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Associated path detection is considered as the major concern of the traditional shortest path issue. The associated path is generally represented by the shortest distance among the source and destination. In the transportation network, distance or cost detection may identify this associated path. Specifically, it is very important to discover the shortest distance that has a minimum number of nodes, and it will give the most optimized result. In this paper, the Fuzzy based Pareto Optimal (FPO) approach is used to discover the shortest paths in a network graph. Initially, the FPO technique finds the shortest paths in a network by using set of rules. Then, the Lexicographical model uses a set of rules to rank the shortest distance based on minimum distance value. From the ranking results, the optimal shortest path is selected based on the proposed Ant Lion Optimization (ALO) algorithm. So, this paper achieves multi objectives like shortest path ranking and selection of the optimal shortest path. Time, distance or cost, convergence time, fitness function, and mean square error are the parameters used to relate the performance of the proposed technique with state-of-the-art techniques. Comparative results display the robustness and proficiency of the proposed system with several works.

Shortest Path Problem (SPP) is mainly used in network optimization, which has a wide range of applications such as routing, scheduling, communication and transportation. The main objective of this work is to find the shortest path between two specified nodes by satisfying certain constraints. This modified version of SP is called Constraint Shortest Path (CSP) which establishes a certain limit on selected constraints for the path. The limit for constraint values is precisely specified in traditional CSP problems. But, the precise data may vary due to some reasons like environmental conditions, traffic and payload. That is why proposed CSP make use of intuitionistic fuzzy numbers to deal with these kinds of imprecise data. As well as, it is difficult to find an optimal solution in complex search space of an undirected network. Hence, Particle Swarm Optimization (PSO) is used in the proposed work to get the optimal global solution within feasible regions. A numerical example is also illustrated along with the implementation of proposed work in Matlab 2016a working environment.