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Table 2 Summary of solution approaches to RA problems in CRN

From: Solving resource allocation problems in cognitive radio networks: a survey

S/N Solution approaches Solution methods and/or models Features Drawbacks
1. Classical optimisation e.g. LP, convex optimisation etc. Simplex and its variants (BnB, BnC, LnS, implicit enumeration etc.); inte rior point method and its variants (barrier method, Newton’s method etc.); Lagrangian duality; knapsack; travelling salesman problem etc. Approach gives optimal solutions; solutions act as bounds (upper or lower) to other solution models. Usually, most RA problems do not fit into any class of classical optimisation; proving convexity can be very challenging; obtaining solutions can be rather computationally complex and time consuming.
2. Studying problem structure Decomposition; linearisation; relaxation; approximation; reformulation. Solutions can be optimal or very close to optimal; computational complexity is significantly lowered. Special features might be unavailable or difficult to find; transformed problem may be a far cry from the original; new problem may generate more decision variables than in the original one; solutions are mostly suboptimal.
3. Heuristics Greedy algorithms; water-filling algorithms; pre-assignment and reassignment algorithms; iterative-based and recursive-based algorithms. Solutions are quick to find; less computational complexity; requires little or no numerical analysis; solutions usually suboptimal but could be close to optimal; approach is suitable for large and practical networks. Solutions are problem-specific and most times are not transferable; solutions can not be numerically analysed; solutions are always suboptimal.
4. Meta-heuristics Genetic algorithms; simulated annealing; evolutionary algorithms; tabu searches. Algorithms are mostly nature-inspired; they make use of stochastic components (e.g. random variables); they are good with large, practical and/or computationally demanding problems that have large search spaces; they use ‘tricks’ so as to not get stuck at a local optimal but to try obtain a global optimal solution. Solutions are not transferable; solutions cannot be analysed numerically.
5. Multi-objective optimisation (using game theory) Cooperative game; non-cooperative game; Nash bargaining (Pareto optimisation); Stackelberg game. They are good with problems that have multiple objectives; they employ ideas from game theory to solve optimisation problems; they are useful for large, practical networks with large search spaces. Solution models can be complex; they are not transferable; there may be difficulty in achieving analytical modelling of solutions.
6. Soft computing-based optimisation Artificial intelligence; neural networks; Q-learning; fuzzy systems etc. Software/computer-based programming are used in allocating resources to users within the network; the developed programmes use intelligent and very powerful/sophisticated techniques. They are very difficult and complex to develop, analyse and apply in real life scenarios.