Hybrid cuckoo search optimization algorithms applied to complex wellbore trajectories aided by dynamic, chaos-enhanced, fat-tailed distribution sampling and metaheuristic profiling

Hybrid cuckoo search optimization (hCSO) algorithms are shown to be effective and efficient for complex wellbore trajectory design. The hCSO involves potentially eight metaheuristic components that complement each other in their search contributions and operate as a “tool box” of modules such that six of them can be easily switched on or off. The metaheuristics are coordinated to progress through five distinct steps that constitute hCSO: (1) initialization; (2) exchange; (3) modification; (4) replacement; (5) metaheuristic labelling, ranking and carry forward.Key amendments introduced to hCSO involve replacing Levy flight solution space sampling with stochastic random sampling of simpler fat-tailed distributions with dynamic sampling windows that move through the distribution as iterations of the algorithm advance. The left-hand graph illustrates how that sampling is configured and adjusted with a chaotic sequence to provide a useful adjustment factor resulting in a more controlled search of the solution space. Equations are provided to show how this can be achieved using simplified fat-tailed distributions as an alternative to Levy flights. The scaled-chaotic sequences sampled provide more flexibility and control over the granularity of the sampling of the solution space, which has potential for other applications. Other metaheuristics are added to the standard CSO that improve the balance of the algorithm between local and global searching. Three of the metaheuristics include chaotic adjustments to dynamic stochastic sampling of search metrics distributions (fat-tailed and other, highly non-linear, stepped ranges). Another, highly effective dynamic sampling technique of a customized, stepped and tapered range of adjustment factors (right-hand graph) is used to control another metaheuristic in hCSO. The combined functioning of the metaheuristics making up the hCSO algorithm using contrasting distribution sampling, as shown in the two figures, is part of the reason that hCSO balances local and global searches of the solution space very effectively. Detailed metaheuristic profiling is used to illustrate the relative contributions of the metaheuristic components in several high-performing configurations of the hCSO algorithm.337