^{1}

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This study treats the determination of routes for evacuation on foot in earthquake disasters as a multi-objective optimization problem, and aims to propose a method for quantitatively searching for evacuation routes using a multi-objective genetic algorithm (multi-objective GA) and GIS. The conclusions can be summarized in the following three points. 1) A GA was used to design and create an evacuation route search algorithm which solves the problem of the optimization of earthquake disaster evacuation routes by treating it as an optimization problem with multiple objectives, such as evacuation distance and evacuation time. 2) In this method, goodness of fit is set by using a Pareto ranking method to determine the ranking of individuals based on their relative superiorities and inferiorities. 3) In this method, searching for evacuation routes based on the information on present conditions allows evacuation routes to be derived based on present building and road locations. Further, this method is based on publicly available information; therefore, obtaining geographic information similar to that of this study enables this method to be effective regardless of what region it is applied to, or whether the data regards the past or the future. Therefore, this method has high degree of spatial and temporal reproducibility.

Based on experiences in the Great Hanshin Earthquake (1995) and the Great East Japan Earthquake (2011), in recent years in Japan, reduction of the effects of natural disasters through self-help and mutual help is being emphasized, and effort is being put into the formulation of evacuation plans by independent disaster prevention organizations and the like. In 2011, in “Towards Reconstruction” [

Based on the above-mentioned background, this study treats the determination of routes for evacuation on foot in earthquake disasters as a multi-objective optimization problem, and aims to propose a method for quantitatively searching for evacuation routes using a multi-objective genetic algorithm (multi-objective GA). Further, the method of this study is applied to the region studied, and multiple evacuation route candidates that are derived are visualized on a digital map using GIS and evaluated. This study aims to use the method to derive routes in order to efficiently provide information for natural disaster reduction efforts carried out through self- help and mutual help—that is, to efficiently provide information for the formulation of evacuation plans by individuals and independent disaster prevention organizations.

This study is related to 1) Evacuation routes; 2) Optimal solution searches using GA; 3) Spatial analysis using GIS; and 4) Multi-objective optimization problems. The study by Liu et al. (2006) [

As examples of research related to (2), Inoue et al. (2013) [

4) In the area of research regarding multi-objective optimization problems, there are many studies which have conducted optimal solution searches using a multi-objective GA. These searches apply the GA multipoint search feature. Hara et al. (2006) [

Based on the results of the above-mentioned related research, this study demonstrates uniqueness and value in the field of disaster research in that it aims to use a multi-objective GA to quantitatively search for evacuation routes, in order to provide effective information for evacuation plan formulation carried out using self-help and mutual help methods, which are more direct forms of natural disaster reduction help; that is, it aims to use a multi-objective GA to quantitatively search for evacuation routes in order to provide effective information for evacuation plan formulation by individual evacuees and regional disaster prevention organizations.

In Section 4, the challenges of avoiding each of the various causes of obstruction of evacuation are set as the objectives in the evacuation route optimization, and in order to solve the multi-objective optimization problem of optimizing these objectives, an evacuation route search algorithm which employs a GA is designed and created. In Section 5, road network data for the district studied is created using GIS, and information about obstructions which occur during evacuation is added to this data for each road. In Section 6, an evacuation route search algorithm is applied to the road network that was created, evacuation starting points and destinations are set, and an evaluation experiment is performed. Further, the convergence of evaluation values for each objective is examined, and whether or not an effective search is being conducted or not is investigated. In Section 7, the parameters which resulted in the most effective search in Section 6 are applied to the GA, and an evacuation route search is conducted again. Further, the routes derived are visualized in GIS, and superposed with information for each road, such as information on blockage probability. This allows a visual evaluation to be performed, and superior routes are proposed. Additionally, Esri Inc.’s ArcGIS Ver. 10.1 is used as the GIS. The GIS is used to create road network data, perform spatial analysis, and visualize evacuation route search results.

The district chosen for study was the northern part of Sumida City (

Python 2.7 was used as the programming language for the design of the evacuation route search algorithm.

1) Acquisition of internodal adjacent information and road link information

Change the CSV data of the node-related adjacent information and the CSV data of the road link information into list form, and input the data into the GA.

2) Genetic coding

Determine how each of the routes, which are individuals, will be expressed in the GA.

3) Generation of initial population

Randomly generate a number of routes equal to the population size (the number of individuals which are to be in the population) and form the initial population.

4) Goodness-of-fit evaluation employing the Pareto ranking method

Using the evaluation values for each objective (road information), calculate goodness-of-fit of each route based on the Pareto ranking method.

5) Sharing

To the goodness-of-fit calculated in (4), add revisions which take into account similarities between individuals, and create a new goodness-of-fit.

6) Selection/Culling

Based on the goodness-of-fit to which revisions were added in (5), determine which routes to preserve for the next generation. As a selection method, use a combination of roulette-wheel selection and the preservation of Pareto strategy (elite preservation strategy in a single-objective optimization GA).

7) Crossover

Select two routes from the population to be parents, and by crossing these over at a crossover point, generate two routes which are children.

8) Mutation

Select one route from the population, and once again randomly generate routes at and after the mutation point, in order to generate new routes.

