flowchart of the algorithms in the literature [

To evaluate the performance of the improved MSSA algorithm, the time complexity analysis was conducted. In this analysis,

After initialization, the algorithm enters the iteration loop stage, with

Since

Based on the above analysis, it can be concluded that the time complexity of the SSA algorithm and MSSA algorithm is of the same order of magnitude. MSSA algorithm not only enhances global search and local search capabilities, but also does not affect the actual operational efficiency of the algorithm.

The performance testing of intelligent optimization algorithms requires the application of the standard test functions and functionalized engineering problems. Speed and robustness should be assessed by comparing the results. The specific steps involve determining the performance of different intelligent optimization algorithms by comparing their optimal values, average values, and variance using standard test functions under the same experimental environment. Alternatively, by examining the optimal solution change curve of the algorithm during the iteration process, we could analyze which algorithm exhibits a faster descent speed from the origin to any number of iterations to assess their convergence speed. The above performance testing methods mainly evaluate the performance of intelligent optimization algorithms from two perspectives: computer resource consumption and the quality of results obtained. These criteria are vital for evaluating algorithm performance.

In response to the MSSA algorithm proposed in _{1}∼F_{5} are the unimodal test functions, and the functions F_{6}∼F_{10} represent multimodal testing functions. Additionally, the whale algorithm (WOA), grey wolf algorithm (GWO), and improved grey wolf algorithm (IGWO) integrating CS algorithm strategy are introduced for comparative testing of optimization capabilities. The test results are analyzed based on two criteria: optimization accuracy and convergence speed, which are aimed at verifying the effectiveness of the improved optimization strategy. To ensure accuracy, reliability and mitigate the impact of sporadic results on the evaluation of algorithm performance, the five algorithms participating in comparative analysis will undergo 50 repeated experiments. These experiments will analyze the optimal value, average value, and variance of the results. The optimal value of the search results reflects the upper limit of the search ability of each algorithm, i.e., the ability to approximate the optimal value of the test function. The average value represents the central value within the set of multiple search results, thereby avoiding the impact of accidental optimal results on the assessment of the algorithm’s search ability. By calculating the variance of the solution results, it is possible to visually assess the degree of dispersion in the distribution of each algorithm’s solution results, thereby reflecting the advantages and disadvantages of each algorithm. In addition, the simulation experiment software and hardware platforms used are consistent. The operating system is Windows 10, and the simulation software employed MATLAB R2018b.

Number | Function | Function dimension N | Variable value range S | Optimal value F |
---|---|---|---|---|

Unimodal test function | ||||

F_{1} |
Sphere Function | 30/60/90 | [−100;100]^{n} |
0 |

F_{2} |
Schwefel’s Problem 2.22 | 30/60/90 | [−10;10]^{n} |
0 |

F_{3} |
Schwefel’s Problem 1.2 | 30/60/90 | [−100;100]^{n} |
0 |

F_{4} |
Schwefel’s Problem 2.21 | 30/60/90 | [−100;100]^{n} |
0 |

F_{5} |
Generalized Rosenbrock’s Function | 30/60/90 | [−30;30]^{n} |
0 |

Multimodal test function | ||||

F_{6} |
Generalized Schwefel’s Problem 2.26 | 30/60/90 | [−500;500]^{n} |
−12569.5 |

F_{7} |
Generalized Rastrigin’s Function | 30/60/90 | [−5.12;5.12]^{n} |
0 |

F_{8} |
Ackley’s Function | 30/60/90 | [−32;32]^{n} |
0 |

F_{9} |
Generalized Griewank’s Function | 30/60/90 | [−600;600]^{n} |
0 |

F_{10} |
Generalized Penalized Function 1 | 30/60/90 | [−50;50]^{n} |
0 |

Function | Algorithm | d = 30 | d = 60 | d = 90 | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Optimal | Mean | Variance | Optimal | Mean | Variance | Optimal | Mean | Variance | ||

