Efficient algorithms for solving nonlinear fractional programming problems

In this paper, an efficient algorithm based on the Pascoletti-Serafini scalarization (PS) approach is proposed to obtain almost uniform approximations of the entire Pareto front of bi-objective optimization problems. Five test problems with convex, non-convex, connected, and disconnected Pareto fronts are applied to evaluate the quality of approximations obtained by the proposed algorithm. Results are compared with results of some algorithms including the normal constraint (NC), weighted constraint (WC), Benson type, differential evolution (DE) with binomial crossover, non-dominated sorting genetic algorithm-II (NSGA-II), and S metric selection evolutionary multiobjective algorithm (SMS-EMOA). The results confirm the effectiveness of the presented bi-objective algorithm in terms of the quality of approximations of the Pareto front and CPU time. In addition, two algorithms are presented for approximately solving fractional programming (FP) problems. The first algorithm is based on an objective space cut and bound method for solving convex FP problems and the second algorithm is based on the proposed bi-objective algorithm for solving nonlinear FP problems. In addition, several examples are provided to demonstrate the performance of these suggested fractional algorithms.

Stable-Matching-Based Energy-Efficient Context-Aware Resource Allocation for Ultra-Dense Small Cells

Implementing caching to ultra-densely deployed small cells provides a promising solution for satisfying the stringent quality of service (QoS) requirements of delay-sensitive applications with limited backhaul capacity. With the rapidly increasing energy consumption, in this chapter, the authors investigate the NP-hard energy-efficient context-aware resource allocation problem and formulate it as a one-to-one matching problem. The preference lists in the matching are modeled based on the optimum energy efficiency (EE) under specified matching, which can be obtained by using an iterative power allocation algorithm based on nonlinear fractional programming and Lagrange dual decomposition. Next, on account of the Gale-Shapley algorithm, an energy-efficient matching algorithm is proposed. Some properties of the proposed algorithm are discussed and analyzed in detail. Moreover, the authors extend the algorithm to the matching with indifferent and incomplete preference lists. Finally, the significant performance gain of the proposed algorithm is demonstrated through simulation results.

Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems

Some assumptions for the objective functions and constraint functions are given under the conditions of convex and generalized convex, which are based on theF-convex,ρ-convex, and(F,ρ)-convex. The sufficiency of Kuhn-Tucker optimality conditions and appropriate duality results are proved involving(F,ρ)-convex,(F,α,ρ,d)-convex, and generalized(F,α,ρ,d)-convex functions.