1) Creation of adjacency list

Transform CSV data which contains the internodal adjacency relationships into adjacency list form, and input it into the GA. Concerning the adjacency list, it is given a triple structure, node numbers are made to correspond with the adjacency list index, and adjacency information is stored. As adjacency information, node numbers adjacent to each node and link numbers which link nodes are stored.

2) Creation of road link information list

A link list, formed by transforming CSV data containing road link information into a list, is input into the GA. When this is done, link numbers are made to correspond with the link list index, and road information is stored.

This study deals with routes; therefore, the order of node numbers, which forms routes, is an issue. Therefore, in this study, genetic coding is performed using path expression. Path expression is a method in which genes are node numbers, and routes are expressed by lists arranged in the order in which node numbers are passed through. Path expression can be said to be the most natural method. Further, since lists express routes as is, path expression is characterized by the fact that decoding from genotype to phenotype is not necessary. Gene length varies with the number of nodes passed through; therefore, it is variable.

A number of the individuals coded in the previous section that is equal to the population size number N is randomly generated to form the initial population. The population is represented as a list with a dual structure. In order to prevent routes from looping, nodes which have already been passed through are not used. Further, individuals are generated based on the adjacency list created in Section 4.2.1, and this ensures that only feasible solutions—that is, only routes that are connected—are generated. In this method, the genetic operations of selection/culling, crossing, and mutation are performed on the population generated in the manner described above.

1) Determination of evaluation values regarding each objective

In this study, the four objectives of reduction of evacuation distance increase in the probability of arriving at the destination which takes road blockages into account, avoidance of hazard caused by fire, and reduction of evacuation time were taken into account in evacuation route optimization. Therefore, firstly, for all individuals, evaluation values for each objective (distance, arrival probability, degree of fire hazard in roads, and estimated evacuation time) were defined using the undermentioned Equations (1) to (3) and (6).

a) Evaluation value for distance

The evaluation value for distance was found as the total evacuation distance to the destination, using the following Equation (1).

_{i} [m];

_{i} passes through [m];

_{i} passes through;

b) Evaluation value for arrival probability

Concerning the evaluation value for arrival probability: For each link, the probability of being able to pass through the link was calculated based on the probability of road blockage for the link. The probability that it would be possible to pass through all road links in the route was the arrival probability. The evaluation value for arrival probability was found as an evaluation value for these probabilities.

_{i};

_{i} passes through;

_{i} passes through will be passable;

_{i} passes through.

c) Evaluation value for degree of fire hazard in roads

The evaluation value for the degree of fire hazard in roads is the sum total of the degree of fire hazard in roads for each link, and is found using Equation (3).

_{i};

_{i} passes through;

_{i} passes through.

d) Evaluation value for estimated evacuation time

The evaluation value for estimated evacuation time is the sum total of the periods of time an evacuee spends passing through links, and is calculated based on the distance, road width, and estimated evacuation population in the road for each link. Based on material from the Urban Disaster Prevention Office of the City Bureau of the Ministry of Construction (1997) [

Here, the evacuation population density indicates the number of people that can evacuate per 1 m^{2}. Generally, one person per square meter is used as the evacuation population density during a disaster. That is equivalent to the density on a crowded train station platform. Further, usually 2 km/h is used as the walking speed during a disaster. This is based on the opinion that it is advisable for designated large-area evacuation sites to be located such that the time it takes to evacuate to them is within an hour and the evacuation distance is within 2 km. With reference to the above-mentioned equation for deriving road width, in the present method, the transit time t_{j} for link j is defined by Equation (5), given below.

^{2}] (=1 P/m^{2});

Here, the second term on the right side of Equation (5) expresses the evacuation time, found based on the equation for deriving road width. Further, concerning the estimated evacuation population, when a link is passed through, the estimated evacuation population at that link increases cumulatively. Based on the above, the total evacuation time for individual X_{i} is defined by the Equation (6), given below, and is an evaluation value.

_{i} [h];

_{i} passes through.

The Pareto ranking method is used based on the evaluation values for each of these objectives, to determine objective functions for calculating the goodness of fit of individuals.

2) Goodness of fit evaluation employing the Pareto ranking method

By using the Pareto ranking method based on evaluation values for each objective defined in (1), a rank which expresses the superiority or inferiority of each individual is determined. In the case below, the individual X_{i} is defined as being “dominated by” X_{i}.

That is, in the case where individual X_{i} has a longer distance, a lower probability of arriving, a higher degree of fire hazard in roads, and a longer total evacuation time than individual X_{i}, individual X_{i} is defined as being “dominated by” individual X_{i}. Based on this definition, the rank of individual X_{i} (expressed by “_{i} is dominated by a number of individuals equal to n_{i} is determined by Equation (8), given below.

An individual for which R = 1 holds true indicates a Pareto optimal solution, which is a solution that is not inferior to any other solution. This rank is used to set objective functions, as in Equation (9) below. Equation (9) is set such that the higher the rank (the closer to 1), the better the goodness of fit.

Thus, objective functions are set based on ranks found using the Pareto ranking method.

In the method of this study, sharing in the representational space is conducted. If sharing in the objective space was applied to the method, and routes with similar evaluation values for each objective existed within the population, those routes would be regarded as being similar. However, because routes are focused on in this study, even if evaluation values are similar, it is possible that in the representational space the nodes which form the routes may be completely different; therefore, the routes cannot be regarded as being similar. Due to this reason, in the method of this study, similarity as routes is taken into account, and unique sharing in the representational space is applied. The specific method of sharing in this study is outlined below.