SSA | 1.25E − 18 | 8.72E − 66 | 7.61E − 13 | 0.00E + 00 | 2.09E − 18 | 4.35E − 35 | 4.23E − 15 | 1.14E − 68 | 1.31E − 135 | |

MSSA | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 8.17E − 97 | 6.01E − 192 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | |

F_{1} |
WOA | 5.19E − 72 | 8.11E − 62 | 6.57E − 12 | 2.34E − 71 | 7.74E − 66 | 4.96E − 130 | 5.22E − 71 | 1.27E − 58 | 1.61E − 115 |

GWO | 3.38E − 29 | 8.42E − 28 | 6.03E − 55 | 0.00E + 00 | 1.13E − 17 | 8.59E − 35 | 5.42E − 14 | 2.11E − 13 | 2.27E − 26 | |

IGWO | 8.30E − 35 | 3.17E − 33 | 2.23E − 65 | 0.00E + 00 | 6.57E − 22 | 1.31E − 42 | 1.07E − 17 | 6.86E − 17 | 2.55E − 33 | |

SSA | 6.60E − 67 | 6.94E − 37 | 3.00E − 72 | 1.63E − 79 | 3.16E − 34 | 9.07E − 67 | 2.55E − 73 | 1.03E − 34 | 1.06E − 67 | |

MSSA | 3.29E − 18 | 1.99E − 16 | 0.00E + 00 | 1.49E − 18 | 9.72E − 16 | 0.00E + 00 | 1.02E − 18 | 1.17E − 16 | 0.00E + 00 | |

F_{2} |
WOA | 5.21E − 54 | 8.62E − 48 | 6.35E − 94 | 1.43E − 54 | 3.28E − 47 | 5.94E − 93 | 1.89E − 52 | 4.44E − 44 | 8.65E − 87 |

GWO | 8.94E − 18 | 9.66E − 17 | 4.06E − 33 | 2.25E − 11 | 3.55E − 11 | 8.18E − 23 | 7.96E − 09 | 1.18E − 08 | 2.35E − 17 | |

IGWO | 2.03E − 21 | 1.96E − 20 | 4.23E − 40 | 5.77E − 14 | 1.55E − 13 | 6.33E − 27 | 4.39E − 11 | 7.89E − 11 | 1.63E − 21 | |

SSA | 1.25E − 12 | 3.12E − 54 | 9.74E − 11 | 2.64E − 28 | 1.34E − 56 | 1.75E − 111 | 1.81E − 23 | 4.36E − 64 | 1.88E − 126 | |

MSSA | 1.10E − 30 | 1.88E − 26 | 0.00E + 00 | 1.35E − 30 | 1.65E − 26 | 0.00E + 00 | 2.13E − 29 | 7.19E − 23 | 0.00E + 00 | |

F_{3} |
WOA | 1.78E + 04 | 5.21E + 04 | 2.12E + 08 | 2.40E + 05 | 3.77E + 05 | 7.60E + 09 | 2.66E + 05 | 4.10E + 05 | 1.91E + 10 |

GWO | 1.67E − 07 | 1.03E − 05 | 6.19E − 10 | 1.75E − 01 | 3.64E + 00 | 1.63E + 01 | 1.97E + 01 | 2.01E + 02 | 2.95E + 04 | |

IGWO | 9.74E − 10 | 2.48E − 07 | 3.65E − 13 | 3.73E − 04 | 3.35E − 01 | 6.63E − 01 | 1.58E − 01 | 1.45E + 02 | 2.45E + 04 | |

SSA | 3.34E − 76 | 4.36E − 37 | 1.65E − 72 | 1.75E − 11 | 2.34E − 40 | 5.49E − 79 | 7.14E − 10 | 2.35E − 41 | 5.55E − 81 | |

MSSA | 4.37E − 20 | 5.54E − 17 | 0.00E + 00 | 4.19E − 30 | 5.78E − 17 | 0.00E + 00 | 3.00E − 19 | 3.48E − 16 | 0.00E + 00 | |

