Combinatorial Optimization Essay

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1. DEFINITION OF THE COMBINATORIAL OPTIMIZATION PROBLEM.
Combinatorial optimization is defined as a combination of techniques of combinatorial operation research, linear programming and the theory of algorithms in the field of applied mathematics. The main aim of combinatorial optimization studies is to find an optimal solution from a finite set of objects.. Besides that, it solves optimization problems over discrete structures. Artificial intelligence, software engineering, , mathematics and machine learning are several fields which have been applying the combinatorial optimization techniques.
From the literature studies, according to F. Neumann, C. Witt, the goal of combinatorial optimization problem is either minimizing or maximizing a
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Their level of quality is similar. The last rows of these tables indicate that regular nurse shortages are well distributed over the weeks and that it is equal to zero on Monday and Friday of each week. The row 'supervising personnel shortage' indicates that obj 4 is satisfied. Furthermore, it is easy to verify that days off are grouped for Nurses 3, 4, and 5, and weekends off are extended for Nurses 1 and 2. Finally, special requests for days off and for consecutive working days are fulfilled. Needless to say, the head-nurse was fully satisfied with these schedules.
(ii) Cutting-stock problem
DEFINITION:
The cutting-stock problem is defined as a nondeterministic polynomial time –complete optimization problem and also an integer linear programming problem. It is a technique to find optimum cutting patterns. There are one and two dimensional cutting stock problems.
Based on the literature studies, the Russian economist, Kantorovich(1960) has given the first formulation of cutting stock problem. Next, Gilmore(1961) and Gomory(1963) described their delayed pattern generation technique for solving the one dimensional minimization problem using linear programming.

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