Using Moore Dijkstra Algorithm with Multi-agent System to Find Shortest Path over Network

—finding the shortest path over network is very difficult and it is the target for much research, after many researches get the result in many of algorithm and many a mount based on the performance for these algorithm .Shortest paths problems are familiar problems in computer science and mathematics. In these problems, edge weights may represent distances, costs, or any other real-valued quantity that can be added along a path, and that one may wish to minimize. Thus, edge weights are real numbers and the specific operations used are addition to compute the weight of a path and minimum to select the best path weight. In this paper we use the Dijkstra's algorithm with new technique to find the shortest path over network to reduce the time we need to find the best path, in this paper we use node for network with the same value which can be use it to find the shortest path but this depend on the number of transition for every node when the node have high number then the node have the high priority to choose it by using this method we descries the time to find the short path .to make this algorithm more distinguish apply multi-agent system (Automata with multiplicities) to find the short path.


INTRODUCTION
The most common operation is finding the short path from vertex to another the shortest path from vertex u to vertex v is path with minimum weight we can define the shortest path algorithm as the following [3] Digraph w r v s v rt x n s n t r p t w t un t on : R t o p t p v v v s the sum of the weights of its constituent edges is minimized.p ∑ w v vi+1) Formatter will need to create these components, incorporating the applicable criteria that follow.
They are many types for shortest path problem such as single-destination shortest-path problem, single-pair shortest path problem, all pair shortest-path problem.
In this paper we will work on single source shortest path problem from vertex v as the source to all other vertices, we have many algorithm to solve this problem and evaluate the shortest path problem, we will make enhancement to the Dijkstras algorithm by when we have two node have the same value we will added many information to node itself.
In past we choose the node randomly but by using the Dijkstras algorithm enhancement we have decision to choose the node based on the number of transition for the node it self We added multi agent system as a new technique in addition to the Dijkstras algorithm enhancement we use the automata multiplicities in this method there is addresses for every path II.PROPOSED METHOD Dijkstra's algorithm, conceived by computer scientist Edsger Dijkstra in 1956 and published in 1959, [1][2] is a graph search algorithm that solves the singlesource shortest path problem for a graph with nonnegative edge path costs, producing a shortest path tree.This algorithm is often used in routing and as a subroutine in other graph algorithms.The main point for this algorithm it is started at the source vertex s and the tree is T every vertices added to T firstly is start S then the vertices which is closest to S t n n xt los st t [ ]

A. Dijkstra's Algorithm Enhancement
The enhancement Dijkstra's algorithm is represented when we have more than two edges with the same weight such as (VU) and (VW) in this case we choose the vertex which have the maximum transition if (U) has the maximum transition than (W) we use the vertex (U) otherwise we choose (W).

DIJKSTRA'S ALGORITHM ENHANCEMENT (GRAPH G = (V, E),
L = labels for every vertex (weight and path) For I = 1 to n L (V I ) = infinity L (start) = (0, empty) S = {} l S o sn't ont n n { U = vertex not in S with minimal L (u) If there are more than two nodes have the same L (u) Choose vertex node u which has the maximum transition Add u into S For all vertices v not in S that u is adjacent to

C. Example for Dijkstra's Algorithm Enhancement
If we have the graph contains 8 vertexes as shown in figure 1 we compute the shortest path by two algorithm Dijkstra's Algorithm and Dijkstra's Algorithm Enhancement www.ijacsa.thesai.orgIf we compute the shortest path by using the Dijkstra's Algorithm from source vertex 1 to 8 The path is → →5→7→8 n t s ort st p t s 7 but omput t shortest path by using Dijkstra's Algorithm Enhancement we n t p t s →3→4→7→8 n t s ort st p t s 7 n this case choose vertex 3 (1 3)because vertex 3 has 3 transition (3→4 3→ 3→ w r s v rt x s tr ns t on → 5 → 4 w v two v rt s 3 w t s m v lu w t 3 →3 → The difference between two algorithms in Dijkstra's Algorithm the counter for the time is (7) but the Dijkstra's Algorithm Enhancement is (4)

III. MULTIAGENT SYSTEM AND AUTOMATA MULTIPLICITIES
The multiagent system consists of number of agent, the agent interacts and represent as a user with different goals, and these agents show the ability to cooperate, coordinate and negotiate with each other [1].
An Automaton is advice with permit to assign to every word a coefficient in a smearing and this in an implementable form mainly using matrix computation [8].
We will be able to build effective operation on such automata using of the algebraic structures of the output data [6].
Let k a smearing then an automaton is the data a five up let Q A μ λ γ w t : Where T = {(q1,a μ q q q } q q € Q μ (a) q1,q2# 0 [11].
m is an element of T Now we associate the support of T for the weighted graph with edges [6].
s TT { q α r € Q* A*K*Q} T s m ns t t v ry s q→r s sup rscripted by the pair such that T q r α #0 The automaton can be observed by means the function it generates this function will be called the behavior of the automaton.
T lo l b v or o A b tw n two st t s p;q € Q or t l b l w € A* s t pro u t o t n t l w t λ p t tot l weight of the set of path between p and q with label w and the n l w t γ q t r [8] A(p,q) ∑p.q € Q p q

A. An Agent Modeling Framework Based on Automata Multiplicities
The formalism which is used in our work for the representation of agent behavior produced by perception and action is automata with output the finite inputs alphabet corresponds to the actions set from this output alphabets we build a smearing corresponding to the polynomials over this output alphabet [8].As we described an automaton with multiplicities over a finite lp b ts ∑ n sm r n K s 5 tupl ∑; Q; I; T; δ w t Q n t s t o st t s n I T δ being mapping such that [8].
Where I is the set of initial states and T is the set of final st t s n s δ t tr ns t on unction Such a structure is us ul w n tr ns t on v outputs to nput wor o ∑ s associated an output element of K thus the behavior of an automaton with multiplicities is a series

Example
We have the same graph Q = {1, 2, 3, 4, 5, 6, 7, 8} A={a ,b , c} Now we compute the shortest path by using two algorithms www.ijacsa.thesai.orgFig. 2. computing the shortest path by using two algorithms The value of shortest path for this graph from vertex (1) to (8) by using Dijkstra's Algorithm is (7)= (3+1+2+1) in order w r t p t s → →5→7→8 w t out ny r ss n because this algorithm applied without using automata with multiplicities but if we apply new algorithm we find that path s →3→4→7→8 w t t s m v lu o s ort st p t 7 =(3+2+1+1) in order but this method we distinguish this path by (bcbc) addressing which is obtained from A ={a, b,c} where edge (1,3) has label (b), edge (7,8) has label (c) edge(4,7) has label b and edge (7,8) has label c so the final addressing for this path (concatenated) is (bcbc)

IV. RESULTS
We used different graph to find shortest path by using two algorithms: Dijkstra's Algorithm and Dijkstra's Algorithm enhancement applied on multiagent system.The performance of our proposed vision of Dijkstra's Algorithm is depending on analysis of algorithm and the criteria which are used for prove performance for our algorithm.