F_{4} |
WOA | 1.77E + 01 | 5.76E + 01 | 4.52E + 02 | 6.42E + 01 | 8.51E + 01 | 7.61E + 01 | 1.12E + 01 | 6.19E + 01 | 1.11E + 03 |

GWO | 9.56E − 08 | 9.87E − 07 | 1.17E − 12 | 3.73E − 04 | 2.75E − 03 | 1.02E − 05 | 4.15E − 02 | 3.62E − 01 | 4.47E − 01 | |

IGWO | 6.92E − 10 | 5.76E − 09 | 3.33E − 17 | 1.55E − 05 | 5.28E − 05 | 4.78E − 10 | 1.30E − 03 | 5.46E − 03 | 4.68E − 05 | |

SSA | 7.12E − 07 | 5.51E − 05 | 6.75E − 09 | 9.01E − 05 | 2.61E − 04 | 2.34E − 08 | 5.00E − 08 | 1.79E − 04 | 7.41E − 08 | |

MSSA | 3.11E − 09 | 4.28E − 05 | 3.94E − 09 | 8.10E − 07 | 3.71E − 04 | 5.69E − 07 | 1.15E − 06 | 4.61E − 04 | 1.12E − 06 | |

F_{5} |
WOA | 2.77E + 01 | 2.82E + 01 | 2.00E − 01 | 5.77E + 01 | 5.84E + 01 | 7.78E − 02 | 8.82E + 01 | 8.84E + 01 | 1.59E − 02 |

GWO | 2.56E + 01 | 2.69E + 01 | 7.48E − 01 | 5.70E + 01 | 5.79E + 01 | 3.89E − 01 | 8.60E + 01 | 8.76E + 01 | 5.52E − 01 | |

IGWO | 2.63E + 01 | 2.71E + 01 | 3.22E − 01 | 5.69E + 01 | 5.77E + 01 | 5.02E − 01 | 8.61E + 01 | 8.80E + 01 | 6.51E − 01 | |

SSA | −8.97E + 03 | −7.90E + 03 | 4.36E + 05 | −1.58E + 04 | −1.48E + 04 | 7.21E + 05 | −2.37E + 04 | −2.17E + 04 | 2.23E + 06 | |

MSSA | −1.26E + 04 | −1.20E + 04 | 6.13E + 05 | −1.50E + 04 | −1.50E + 04 | 1.47E − 23 | −3.77E + 04 | −3.57E + 04 | 6.66E + 05 | |

F_{6} |
WOA | −1.25E + 04 | −9.83E + 03 | 2.47E + 06 | −2.51E + 04 | −2.17E + 04 | 1.55E + 07 | −3.64E + 04 | −2.77E + 04 | 1.20E + 07 |

GWO | −6.97E + 03 | −6.17E + 03 | 4.28E + 05 | −1.26E + 04 | −9.72E + 03 | 4.58E + 06 | −1.78E + 04 | −1.56E + 04 | 2.33E + 06 | |

IGWO | −5.07E + 03 | −4.43E + 03 | 1.71E + 05 | 1.12E + 04 | −8.04E + 03 | 4.99E + 06 | −1.48E + 04 | −1.16E + 04 | 2.96E + 06 | |

SSA | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | |

MSSA | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | |

F_{7} |
WOA | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 |

GWO | 5.68E − 14 | 7.44E − 01 | 4.07E + 00 | 1.59E − 12 | 3.97E + 00 | 1.59E + 01 | 8.29E − 11 | 3.56E + 00 | 1.44E + 01 | |

IGWO | 0.00E + 00 | 8.19E − 13 | 2.03E − 24 | 2.27E − 13 | 1.23E + 00 | 8.10E + 00 | 1.02E − 12 | 4.03E − 01 | 1.62E + 00 | |

SSA | 8.88E − 16 | 3.73E − 15 | 8.08E − 29 | 8.88E − 16 | 8.88E − 16 | 4.32E − 62 | 8.88E − 16 | 8.88E − 16 | 4.32E − 62 | |

