Innovative Ways of Developing and Using Specific Purpose Alternatives for Solving Hard Combinatorial Network Routing and Ordered Optimisation Problems

Abstract

This paper reviews some recent contributions by the authors and their associates and highlights a few innovative ideas, which led them to address some hard combinatorial network routing and ordered optimisation problems. The travelling salesman, which is in the NP hard category, has been reviewed and solved as an index-restricted shortest connected graph, and therefore, it opens a question about its ‘NP Hard’ category. The routing problem through ‘K’ specified nodes and ordered optimum solutions are computationally demanding but have been made computationally feasible. All these approaches are based on the strategic creation and use of an alternative solution in that situation. The efficiency of these methods requires further investigation.

Keywords

• shortest connected network
• minimum travelling salesman tour
• NP Hard problems
• path through K specified nodes
• index-balancing theorem
• index-restricted connected network