1) The number of nodes which overlap between individuals X_{i} and X_{j} are counted. However, the evacuation starting point and destination are not counted.

2) The total number of nodes which form X_{i} and X_{j} is counted. However, the evacuation starting point and destination are not counted.

3) The proportion of nodes that overlap between X_{i} and X_{j} (expressed as “

4) Steps (1) to (3) are conducted between all individuals in the population, and the proportion of nodes which overlap between individuals is found for every individual in relation to every other individual.

5) For each individual, a niche number, which is the number of individuals which are similar to that individual, is calculated. The niche number _{i} is defined by Equation (10), given below.

_{i} and X_{j};

The sharing function

In this study, the sharing rate r_{share} is equivalent to the sharing radius _{share}. That is, in the case where the proportion of nodes which overlap between individuals is equal to or greater than the sharing rate, those individuals are regarded as being similar, and their niche numbers are counted.

6) By dividing the goodness of fit F of each individual by the niche number found for each individual, a new goodness of fit shareF which takes into account similarity between individuals is created. The goodness of fit of the individual X_{i}, indicated by shareF_{i}, is expressed by Equation (12), given.

By conducting selection and culling based on the value for the goodness of fit shareF_{i} for which the sharing described above has been conducted, the diversity of individuals in the population is maintained, and a more global search, which is important in seeking a set of Pareto optimal solutions, can be conducted. Concerning the effectiveness of the sharing conducted in the method of this study, in Section 6.1 an evaluation experiment is conducted, and the dispersion of individuals within the population is checked to verify whether or not sharing has been conducted effectively.

In the method of this study, the strategy of preserving Pareto optimal solutions and roulette-wheel selection are used in combinationas selection and culling operations. Each operation is described below. Selection other than that for individuals whose preservation for the next generation has been determined using the strategy of preserving Pareto optimal solutions is performed using roulette-wheel selection. The probability of selection for individuals in roulette-wheel selection is indicated by pselect. It is based on the goodness of fit for which sharing has been conducted, which is indicated by shareF, and is determined by Equation (13), given below.

Based on the probability of selection for each individual, which is determined by Equation (13), roulette- wheel selection is repeated until the number of next-generation individuals reaches the population size N. By determining probability selection based on goodness of fit which, through the use of sharing, takes into account similarity between individuals, as in Equation (13), a next generation population in which individuals are dispersed evenly and there is no prevalence of similar individuals is generated.

The crossover method of this study is described below. As the crossover method, one-point crossover is used.

1) Two individuals are randomly selected from the population to be parent individuals. In the case that the two individuals are formed using exactly the same nodes, the individual generated will be the same as the parent individuals; therefore, crossover is not performed with such individuals.

2) From nodes which overlap between the two individuals (not including the evacuation starting points and destination points), one point is randomly selected as a crossover point. If there are no overlapping nodes, crossover is not conducted.

3) Nodes at and after the crossover point of the parent individuals are swapped, and two child individuals are generated.

4) If a route loops in a child individual, the loop is removed.

The above-described operations are performed based on the crossover probability C, and generated child individuals are added to the population.

The mutation method used in the method of this study is described below.

1) One individual is randomly selected from the population.

2) One point is randomly selected from nodes which form the selected individual, and used as a mutation point. However, evacuation starting point and destination points are not selected as mutation points.

3) From the mutation point node, a route which links to the destination point is randomly generated. Route generation is performed based on adjacency lists, similarly to initial population generation, and only feasible solutions, or unbroken routes, are generated.

4) The part of the individual selected in (1) that is at and beyond the mutation point is replaced by the randomly generated route, resulting in the generation of a new route.

5) If a route generated in (4) loops, the loop is removed.

The above-described operations are performed based on the mutation rate M, and generated individuals are added to the population.

The Tokyo Metropolitan Government [

Each district is assigned a set large-area evacuation site. In the district studied, the 3-chome Kyoujima area has the highest total degree of danger, according to Sumida City [

In this study, the road blockage probability was calculated based on the positional relationship between the debris width buffer caused by roadside wooden buildings, and the road centerline located in front of that. Therefore, the road centerline was extracted from land use data, and was used to create node data which showed intersections and crossroads, and link data which showed roads which connected the intersections and crossroads. Road network data was created by further integrating these sets of data.

Data used | Data processing method |
---|---|

Land use survey for FY2012 (Bureau of Urban Development, Tokyo Metropolitan Government) | Road network generation |

Building use survey for FY2012 (Bureau of Urban Development, Tokyo Metropolitan Government) Total building collapse rate, sorted by ground area and building type (Bureau of Urban Development, Tokyo Metropolitan Government: “District-based assessment of vulnerability to earthquake disaster (No. 7)”) | Road blockage probability calculation and its addition to road network |

Land use survey for FY2012 (Bureau of Urban Development, Tokyo Metropolitan Government) | Road width measurement |

Vulnerability to fire, sorted by block/subdivision (Bureau of Urban Development, Tokyo Metropolitan Government: “District-based assessment of vulnerability to earthquake disaster (No. 7)”) | Addition of degree of fire hazard to road network |

Data on nighttime population, taken from data on the night and day populations, sorted by block, subdivision, aza, and other administrative units (Statistics Bureau, Ministry of Internal Affairs and Communications: “Heisei 22-nen Kokusei Chousa [2010 National Census]”) Building use survey for FY2012 (Bureau of Urban Development, Tokyo Metropolitan Government) | Calculation of estimated population in roads and its addition to road network |

created as described above, and road information was added to this data.