MSSA | 8.88E − 16 | 8.88E − 16 | 4.32E − 62 | 8.88E − 16 | 8.88E − 16 | 4.32E − 62 | 8.88E − 16 | 8.88E − 16 | 4.32E − 62 | |

F_{8} |
WOA | 8.88E − 16 | 4.09E − 15 | 4.07E − 30 | 0.00E + 00 | 4.35E − 15 | 9.19E − 30 | 8.88E − 16 | 4.09E − 15 | 4.07E − 30 |

GWO | 7.90E − 14 | 9.82E − 14 | 1.04E − 28 | 1.84E − 10 | 4.70E − 10 | 5.96E − 20 | 8.33E − 10 | 5.75E − 08 | 1.69E − 15 | |

IGWO | 2.93E − 14 | 3.39E − 14 | 2.26E − 29 | 1.15E − 12 | 3.34E − 12 | 3.33E − 24 | 6.32E − 10 | 9.90E − 10 | 2.79E − 19 | |

SSA | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | |

MSSA | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | |

F_{9} |
WOA | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 | 0.00E + 00 |

GWO | 0.00E + 00 | 1.12E − 02 | 1.39E − 04 | 0.00E + 00 | 7.81E − 03 | 1.67E − 04 | 3.89E − 14 | 2.05E − 03 | 4.20E − 05 | |

IGWO | 0.00E + 00 | 1.54E − 03 | 2.38E − 05 | 0.00E + 00 | 2.31E − 03 | 5.32E − 05 | 0.00E + 00 | 3.73E − 03 | 6.20E − 05 | |

SSA | 1.01E − 11 | 1.42E − 03 | 2.01E − 05 | 5.43E − 10 | 9.48E − 09 | 1.26E − 16 | 7.82E − 10 | 5.57E − 08 | 1.73E − 14 | |

MSSA | 7.20E − 11 | 4.03E − 09 | 4.93E − 17 | 4.13E − 12 | 4.95E − 08 | 1.05E − 14 | 6.50E − 13 | 2.18E − 09 | 2.59E − 15 | |

F_{10} |
WOA | 3.42E − 02 | 1.14E − 01 | 3.30E − 02 | 0.00E + 00 | 4.35E − 15 | 9.19E − 30 | 4.70E − 02 | 9.15E − 02 | 2.09E − 03 |

GWO | 2.08E − 02 | 5.26E − 02 | 8.39E − 04 | 7.72E − 02 | 1.42E − 01 | 2.65E − 03 | 1.27E − 01 | 2.21E − 01 | 3.28E − 03 | |

IGWO | 1.08E − 02 | 3.34E − 02 | 2.84E − 04 | 5.21E − 02 | 1.02E − 01 | 1.71E − 03 | 1.72E − 01 | 2.25E − 01 | 1.71E03 |

To analyze the performance of the MSSA algorithm more intuitively, we compared the results (including optimal value, mean value, and variance) under identical conditions.

_{1}∼F_{10} intuitively illustrate that the MSSA algorithm exhibits rapid convergence speed and can quickly approach the optimal value of the function during the early stages of convergence, which has a significant advantage compared to other algorithms. By conducting a detailed analysis of the convergence curves, it can be concluded that the MSSA algorithm has a significant advantage in convergence speed during solving the functions F_{1}, F_{2}, F_{3}, F_{4}, F_{6}, F_{8}, F_{9}, and F_{10}. While solving the function F_{5}, the SSA algorithm initially exhibits slightly faster convergence speed than the MSSA algorithm. However, it becomes evident that the MSSA algorithm possesses a stronger ability to escape local optima and converge towards the optimal value faster after 200 iterations. Moreover, when solving the function F_{7}, there is no significant difference in convergence speed among the five algorithms during the initial iteration stage. However, in the middle of the iteration, all five algorithms fall into local optima, and the convergence curves become horizontal. In the later stage of the iteration, the MSSA algorithm outperforms others by successfully escaping local optima and approaching the optimal value, hereby exhibiting distinct advantages over other comparative algorithms.

