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Moreover, it is this subtask that accounts for the computational difficulty of both forms of reasoning.
The computational difficulty of these approaches, however, makes it very hard for practicing engineers to perform these analyses.
Though some evidence of the computational difficulty of such problems can be found in the literature, no formal NP-hardness proof was available up to now.
Given the computational difficulty of the model, two hybrid approaches, one combining a genetic algorithm and linear programming (GALP) and the other combining simulated annealing and linear programming (SALP), are proposed to efficiently solve real-sized problems.
However, the computational difficulty of the projection might seriously affect the efficiency of the method.
Together with the metaheuristic optimization approaches, the methodology overcomes the well-known computational difficulty of Nash equilibrium search, particularly for a large-scale problem.
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In addition, the computational difficulties of these optimization tasks increase rapidly with the increasing number of decision variables.
Then, considering the computational difficulties of solving this model, the grouping genetic algorithm hybridizing the local neighborhood search heuristic is proposed.
Constraint grouping enhances handling of multiple constraints for vectorized problems, by combining several constraints within a single-objective function, thus reducing the computational time and computational difficulties of high-dimensional spaces created by vectorization.
Conventional network structure modifications for retrofitting heat exchanger networks (HENs) usually require a large network superstructure, which might lead to very large scale retrofit models, and thus increases the computational difficulties of optimization, especially for industrial applications.
Despite its relevance, computing the boundary of the set swept by a non-polyhedral moving object is largely an open problem due to well-known theoretical and computational difficulties of the envelopes.
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