Road blockage probability was added to the road network data in

1) Roadside building extraction and classification

Roadside buildings, which are a primary factor in road blockage, were extracted. First, a buffer from the road centerline was created on the right side only, and the spatial search function of the GIS was used to extract buildings which intersected with the buffer. Similarly, next a buffer from the road centerline was created on the left side only, and buildings which intersected with the buffer were extracted. By following these steps, buildings were classified into those located on the right side of the road and those located on the left side of the road.

2) Extraction of roadside wooden buildings and addition of probability of collapse

Using the GIS attribute search function, wooden buildings were extracted from both the buildings on the right side and the buildings on the left side. Further, probability of collapse was added as an attribute to each of the wooden buildings.

3) Extraction of pairs of buildings which would cause blockage

a) Case of single blockage

A buffer with a radius equal to the width of debris which would be produced from a wooden building on the right side of the road if it collapsed was created, and the GIS spatial search function was used to extract any building on the left side of the road which intersected with the buffer. The same was done for the left side of the road, and pairs of buildings which would cause single blockage were extracted. Concerning the outflow of debris that occurs when a building collapses, the case of maximum damage was imagined, and it was assumed that debris would flow out evenly in all directions. Further, concerning the debris width, with reference to Ichikawa et al. (2001) [

b) Case of combined blockage

Debris width buffers were created for wooden buildings on both the left and right sides of the road. The GIS spatial search function was used to extract left-side debris buffers which intersected with right-side debris buffers and right-side debris buffers which intersected with left-side debris buffers. These steps were performed to extract buildings on the right side and buildings on the left side which would cause combined blockage.

4) Generation of road section lines

With reference to Yoshikawa et al. (2003) [

5) Addition of blockage probability to road network

Using the GIS spatial coupling tool, to each road link which intersected with the three types of section line generated in (4), blockage probability (indicated by p_{k}) for each of the points on section lines (indicated by k) was added.

6) Calculation of road blockage probability

Through the above operations, to each road link, blockage probabilities (indicated by p_{k}) for points on section lines (these points were indicated by k) were added. The probability P_{s} that all points k on the section lines of each road link would be passable was calculated using the blockage probability p_{k}, and is expressed by Equation (15) (Takeuchi et al. (2002) [

Therefore, the road link blockage probability P_{b} was found using the Equation (16) below:

Using the GIS field arithmetic function, the above-described calculations were performed on a road link data attribute table, and blockage probability was calculated for each road link.

Road width was measured based on road edge line data and road centerlines (road links) created in Section 5.2.1. Road width is necessary when calculating fire hazard and evacuation time. The method for measuring road width is described below.

1) Based on road edge line data, buffers with a radius of 0.5 m were generated, and road links which intersected with the buffers were extracted using the GIS spatial search function. This enabled roads with a width of less than 1 m to be extracted.

2) A width of 1 m (the case where the buffer radius is 0.5 m) was given to the extracted road links as an attribute.

3) Road links extracted in (2) were excluded from the overall body of road link data.

4) Once again, buffers were generated from road edge line data. When performing this step, the buffer radius was a value obtained by adding 0.5 m to the buffer radius set in (1). Further, using the GIS spatial search function, the group of road links which did not include roads with a width of less than 1 m (which was created in (3)) was superposed with the buffers, and road links which intersected with the buffers were extracted. This step enabled roads with a width greater than or equal to 1 m and less than 2 m to be extracted.

Steps (1) to (4) were repeated, increasing the buffer radius by 0.5 m each time. Through this, road link data was extracted for widths every meter up to a maximum width. Finally, the road link data extracted for widths every meter was integrated using the GIS merge function to create one set of road link data containing the addition of width information for every road link.

described above has been added.

The degree of fire hazard for each block and chome* (* a numbered subdivision of an area in an address) from “District-based assessment of vulnerability to earthquake disaster (No. 7)” [

1) The degree of fire hazard for each block and chome was added as an attribute to block and chome polygon data taken from data on the present land use situation.

2) Using a GIS spatial coupling tool, degree of fire hazard was added to road links which intersected with each block and chome polygon. The Great Hanshin Earthquake clearly showed that roads with a width equal to or greater than twelve meters have the effect of interrupting the spread of fire. Therefore, roads with a width of twelve meters or more were assigned a fire hazard degree of zero. Concerning road width data, the values measured in Section 5.2.3 were used.