Based on the achievement test of the improved algorithm in the fourth section, the path planning capability of the algorithm in evacuation scenarios is evaluated. Initially, the grid method is employed to construct evacuation path planning scenes with different types of obstacles. Subsequently, the five algorithms are utilized for path planning experiments, and the path results are compared and analyzed. Additionally, based on the actual teaching building environment, a simplified grid map is created. Consequently, the MSSA algorithm is then applied in multi-exit evacuation path planning simulation experiments to verify the improved algorithm’s evacuation path planning efficacy in multi-exit environments.

There are two types of map types set up in the simulation experiment. The obstacle layout of map 1 mainly considers the pathfinding ability of the test algorithm under the scattered distribution of obstacles, while the obstacle layout of map 2 mainly considers the pathfinding ability of the test algorithm in multi-corner terrain. Both maps are 40 grids * 40 grids in size, as depicted in

(1) Qualitative description of the optimal path

In the case of map 1, the optimal path planning results of five comparative algorithms are shown in

(2) Qualitative analysis of the optimal path

To avoid errors caused by a single simulation result, we used the above five intelligent algorithms to plan the path for map 1 with 50 times simulation. The results, including the optimal path length, average path length, iteration times of optimal path length, and minimum inflection points, are shown in

Algorithm | The optimal path length | Average path length | Iteration times of the optimal path length | Minimum inflection points |
---|---|---|---|---|

SSA | 125.5 | 129.6 | 196 | 50 |

MSSA | 68.7 | 70.1 | 78 | 25 |

WOA | 128.5 | 134.8 | 73 | 48 |

GWO | 120.1 | 125.4 | 195 | 48 |

IGWO | 110.3 | 113.5 | 185 | 47 |

With regard to the number of iterations required for the optimal paths, the order of iteration times from least to most is as follows: the WOA algorithm, the MSSA algorithm, the IGWO algorithm, the GWO algorithm, and the SSA algorithm. While the number of iterations of the MSSA algorithm is only 5 times more than that of the WOA algorithm, the average path distance planned by the MSSA is reduced by 47.99% compared to the WOA algorithm. It demonstrates that the WOA algorithm achieves fewer iterations at the expense of sacrificing path length. As for the number of inflection points in the path, the MSSA algorithm has the least number of inflection points, which is about half the number of inflection points given by other algorithms. The number of inflection points in the paths of SSA, WOA, GWO, and IGWO algorithms is in the range of 47 to 50. The path planning results visually demonstrate that these paths are not smooth. In summary, the path planning results of the MSSA algorithm in map 1 are significantly higher than other comparative algorithms.

(1) Qualitative description of the optimal path

The optimal path planning results of five comparative algorithms in map 2 are shown in

(2) Qualitative analysis of the optimal path

To avoid errors caused by a single simulation result, we used the above five intelligent algorithms to plan the path for map 2 with 50 times simulation. The results, including the optimal path length, average path length, iteration times of optimal path length, and minimum inflection points, are shown in

Algorithm | The optimal path length | Average path length | Iteration times of the optimal path length | Minimum inflection points |
---|---|---|---|---|

SSA | 101.4 | 104.5 | 168 | 31 |

MSSA | 56.3 | 59.6 | 48 | 10 |

WOA | 85.0 | 90.3 | 50 | 22 |

GWO | 90.3 | 96.5 | 113 | 28 |

IGWO | 72.1 | 76.5 | 185 | 21 |

In

Compared to the SSA algorithm, the WOA algorithm, the GWO algorithm, and the IGWO algorithm, the average path length planned by the MSSA algorithm is significantly shortened with 42.96%, 33.99%, 38.23%, and 22.09%, respectively. Although the MSSA algorithm’s advantage is slightly diminished in map 2 compared to map 1, it still surpasses other comparative algorithms. Concerning optimal path iteration times, the order of iteration times from least to most is MSSA, WOA, GWO, SSA, and IGWO. Meantime the MSSA algorithm has the least number of inflection points and the path is the smoothest. In summary, the path planning results of the MSSA algorithm in map 2 are significantly better than other comparative algorithms. The analysis of the path planning results for map 1 and map 2 demonstrates the high application value of the MSSA algorithm.

