The shortest path problem in which the (s, t)-paths P of a given digraph G = (V,E) are compared with respect to the sum of their edge costs is one of the best known problems in combinatorial optimization. The paper is concerned with a number of variations of this problem having different objective functions like bottleneck, balanced, minimum deviation, algebraic sum, k-sum and k-max objectives,...

Many real world problems are NP-Hard problems are a very large part of them can be represented as graph based problems. This makes graph theory a very important and prevalent field of study. In this work a new bio-inspired meta-heuristics called Green Heron Swarm Optimization (GHOSA) Algorithm is being introduced which is inspired by the fishing skills of the bird. The algorithm basically suite...

The multi-criteria shortest path problem is concerned with the minimization of multiple, possibly conflicting objectives such as travel time and highway tolls. Sanders and Mandow [60] present a parallel algorithm for this problem. They generalize Dijkstra’s [18] single-criterion shortest path algorithm to multiple criteria, while parallelizing all additional work induced by this generalization....

We study the problem of finding shortest paths in the plane among h convex obstacles, where the path is allowed to pass through (violate) up to k obstacles, for k ≤ h. Equivalently, the problem is to find shortest paths that become obstacle-free if k obstacles are removed from the input. Given a fixed source point s, we show how to construct a map, called a shortest k-path map, so that all dest...

Dynamic programmingis well-known as a powerful modeling techniquefor dealing with the issue of making optimal decisions sequentially. Many practical problems, such as nding shortest paths in route planning, multi-stage optimal control, can be formulated as special cases of the general sequential decision process. This paper proposes a connectionist network architecture, called the binary relati...

Shortest path problems occupy an important position in Operations Research as well as in Artificial Intelligence. In this paper we study shortest path algorithms that exploit heuristic estimates. The well-known algorithms are put into one framework. Besides we present an interesting application of binary numbers in the shortest path theory.