3) The degrees of fire hazard added to road links in step (2) were constant within each block/chome. Therefore, the degree of fire hazard did not differ between the road links in a block/chome. This meant that no matter what road in the block/chome was passed through, the degree of fire hazard would be the same. However, for evacuation in the case where a fire has broken out, speedy evacuation to roads with a wide width which will not suffer damage from fire or the spread of fire is important; therefore, evacuation distance is thought to be closely related. Here, based on the idea that “The longer the evacuation distance travelled in a block/chome with a high degree of fire hazard, the more likely it is that fire hazard will be encountered”, as a new indicator showing the degree of hazard due to fire in a road, a value found by multiplying the degree of fire hazard with the road link distance was used as the degree of fire hazard in a road. Further, the degree of fire hazard in roads for each road was calculated using the GIS field arithmetic function in a road link attribute table. Doing this enabled the degree of fire hazard in roads within a block/chome to be varied.

The estimated population of evacuees which would occur in each road at the time of a disaster outbreak was calculated, and was added to road links as an attribute. Estimated population is used in the GA when calculating evacuation time for a route. Below, methods for calculating the estimated population within a road and adding it to the road network are described

1) Using the GIS spatial search function, based on data on present use of buildings which intersected with block/chome polygon data taken from data on the present land use situation, for each block/chome, the buildings in the block/chome were extracted.

2) Using the GIS attribute search function, from the data on buildings extracted in step (1), only the single or detached houses and apartment buildings or housing complexes with many nighttime evacuees were extracted.

3) Using Equation (17), estimated populations which matched the total floor space of each residence were assigned. Calculation for Equation (17) was performed using the GIS field arithmetic function in attribute fields for building data.

4) Using the GIS spatial coupling tool, the estimated evacuation population of each residence was assigned to the road link closest to the residence.

All road information for the road network created in Sections 5.2.1 to 5.2.6 was integrated into a single GIS attribute table and output. The method of doing so is described below.

1) Using the GIS dissolve function, all road information was summarized based on road link IDs. This enabled the distance (

2) The GIS tool for exporting feature attributes to ASCII was used to output the road information in step (1) to a CSV file.

Road link data output as described above is input to the GA as road information when route search is performed.

In this section, an evaluation experiment conducted in order to demonstrate the validity of the method of this study is described. In Section 6.1, in order to demonstrate the validity of the unique sharing method of the method of this study, whether or not effective sharing was conducted is verified. This is done by checking the distribution of solutions. At the same time, by considering the change in solutions derived that occurs when the sharing rate r_{share} is changed, an appropriate r_{share} value is clarified. In Section 6.2, by considering the change in solutions in the case where the number of objectives is changed, and the convergence of solutions, whether or not multi-objective optimization was conducted appropriately is examined. Further, at the same time, GIS is

used to visualize derived routes, and a visual evaluation is conducted.

In the evaluation experiment in this section, in order to compare derived routes, the same evacuation starting point and the same evacuation destination point were used throughout the experiment. Specifically, as shown in,

In this section, in order to examine the effects of the unique sharing of this study, the distribution of individuals within the population for the case where sharing is not conducted and the case where sharing is conducted and the sharing rate r_{share} is changed are compared. Doing this enables verification of whether or not the objective of sharing, which is “the maintenance of diversity in solutions within the population”, was achieved successfully. In this section, optimization is conducted using two objectives for which distribution of individuals is easy to grasp visually (evacuation distance and arrival probability).

_{share} being the same for every case.

Case | (1) | (2) | (3) | (4) | (5) | (6) |
---|---|---|---|---|---|---|

Sharing rate: r_{share} | 0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |

Population size: N | 100 | 100 | 100 | 100 | 100 | 100 |

Number of trial generations: G | 1000 | 1000 | 1000 | 1000 | 1000 | 1000 |

Crossover rate: C [%] | 100 | 100 | 100 | 100 | 100 | 100 |

Mutation rate: M [%] | 1 | 1 | 1 | 1 | 1 | 1 |

Route | (1) | (2) | (3) | (4) | (5) | (6) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Evacuation distance [m] | Arrival probability | Evacuation distance [m] | Arrival probability | Evacuation distance [m] | Arrival probability | Evacuation distance [m] | Arrival probability | Evacuation distance [m] | Arrival probability | Evacuation distance [m] | Arrival probability | |

1 | 543.5 | 0.0051 | 543.5 | 0.0051 | 543.5 | 0.0051 | 543.5 | 0.0051 | 543.5 | 0.0051 | 543.5 | 0.0051 |

2 | 559.9 | 0.0110 | 559.9 | 0.0110 | 559.9 | 0.0110 | 559.9 | 0.0110 | 559.9 | 0.0110 | 559.9 | 0.0110 |

3 | 583.8 | 0.0190 | 583.8 | 0.0190 | 583.8 | 0.0190 | 583.8 | 0.0190 | 583.8 | 0.0190 | 583.8 | 0.0190 |

4 | 598.3 | 0.1000 | 598.3 | 0.1000 | 598.3 | 0.1000 | 598.3 | 0.1000 | 598.3 | 0.1000 | 598.3 | 0.1000 |

5 | 614.7 | 0.2400 | 614.7 | 0.2400 | 614.7 | 0.2400 | 614.7 | 0.2400 | 614.7 | 0.2400 | 614.7 | 0.2400 |

6 | - | - | 678.0 | 0.7400 | 654.7 | 0.3600 | 654.7 | 0.3600 | 654.7 | 0.3600 | 654.7 | 0.3600 |

7 | - | - | - | - | 678.0 | 0.7400 | 678.0 | 0.7400 | 678.0 | 0.7400 | 666.7 | 0.4900 |

