On some geometric optimization problems in layered manufacturing
Computational Geometry: Theory and Applications
Protecting critical facets in layered manufacturing
Computational Geometry: Theory and Applications
Monotonic Optimization: Problems and Solution Approaches
SIAM Journal on Optimization
Minimization of the sum of three linear fractional functions
Journal of Global Optimization
Solving the Sum-of-Ratios Problem by an Interior-Point Method
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
A Unified Monotonic Approach to Generalized Linear Fractional Programming
Journal of Global Optimization
Global optimization for the sum of linear ratios problem over convex feasible region
ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part II
A practical but rigorous approach to sum-of-ratios optimization in geometric applications
Computational Optimization and Applications
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In this paper, we point out a theoretical flaw in Kuno [(2002)Journal of Global Optimization 22, 155---174] which deals with the linear sum-of-ratios problem, and show that the proposed branch-and-bound algorithm works correctly despite the flaw. We also note a relationship between a single ratio and the overestimator used in the bounding operation, and develop a procedure for tightening the upper bound on the optimal value. The procedure is not expensive, but the revised algorithms incorporating it improve significantly in efficiency. This is confirmed by numerical comparisons between the original and revised algorithms.