Probabilistic combinatorial optimization problems on graphs: a new domain in operational research

Article Abstract:

Probabilistic combinatorial optimization (PCO) problems refer to the class of optimization problems with random data due to uncertainty or unreliable predictions. At present, it is a new field of study in operations research and as such, many methodological and conceptual problems still exist. One examples include the definition of functionals for minimization PCOs. This is evident in the analysis of PCOs defined on graphs such as the traveling salesman problem, minimum spanning tree problem and vehicle routing problem.

Operations research, Management science, Probability theory, Combinatorial optimization, Optimization theory, Graph theory, Traveling-salesman problem, Mathematical programming, Combinatorial probabilities

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A generalization of Konig-Egervary graphs and heuristics for the maximum independent set problem with improved approximation ratios

Article Abstract:

An exact polynomial time algorithm for generating solutions to maximum independent set problems was developed based on generalizations of the Konig-Egervary (KE) graphs and the class of kappa-KE graphs. The maximum independent set problem was generalized to obtain a weighted version that was produced by maximizing the sum of weights of the vertices of an independent set. Furthermore, the approximation ratios for maximum independent set problem was improved by the generic approximation of independent set algorithms.

Heuristic, Heuristics (Psychology)

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A genetic algorithm solution for one-dimensional bundled stock cutting

Article Abstract:

A genetic search algorithm was proposed for a one-dimensional cutting stock problem. The proposed algorithm, which are based on natural selection and natural genetics, takes into account trim loss, stock usage and ending inventory levels. It involves assigning a probability of survival based on the value of the objective function after initial strings were randomly generated. Analysis shows that the above problem cannot be solved by integer programming procedures.

Heuristic programming

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