8 | - | - | - | - | - | - | - | - | - | - | 678.0 | 0.7400 |

the final generation for each of Cases (1) to (6) in _{share} = 0.2, because sharing was conducted, compared to Case (1) there are more types of individual in the population, and further, six Pareto optimal solutions were derived. This is thought to be due to the fact that because individuals in the population were diverse, the number of types of parent individual in the genetic operations of crossover and mutation increased. That is, due to the number of types of parent individual increasing, child individuals generated based on those parent individuals also became diverse, and therefore a more global search was possible. This is also thought to be the reason why more Pareto optimal solutions were derived in Cases (3) to (6), with seven being derived in each of Cases (3) to (5), and eight being derived in Case (6). Further, comparing Cases (3) to (6), it can be seen that individuals in the population are most diverse in Case (6), for which r_{share} = 1.0.

r_{share} = 1.0 indicates the case where sharing which lowers the goodness of fit of individuals formed with exactly the same nodes is performed in the population. In the method of this study, when the two individuals that are parents are formed with exactly the same nodes, crossover operations are not performed. This is because even if the parents were crossed, child individuals which were exactly the same as the parents would be generated. By lowering the goodness of fit of individuals with exactly the same structure through sharing for which r_{share} = 1.0, more diverse individuals are selected in the population through selection and culling, and therefore crossover can be performed effectively. Through this, since crossover allows a greater variety of child individuals to be generated, a greater variety of individuals exists within the population. Due to the above-mentioned reasons, it is thought that in the method of this study, sharing for which r_{share} = 1.0 was the most effective sharing.

Due to these reasons, it was confirmed that the sharing in this study had the effect of maintaining the diversity of individuals within the population, and consequently a global search is possible; therefore, it is likely that a greater number of Pareto optimal solutions will be found. Further, it was confirmed that in the method of this study, sharing is most effective when r_{share} = 1.0. Therefore, r_{share} = 1.0 is used in this method, as it is considered to be the best sharing rate.

This section describes an evaluation experiment which was carried out in order to verify whether or not multi- objective optimization of evacuation routes was carried out appropriately by the method of this study. The GA parameters in the evaluation experiment were as follows. Sharing rate: r_{share} = 1.0; Population size: N = 100; Number of trial generations: G = 1000; Crossover rate: C [%] = 100; and Mutation rate: M [%] = 1.

Derived route | Evacuation distance [m] | Arrival probability | Degree of hazard due to fire in the road | Evacuation time [h] | Total evacuation population [p] |
---|---|---|---|---|---|

1 | 543.5 | 0.0052 | 1839.5 | 0.43 | 150 |

2 | 559.9 | 0.0110 | 1921.3 | 0.46 | 158 |

3 | 561.8 | 0.0020 | 1794.9 | 0.45 | 172 |

4 | 583.8 | 0.0190 | 2040.8 | 0.49 | 185 |

5 | 598.4 | 0.1100 | 2113.6 | 0.56 | 222 |

6 | 600.0 | 0.0170 | 1525.1 | 0.47 | 149 |

7 | 600.2 | 0.0430 | 2122.6 | 0.53 | 173 |

8 | 608.8 | 0.0320 | 1569.4 | 0.51 | 165 |

9 | 614.7 | 0.2400 | 2195.4 | 0.61 | 230 |

10 | 616.6 | 0.0430 | 2069.1 | 0.60 | 244 |

11 | 619.4 | 0.0720 | 2218.8 | 0.39 | 81 |

12 | 623.2 | 0.0350 | 1413.3 | 0.48 | 187 |

13 | 625.4 | 0.0130 | 1424.2 | 0.47 | 149 |

14 | 629.6 | 0.0350 | 1171.3 | 0.44 | 203 |

15 | 632.0 | 0.0640 | 1457.6 | 0.51 | 165 |

16 | 638.5 | 0.0640 | 1215.5 | 0.47 | 161 |

17 | 654.8 | 0.3600 | 1799.3 | 0.62 | 221 |

18 | 678.0 | 0.7400 | 1687.5 | 0.60 | 198 |

19 | 684.5 | 0.7400 | 1445.4 | 0.56 | 259 |

20 | 1074.9 | 0.4900 | 1018.3 | 0.72 | 221 |

summarizes evaluation values for each objective for routes derived, for which evacuation distance, arrival probability, degree of hazard due to fire in the road, and evacuation time were optimized. Twenty routes were derived as Pareto optimal solutions. Of these, Routes 1, 11, 19 and 20 are shown in

Concerning the derived routes, including Routes 1, 18, 19 and 20, the routes are almost the same as in the case when evacuation distance, arrival probability, and degree of hazard due to fire in the road were optimized; however, a new route, Route 11, which minimizes evacuation time, was derived. Route 11 does not have the shortest evacuation distance, but it has the shortest evacuation time. Route 1, the shortest route, has a total evacuation population of 150 people, while Route 11 has a total evacuation population of 81 people. Further,

The result that is clear from above is that as the number of objectives was increased, multiple routes whose evaluation values for each objective were intrade-off relationships with each other were obtained. These routes were Pareto optimal solutions, meaning that in order to improve an evaluation value for one of the objectives, an evaluation value for one of the other objectives would have to be degraded. Therefore, it is considered that multi-objective optimization was carried out appropriately. Thus, in the method of this study, multiple evacuation route candidates are derived in a single search as Pareto optimal solutions; therefore, from these candidates, multiple evacuation routes which envisage what will happen in a time of disaster can be selected.

