Develop a genetic algorithm for the problem described in Question 19 assuming that there is a river that divides the city into two parts, West and East, at x ¼ 5 km. West and East are connected by a bridge located at x ¼ 5 km and y ¼ 5:5 km, as shown in Figure 9.48.

Find the optimal location of the emergency response unit and compare it with the one obtained in Question 19.

Question 19

Develop a genetic algorithm for optimising the location of an emergency response unit in order to minimise the response time to a medical emergency in a city. The city is mapped into a 7 km * 7 km grid, shown in Figure 9.47. A number in each sector of the grid represents an average number of emergencies per year in a given sector.

A fitness function can be defined as a reciprocal of the sum of distances weighted by emergency rates:

where λn is the emergency rate in sector n; (x_n; y_n) are the coordinates of the centre of sector n; and (x_eru; y_eru) are the location coordinates of the emergency response

unit. It can be assumed that the emergency response unit can be located only in the centre of a sector.

Transcribed Image Text:

3 2 1 3 5 12 42112 8 9 6 3 2 9 8 5 21 896 11 89 4 1 2 1 3 8 13 9 7 44 9 8 5 9 8 7 79 X Lx Figure 9.48 A grid map of a 7 km x 7 km city divided by a river