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The success of any organization in a knowledge-based economy depends on effective knowledge transferring and then proper use of the transferred knowledge. As is known, optimizing the knowledge transferring costs in a product portfolio plays an important role in improving productivity, competitive advantage and profitability of any organization. Therefore, this paper aims to determine an optimal product portfolio by minimizing the konlwedge transferring costs.

Here, a fuzzy binary linear programming model is used to select an optimal product portfolio. The model is capable of considering the knowledge transferring costs while taking into account the human-hours constraints for each product by a fuzzy approach. Using fuzzy ranking functions, a reasonable solution of the model can be achieved by classical or metaheuristic algorithms.

Numerical experiments indicate that the proposed fuzzy model is practically effective.

The contributions of this work essentially consist of considering knowledge transferring costs in selecting an optimal product portfolio and using the fuzzy data which make the model more realistic.

The purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.

The well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region (TR) algorithm.

An adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula. Also, a (heuristic) randomized adaptive TR algorithm is developed for solving unconstrained optimization problems. Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods.

The algorithm can be effectively used for solving the optimization problems which appear in engineering, economics, management, industry and other areas.

The proposed randomization scheme improves computational costs of the classical TR algorithm. Especially, the suggested algorithm avoids resolving the TR subproblems for many times.

Previous RMIL versions of the conjugate gradient method proposed in literature exhibit sufficient descent with Wolfe line search conditions, yet their global convergence depends on certain restrictions. To alleviate these assumptions, a hybrid conjugate gradient method is proposed based on the conjugacy condition.

The conjugate gradient (CG) method strategically alternates between RMIL and KMD CG methods by using a convex combination of the two schemes, mitigating their respective weaknesses. The theoretical analysis of the hybrid method, conducted without line search consideration, demonstrates its sufficient descent property. This theoretical understanding of sufficient descent enables the removal of restrictions previously imposed on versions of the RMIL CG method for global convergence result.

Numerical experiments conducted using a hybrid strategy that combines the RMIL and KMD CG methods demonstrate superior performance compared to each method used individually and even outperform some recent versions of the RMIL method. Furthermore, when applied to solve an image reconstruction model, the method exhibits reliable results.

The strategy used to demonstrate the sufficient descent property and convergence result of RMIL CG without line search consideration through hybrid techniques has not been previously explored in literature. Additionally, the two CG schemes involved in the combination exhibit similar sufficient descent structures based on the assumption regarding the norm of the search direction.