# Evacuation Planning Optimization Based on a Multi-Objective Artificial Bee Colony Algorithm

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## Abstract

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^{8}for distance function, within 161 s of execution time. Additionally, in this research we compare the proposed algorithm with Non-Dominated Sorting Genetic Algorithm II and the existing Multi-Objective Artificial Bee Colony algorithm. The experimental results show that the proposed MOABC outperforms the current methods both in terms of computational time and better solutions with minimum fitness values. Therefore, developing MOABC is recommended for applications such as evacuation planning, where a fast-running and efficient model is needed.

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Multi-Objective Optimization Problem

_{m}) is a vector of decision variable, xi ≥ 0, for i = 1, 2, …, m [12,46].

#### 2.2. Mathematical Model for Evacuation Planning

#### 2.3. Introduction to Artificial Bee Colony Algorithm

_{id}is a real number selected randomly from the interval [−1, 1]; K is the index of food sources, which is different from i; P

_{i}is a probability of the ith food source being selected by an onlooker bee; fit

_{i}is the fitness; and SN is the number of food sources. In ABC, the numbers of worker bees and onlookers are equal to SN (half of the N population): $N=2\times SN.$

## 3. Methodology

#### 3.1. Modified ABC Algorithm for Multi-Objective Evacuation Problem

#### 3.2. Encoding and Initialization of Solutions

#### 3.3. Neighborhood Search Strategies

#### 3.4. Crossover Operator

#### 3.5. Selection of Onlooker Bees

#### 3.6. Exploration of the Scout Bees

#### 3.7. Pareto Optimization for Evaluation Fitness

## 4. Case Study

^{2}[52]. The city is characterized by steep hills separated by valleys. Due to its landscape and intense rainfall, many areas of the city are prone to floods and landslides [53]. Both landslides and flood disasters in Kigali caused a total of 64 deaths, 7953 injured people, and 280 houses destroyed between 2005 and 2013 [54]. An evacuation planning process is relatively nonexistent. Thus, evacuation planning is much needed in Kigali.

#### 4.1. Input Data Preparation

#### 4.1.1. Safe Area Selection and Capacity Computation

^{2}of covered living space per person is considered adequate, excluding cooking and hygiene facilities [56]. Safe areas considered as rescue locations in the study area were determined by setting some criteria based on the international standards of evacuation planning of flood and landslide hazards. By using GIS tools and functions, we selected some open spaces, schools, and churches that met the suitability criteria. The criteria included being located outside of any zone prone to any disaster, being located on low slopes, and having access to resources including water sanitation, food, electricity, and toilets. Therefore, 10 places were selected, with the capacity of hosting 134,462 people. The estimation of 3.5 m

^{2}/person was used to limit the crowding density within safe areas. Figure 6 shows the case study area (a) and the 10 shelter areas (b).

#### 4.1.2. Distance Matrix

## 5. Results and Discussion

#### 5.1. Parameter Setting

#### 5.2. Effectiveness of Combining Neighborhood Search Random Swap and Random Insertion and Crossover Operator for MOABC

#### 5.3. Pareto Optimal Front Analysis

#### 5.4. Optimization Results Analysis

#### 5.5. Comparison with Other Algorithms

#### 5.6. Sensitivity Analyses

#### 5.6.1. Impact of Parameters

#### 5.6.2. Repeatability Analysis

#### 5.7. Potential Use of the Proposed MOABC

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Main steps of the proposed Multi-Objective Artificial Bee Colony (MOABC) for evacuation planning.

**Figure 4.**A neighbor bee generated by neighborhood search operator random insertion (RI) (gray) and random swap (RS) (orange).

**Figure 5.**Crossover operator for sharing information among worker bees. An example of two worker bees (parent1 and parent2) exchange index of points (orange) to generate new worker bees (child1 and child2; gray).

