The Ripple-Spreading Algorithm for the k Shortest Paths Problem in Co-Evolutionary Path Optimization

Reference: HU X B,ZHANG M K,ZHANG Q,et al.Co-evolutionary path optimization by ripple-spreading algorithm[J].Transportation Research:Part B,2017,106:411-432.

The k shortest paths problem aims to find the k shortest paths between two nodes in a dynamic network.

Variables	Meaning
network	Dictionary, {node 1: {node 2: [weight 1, weight 2, ...], ...}, ...}
s_network	The network described by a crisp weight on which we conduct the ripple relay race
source	The source node
destination	The destination node
k	The k shortest paths
orad	The radius of the obstacle
ospeed	The moving speed of the obstacle
nn	The number of nodes
neighbor	Dictionary, {node1: [the neighbor nodes of node1], ...}
v	The ripple-spreading speed (i.e., the minimum length of arcs)
t	The simulated time index
nr	The number of ripples - 1
epicenter_set	List, the epicenter node of the i-th ripple is epicenter_set[i]
path_set	List, the path of the i-th ripple from the source node to node i is path_set[i]
radius_set	List, the radius of the i-th ripple is radius_set[i]
state_set	List, state_set[i] = 1, 2, or 3 means the ripple i is waiting, active, or dead
objective_set	List, the objective value of the traveling path of the i-th ripple is objective_set[i]
omega	Dictionary, omega[n] contains all ripples generated at node n

Example

The first shortest path, length is 162.17650824456905.

The second shortest path, length is 162.32929237033122.

The third shortest path, length is 162.36920013460093.

The fourth shortest path, length is 162.5219842603631.

The fifth shortest path, length is 162.73900697813062.

The obstacle moves from the lower right corner to the upper right corner with radius = orad and speed = ospeed.

if __name__ == '__main__':
    network, x, y = init_network()  # the grid network has 100 nodes
    s = 0  # lower left corner
    d = 99  # upper right corner
    orad = 15  # obstacle radius
    ospeed = 6  # obstacle speed
    k = 5
    print(main(network, s, d, k, x, y, orad, ospeed))

Output:

{
    1: {
        'path': [0, 10, 21, 22, 32, 42, 52, 53, 63, 73, 74, 75, 86, 87, 88, 89, 99], 
        'length': 162.17650824456905
    }, 
    2: {
        'path': [0, 1, 11, 12, 23, 33, 43, 53, 63, 73, 74, 75, 86, 87, 88, 89, 99], 
        'length': 162.32929237033122
    }, 
    3: {
        'path': [0, 10, 21, 22, 32, 42, 52, 53, 63, 64, 74, 75, 86, 87, 88, 89, 99], 
        'length': 162.36920013460093
    }, 
    4: {
        'path': [0, 1, 11, 12, 23, 33, 43, 53, 63, 64, 74, 75, 86, 87, 88, 89, 99], 
        'length': 162.5219842603631
    }, 
    5: {
        'path': [0, 10, 21, 22, 23, 33, 43, 53, 63, 73, 74, 75, 86, 87, 88, 89, 99], 
        'length': 162.73900697813062
    }
}