Optimizing the sum of linear fractional functions
Recent advances in global optimization
Minimizing and maximizing the product of linear fractional functions
Recent advances in global optimization
Linear multiplicative programming
Mathematical Programming: Series A and B
Journal of Global Optimization
A branch-and-bound algorithm for maximizing the sum of several linear ratios
Journal of Global Optimization
Using concave envelopes to globally solve the nonlinear sum of ratios problem
Journal of Global Optimization
Global optimization algorithm for the nonlinearsum of ratios problem
Journal of Optimization Theory and Applications
A Revision of the Trapezoidal Branch-and-Bound Algorithm for Linear Sum-of-Ratios Problems
Journal of Global Optimization
Global optimization for sum of generalized fractional functions
Journal of Computational and Applied Mathematics
Solving the sum-of-ratios problem by a stochastic search algorithm
Journal of Global Optimization
Solving the sum-of-ratios problems by a harmony search algorithm
Journal of Computational and Applied Mathematics
A numerical study on B&B algorithms for solving sum-of-ratios problem
AST/UCMA/ISA/ACN'10 Proceedings of the 2010 international conference on Advances in computer science and information technology
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In this paper, we will propose an efficient and reliable heuristic algorithm for minimizing and maximizing the sum of three linear fractional functions over a polytope. These problems are typical nonconvex minimization problems of practical as well as theoretical importance. This algorithm uses a primal-dual parametric simplex algorithm to solve a subproblem in which the value of one linear function is fixed. A subdivision scheme is employed in the space of this linear function to obtain an approximate optimal solution of the original problem. It turns out that this algorithm is much more efficient and usually generates a better solution than existing algorithms. Also, we will develop a similar algorithm for minimizing the product of three linear fractional functions.