In order to verify whether or not multi-objective simultaneous optimization was effectively carried out, convergence of evaluation values for each objective in a four-objective optimization was examined. The GA parameters in the evaluation experiment were as follows. Sharing rate: r_{share} = 1.0; Population size: N = 100; Number of trial generations: G = 1000; Crossover rate: C [%] = 100; and Mutation rate: M [%] = 1.

However, concerning arrival probability, it can be seen that while the average value for arrival probability of individuals within the population improved overall compared to the initial generation with the repeated creation of generations, a clear convergence could not be confirmed, compared with the other three objectives. The fact that evacuation distance is intimately connected with all three of the other objectives is considered a reason for this. Evacuation distance itself is an evaluation value that is determined by distance, and degree of hazard due to fire in the road is an evaluation value obtained by multiplying the degree of hazard due to fire per block/chome by the distance of each road. Further, evacuation time is an evaluation value obtained by using evacuation distance and walking speed to find the regular transit time, and then adding extra time to that due to crowding. In the case where there is only a small influence from crowding, evacuation time is strongly dependent on evacuation distance. Due to this, it is thought that the more the evacuation distance for individuals in the population converges on a small value, the more evacuation distance, degree of hazard due to fire in the road, and evacuation time will improve. Meanwhile, since arrival probability is not dependent on evacuation distance, it will not improve if the evacuation distance for individuals in the population becomes shorter. Nevertheless, it can be seen that evaluation values for each objective for individuals in the population improved with the addition of each generation, and it is considered that multi-objective simultaneous optimization was carried out adequately.

Points in each area for which evacuation was considered to be most difficult based on the total degree of hazard (which takes into account the degree of difficulty of conducting activities in times of disaster) were selected as representative evacuation starting points. Further, evacuation routes are proposed for two types of evacuation

method in this study—the case of two-stage evacuation, and the case of direct evacuation. Therefore, two points were selected as evacuation destination points—a temporary gathering place, which is the first destination point, and a large-area evacuation site, which is the second destination point. The temporary gathering place is a place designated by Sumida City [

The GA parameters set for route search were as follows. Sharing rate: r_{share} = 1.0; Population size: N = 150; Number of trial generations: G = 1000; Crossover rate: C [%] = 100; and Mutation rate: M [%] = 2.

1) Routes from evacuation starting point to temporary gathering place

As routes from Point A, the evacuation starting point, to Point B, the neighborhood of the temporary gathering place, only the two routes shown in

Route 2 has the shortest distance; however, because it involves passing through roads with a high probability of blockage, it has a low arrival probability of 36%. In contrast to this, Route 1 detours to avoid roads with a high blockage probability, and has an arrival probability of 100%. Further, because Route 1 is not an unnecessarily indirect route, no large differences can be observed between Route 1 and Route 2 for evacuation distance,

Derived route | Evacuation distance [m] | Arrival probability | Degree of hazard due to fire in the road | Evacuation time [h] |
---|---|---|---|---|

1 | 164.3 | 1.00 | 821.5 | 0.140 |

2 | 69.4 | 0.36 | 347.2 | 0.042 |

degree of hazard in the road due to fire, and evacuation time. Accordingly, Route 1, which has a high arrival probability, is thought to be suitable as an evacuation route, and therefore was chosen as a preference solution.

2) Route from temporary gathering place to large-area evacuation site

As routes from Point B, the neighborhood of the temporary gathering place, to Point C, the neighborhood of the large-area evacuation site, thirty-two routes were derived as Pareto optimal solutions.

Derived route | Evacuation distance [m] | Arrival probability | Degree of hazard due to fire in the road | Evacuation time [h] |
---|---|---|---|---|

