A generic framework for handling constraints with agent-based optimization algorithms and application to aerodynamic design

Abstract

A generic constraint handling framework for use with any swarm-based optimization algorithm is presented. For swarm optimizers to solve constrained optimization problems effectively modifications have to be made to the optimizers to handle the constraints, however, these constraint handling frameworks are often not universally applicable to all swarm algorithms. A constraint handling framework is therefore presented in this paper that is compatible with any swarm optimizer, such that a user can wrap it around a chosen swarm algorithm and perform constrained optimization. The method, called separation-sub-swarm, works by dividing the population based on the feasibility of individual agents. This allows all feasible agents to move by existing swarm optimizer algorithms, hence promoting good performance and convergence characteristics of individual swarm algorithms. The framework is tested on a suite of analytical test function and a number of engineering benchmark problems, and compared to other generic constraint handling frameworks using four different swarm optimizers; particle swarm, gravitational search, a hybrid algorithm and differential evolution. It is shown that the new framework produces superior results compared to the established frameworks for all four swarm algorithms tested. Finally, the framework is applied to an aerodynamic shape optimization design problem where a shock-free solution is obtained.

Global Optimization of Wing Aerodynamic Optimization Case Exhibiting Multimodality

“…Furthermore, it is clear that the optimization framework has performed well, resulting in a converged population of particles on a single global optimum. This is a result also repeated when tested on a much larger suite of analytical functions [42]. …”

“…While global optimization can often be more expensive than performing gradient-based optimization, it is more likely to locate a globally optimal solution in a multimodal design space. The optimization framework has been developed by the authors, and shown to be effective an optimizing benchmark analytical problems [42] as well as transonic aerofoil problems [1].…”

“…A comparison of the update approaches between PSO and GSA is given in figure 8. Constraints are not directly handled in the PSO or GSA algorithms, hence the separation-sub-swarm (3S) [42] constraint handling method is applied. The 3S method is a constraint handling framework that can be applied to any swarm intelligence algorithm and works by splitting the overall population into two independent swarms every iteration -one swarm containing all of the feasible particles at that iteration (all constraints are satisfied) and one containing all of the infeasible particles at that iteration (at least one constraint is violated).…”

“…However, to investigate the mutimodality of the ADODG multimodal benchmark problem, a state-of-the-art constrained global optimization framework [42] is employed here. The framework, which uses a parallel decomposition of the search agent population for efficient computation, has previously been used for drag minimization of aerofoils [1] and is used here for the wing optimization.…”

Objective Function and Constraints for Robust Transonic Aerofoil Optimization

“…A hybrid of the particle swarm optimization (PSO), 35 and the gravitational search algorithm (GSA) 36 has been developed and used here such that the memory qualities of PSO complement the global transfer of data that occurs in GSA to obtain a highly efficient global search algorithm. Constraints are not directly handled in the PSO or GSA algorithms, hence the separation-sub-swarm (3S) 37 constraint handling method is applied. The 3S method is a constraint handling framework that can be applied to any swarm intelligence algorithm and works by splitting the overall population into two independent swarms every iteration -one swarm containing all of the feasible particles at that iteration (all constraints are satisfied) and one containing all of the infeasible particles at that iteration (at least one constraint is violated).…”