**Figure 6.**Maps of (

**a**) the geographical location of the selected sectors of the city of Kigali, and (

**b**) the candidate shelters and residential blocks of the selected study area.

**Figure 7.**Parameter analysis. The optimal Pareto fronts when (

**a**) the population size ranges from 20 to 80; (

**b**) the parameter limit is set to population size, which is population size times the dimension size and times 100; (

**c)**the crossover probability ranges from 0.5 to 1; and (

**d**) the tournament size ranges from 2 to 4.

**Figure 9.**Fitness variation in the best values with number of generations. (

**a**) Fitness value of capacity function, and (

**b**) distance function found by methods A, B, and D.

**Figure 12.**Improvement of optimum solutions through generations. The gray lines on the left side of each graph represent the allocation of shelters. The numbers of building blocks assigned to shelters are presented on the right side of each graph (pie chart). (

**a**) Optimal allocation and minimum fitness value obtained from one generation; (

**b**) optimal allocation and minimum fitness values of the 50th generation; (

**c**) optimal allocation and minimum fitness values of the 150th generation; (

**d**) optimal allocation and minimum fitness values of the 250th generation; (

**e**) optimal allocation and minimum fitness values of the 350th generation, and (

**f**) optimal allocation and minimum fitness values of the 500th generation.

**Figure 13.**The Pareto-optimal fronts generated by: (

**a**) the standard MOABC; (

**b**) NSGA-II; and (

**c**) the proposed MOABC. The standardized minimum fitness values of both capacity and distance function.

**Figure 14.**The convergence process for different generations of (

**a**) standard MOABC; (

**b**) NSGA-II; and (

**c**) the proposed MOABC.

**Figure 16.**Repeatability of the proposed MOABC algorithm from five runs. (

**a**) Variation of Pareto front size with numbers of generations; (

**b**) fitness variation of five runs.

**Table 1.**Parameter settings of the Multi-Objective Artificial Bee Colony (MOABC) algorithm in the study.

Parameter | Value |
---|---|

Population size | 20 |

Limit | N × D × 100 |

Crossover probability rate | 0.5 |

Tournament size | 3 |

Maximum number of generations | 500 |

**Table 2.**Comparison of results obtained using different methods. RS—random swap; RI—random insertion.

Method | Algorithm | Population Size | Number of Generations | Final Pareto Front Size | Fcapacity | Fdistance | Execution Time (s) |
---|---|---|---|---|---|---|---|

A | MOABC with Combination of RS and RI | 20 | 500 | 8 | 3.44 | 9.29 × 10^{8} | 199 |

B | MOABC with the basic local search strategy | 20 | 500 | 3 | 3.96 | 8.61 × 10^{8} | 274 |

C | MOABC with crossover operator | 20 | 500 | 8 | 3.44 | 9.29 × 10^{8} | 199 |

D | MOABC without a crossover operator | 20 | 500 | 4 | 6.02 | 9.04 × 10^{8} | 193 |

Algorithm | Minimum Fitness Value of Fcapacity | Minimum Fitness Value of Fdistance | Execution Time (s) |
---|---|---|---|

Standard MOABC | 49.0 | 1.18 × 10^{9} | 163 |

NSGA-II | 38.9 | 1.08 × 10^{9} | 1971 |

Proposed MOABC | 5.8 | 8.72 × 10^{8} | 161 |

Run | Population Size | Number of Generations | Final Pareto Front Size | Fitness Value of Fcapacity | Fitness Value of Fdistance | Variance (Fcapacity) | Variance (Fdistance) |
---|---|---|---|---|---|---|---|

1 | 20 | 500 | 4 | 4.73 | 8.84 × 10^{8} | 0.056 | 0.080 |

2 | 20 | 500 | 6 | 5.85 | 8.89 × 10^{8} | 0.051 | 0.086 |

3 | 20 | 500 | 4 | 5.62 | 8.83 × 10^{8} | 0.058 | 0.080 |

4 | 20 | 500 | 8 | 5.1 | 8.87 × 10^{8} | 0.057 | 0.082 |

5 | 20 | 500 | 4 | 6.29 | 8.91 × 10^{8} | 0.053 | 0.082 |

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**MDPI and ACS Style**

Niyomubyeyi, O.; Pilesjö, P.; Mansourian, A.
Evacuation Planning Optimization Based on a Multi-Objective Artificial Bee Colony Algorithm. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 110.
https://doi.org/10.3390/ijgi8030110

**AMA Style**

Niyomubyeyi O, Pilesjö P, Mansourian A.
Evacuation Planning Optimization Based on a Multi-Objective Artificial Bee Colony Algorithm. *ISPRS International Journal of Geo-Information*. 2019; 8(3):110.
https://doi.org/10.3390/ijgi8030110

**Chicago/Turabian Style**

Niyomubyeyi, Olive, Petter Pilesjö, and Ali Mansourian.
2019. "Evacuation Planning Optimization Based on a Multi-Objective Artificial Bee Colony Algorithm" *ISPRS International Journal of Geo-Information* 8, no. 3: 110.
https://doi.org/10.3390/ijgi8030110