1 | 613.0 | 0.0019 | 2186.7 | 0.51 |

2 | 629.4 | 0.0041 | 2268.5 | 0.55 |

3 | 631.2 | 0.0007 | 2142.1 | 0.54 |

4 | 653.3 | 0.0070 | 2388.0 | 0.57 |

5 | 665.3 | 0.0190 | 2448.3 | 0.63 |

6 | 667.8 | 0.0390 | 2460.9 | 0.65 |

7 | 669.4 | 0.0063 | 1872.4 | 0.56 |

8 | 669.6 | 0.0150 | 2469.8 | 0.62 |

9 | 679.9 | 0.1100 | 2521.2 | 0.71 |

10 | 681.7 | 0.0430 | 2530.2 | 0.69 |

11 | 683.5 | 0.0076 | 2403.8 | 0.67 |

12 | 684.2 | 0.0870 | 2542.7 | 0.71 |

13 | 686.0 | 0.0150 | 2416.3 | 0.68 |

14 | 688.9 | 0.0260 | 2566.0 | 0.48 |

15 | 692.6 | 0.0130 | 1760.6 | 0.56 |

16 | 696.2 | 0.2400 | 2603.0 | 0.77 |

17 | 698.1 | 0.0430 | 2476.6 | 0.75 |

18 | 699.1 | 0.0130 | 1518.5 | 0.52 |

19 | 700.9 | 0.0720 | 2626.3 | 0.54 |

20 | 711.2 | 0.0230 | 1853.6 | 0.61 |

21 | 717.7 | 0.0230 | 1611.6 | 0.56 |

22 | 724.2 | 0.1300 | 2146.5 | 0.70 |

23 | 736.3 | 0.3600 | 2206.8 | 0.77 |

24 | 747.5 | 0.2700 | 2034.7 | 0.68 |

25 | 753.9 | 0.2700 | 1792.7 | 0.63 |

26 | 759.5 | 0.7400 | 2095.0 | 0.74 |

27 | 766.0 | 0.7400 | 1853.0 | 0.69 |

28 | 1006.8 | 0.1800 | 1627.4 | 0.65 |

29 | 1011.7 | 0.1800 | 1651.7 | 0.64 |

30 | 1029.7 | 1.0000 | 572.1 | 0.59 |

31 | 1034.5 | 1.0000 | 596.4 | 0.58 |

32 | 1106.7 | 0.0870 | 389.8 | 0.61 |

Concerning the derived routes, the maximum evacuation distance, which belongs to Route 32, is only 1106.7 m. Therefore, even if the length of either of the routes in Case (1) described above (routes from Point A, the evacuation starting point, to the neighborhood of the temporary gathering place) is added to the length of any of the derived routes in

Twenty-one routes were derived as Pareto optimal solutions for direct evacuation routes from Point A, the evacuation starting point, to Point C, near the large-area evacuation site.

Derived route | Evacuation distance [m] | Arrival probability | Degree of hazard due to fire in the road | Evacuation time [h] |
---|---|---|---|---|

1 | 543.5 | 0.0052 | 1839.5 | 0.43 |

2 | 559.9 | 0.0110 | 1921.3 | 0.46 |

3 | 561.8 | 0.0020 | 1794.9 | 0.45 |

4 | 583.8 | 0.0190 | 2040.8 | 0.49 |

5 | 598.4 | 0.1100 | 2113.6 | 0.56 |

6 | 600.0 | 0.0170 | 1525.1 | 0.47 |

7 | 600.2 | 0.0430 | 2122.6 | 0.53 |

8 | 608.8 | 0.0320 | 1569.4 | 0.51 |

9 | 614.7 | 0.2400 | 2195.4 | 0.61 |

10 | 616.6 | 0.0430 | 2069.1 | 0.60 |

11 | 619.4 | 0.0720 | 2218.8 | 0.39 |

12 | 623.2 | 0.0350 | 1413.3 | 0.48 |

13 | 625.4 | 0.0130 | 1424.2 | 0.47 |

14 | 629.6 | 0.0350 | 1171.3 | 0.44 |

15 | 632.0 | 0.0640 | 1457.6 | 0.51 |

16 | 638.5 | 0.0640 | 1215.5 | 0.47 |

17 | 654.8 | 0.3600 | 1799.3 | 0.62 |

18 | 678.0 | 0.7400 | 1687.5 | 0.60 |

19 | 684.5 | 0.7400 | 1445.4 | 0.56 |

20 | 975.4 | 1.0000 | 1360.1 | 0.65 |

21 | 1074.9 | 0.4900 | 1018.3 | 0.72 |

The derived routes all had an evacuation distance of within two kilometers and an evacuation time of within one hour. Of the derived routes, only three had an arrival probability of over 70%—Routes 18, 19 and 20. Near the evacuation starting point, there are many roads with a high road blockage probability, so it is considered that evacuation is difficult. However, it was possible to find routes such as these three—routes with a high arrival probability and a low fire hazard. Of these three routes, Routes 19 and 20 (

The conclusion of this study can be summarized into the following three points:

1) A GA was used to design and create an evacuation route search algorithm which solves the problem of the optimization of earthquake disaster evacuation routes by treating it as an optimization problem with multiple objectives, such as evacuation distance and evacuation time. By using this method, it is possible to find multiple evacuation route candidates whose objectives are in a trade-off relationship with each other in a single search. Further, selecting preference solutions from among the evacuation route candidates derived enables the determination of multiple evacuation routes in preparation for disaster.

2) In this method, goodness of fit is set by using a Pareto ranking method to determine the ranking of individuals based on their relative superiorities and inferiorities. This enables objective functions to be set without taking into account weightings or orders of priority between each objective. Therefore, the number of objectives can be freely increased, and various objectives which disaster evacuation routes are required to meet can be taken into account. Further, because this method performs searches based on road blockage probability and evacuation distance, which are quantified data, derived routes are routes that have been quantitatively evaluated, and they can be highly effective indicators for determining evacuation routes.

3) In the method, road information concerning obstacles to disaster evacuation was created based on data regarding present conditions, such as building and land use data. In this method, searching for evacuation routes based on the information on present conditions allows evacuation routes to be derived based on present building and road locations. Therefore, this method has a high degree of spatial reproducibility. Further, this method is based on publicly available information; therefore, obtaining geographic information similar to that of this study enables this method to be effective regardless of what region it is applied to, or whether the data regards the past or the future. Therefore, in addition to spatial reproducibility, this method also has a high degree of temporal reproducibility.

Examples of future topics for research are improvement of search accuracy, GIS visualization of trade-off relationships of derived solutions, and further refinement of road information.