There are certain differences between the map scene in

The evacuation path planning results of the SSA algorithm and MSSA algorithm are shown in

From

The quantitative results of the evacuation path length planned by the SSA algorithm and MSSA algorithm are shown in

Algorithm | PA path length | PB path length | PC path length | PD path length |
---|---|---|---|---|

SSA | 39.2 | 35.1 | 33.2 | 32.1 |

MSSA | 33.4 | 30.7 | 28.6 | 28.6 |

The path planning results of the four evacuation exits demonstrate that the MSSA algorithm has significantly shortened the path length compared to the SSA algorithm, shown in

Evacuation path planning has always been a concern of researchers in the security field. This paper applies the sparrow search algorithm to solve this problem. Through several improvement strategies, the search ability and convergence speed of the sparrow search algorithm are improved. To enhance the global search ability, the Golden Sine Algorithm and nonlinear weight factor were introduced in the update stage of the discoverer’s position. To improve the local search ability, a mountain climbing mechanism was adopted for local search, while Gaussian-Cauchy perturbation was introduced to enhance the overall search accuracy and the capacity to jump out of the local optimal value. Then a series of standard function test sets were employed to evaluate the optimization ability of the proposed algorithm as well as the other four intelligent algorithms. The results, including the optimal value, mean value, and variance, showed that the MSSA algorithm exhibited good solving capabilities and stability compared to the other algorithms. Ultimately, the MSSA algorithm and other four comparison algorithms were applied to plan the evacuation paths on different evacuation maps using the gird method. The results include the optimal path length, average path length, iteration times of optimal path length, and minimum inflection points. Important results and conclusions are shown below:

(1) For map 1, compared with the other four comparison algorithms, the MSSA algorithm reduces the optimal path lengths by 45.25%, 46.53%, 42.79%, and 37.71%. Additionally, the MSSA algorithm reduces the average path lengths by 45.91%, 47.99%, 44.09%, and 38.23%.

(2) For map 2, compared with the other four comparison algorithms, the optimal path lengths planned by the MSSA algorithm are significantly shortened with 44.48%, 33.76%, 37.65%, and 21.9%. Moreover, the average path lengths planned by the MSSA algorithm are significantly reduced with 42.96%, 33.99%, 38.23%, and 22.09%, respectively.

(3) In the multi-exit evacuation scenario, compared with the results planned by the original SSA algorithm, the lengths of PA, PB, PC, and PD paths show that the MSSA algorithm reduces the path lengths by 14.8%, 12.5%, 13.9%, and 10.9%, separately.

These results demonstrate that the MSSA algorithm had significant advantages in evacuation path planning over the comparative algorithm, with strong potential for practical applications. However, there are still some limitations in this study. The advantage of the MSSA algorithm compared to the SSA algorithm is not obvious when solving the fixed dimension test function. Additionally, the current research primarily focuses on optimizing path length, neglecting the multi-objective optimization problem and three-dimensional spatial environment, which aligns more closely with real-world demands.

The authors wish to express their appreciation to the reviewers for their helpful suggestions which greatly improved the presentation of this paper.

The present study was supported by National Natural Science Foundation of China (71904006), Henan Province Key R&D Special Project (231111322200), the Science and Technology Research Plan of Henan Province (232102320043, 232102320232, 232102320046), the Natural Science Foundation of Henan (232300420317, 232300420314).

Xiaoge Wei: Conceptualization, Writing—original draft, Methodology, Funding acquisition; Yuming Zhang: Conceptualization, Data curation, Data analysis; Huaitao Song: Writing—review & editing, Funding acquisition; Hengjie Qin: Writing—review & editing; Guanjun Zhao: Writing—review & editing. All authors have read and agreed to the published version of the manuscript.

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

The authors declare that they have no conflicts of interest to report regarding the present study.