Abstract - Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. Combinatorial theory (or combinatorial analysis) is concerned with problems of enumeration and structure of mathematical objects. The objects may represent physical situation or things in applications or may be purely abstract and under study for theoretical reason. It is common practice to refer to the subject matter of combinatorial theory as combinatorics. The availability of reliable software, extremely fast and inexpensive hardware This paper highlights the historical development of combinatorial Optimization techniques specially focuses on network optimization techniques and then describes some very exciting future opportunities.

Keywords: Stochastic, Heuristics, Network flow, Max flow, Optimization, Combinatorics, Shortest Path, Extremal,