PSwarm: a hybrid solver for linearly constrained global derivative-free optimization

Abstract

PSwarm was developed originally for the global optimization of functions without derivatives and where the variables are within upper and lower bounds. The underlying algorithm used is a pattern search method, or more specifically, a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the (optional) search step of coordinate search, the algorithm incorporates a particle swarm scheme for dissemination of points in the feasible region, equipping the overall method with the capability of finding a global minimizer. Our extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods based only on function values.PSwarm is extended is this paper to handle general linear constraints. The poll step now incorporates positive generators for the tangent cone of the approximated active constraints, including a provision for the degenerate case. The search step has also been adapted accordingly. In particular, the initial population for particle swarm used in the search step is computed by first inscribing an ellipsoid of maximum volume to the feasible set. We have again compared PSwarm to other solvers (including some designed for global optimization) and the results confirm its competitiveness in terms of efficiency and robustness.

Globally Convergent Hybridization of Particle Swarm Optimization Using Line Search-Based Derivative-Free Techniques

“…Thus, our result reinforces the theoretical properties of modified PSO schemes. To the best of our knowledge, our result is also among the first attempts to couple PSO with linesearch-based derivative-free schemes (see also Vaz and Vicente 2007 [30], Vaz and Vicente 2009 [31] for extensions to trust-region derivative-free approaches), where a modified PSO scheme is proved to satisfy conditions like (20) or (21). On the basis of our experience, which seems confirmed by the results reported here, we are persuaded that a fruitful coupling of PSO with an iterative globally convergent derivative-free method, should yield a compromise, between the fast progress of PSO (global search) in the early iterations, and the capability to exploit (local search) the objective function.…”

“…We want to show that global convergence properties of a modified PSO scheme may be obtained by properly combining PSO with a linesearch-based derivative-free method, so that convergence to stationary points can be forced at a reasonable cost (see also items (b) and (c) of Sect. [31]), in order to provide again globally convergent methods to stationary points.…”

Differential Evolution Based Bi-Level Programming Algorithm for Computing Normalized Nash Equilibrium

“…For the purposes of comparing DEBLP-SR against others proposed in the literature, we also used PSwarm [25], which is explicitly designed to handle both bound and linear constraints, to solve our test problems. We are unable to include a comparison of DEBLP-SR with PSWARM due to space constraints but instead have made the performance comparison available at http://goo.gl/bupz0.…”

Effective design of semiconductor devices using evolutionary-based derivative free optimization

“…We compare the performance of CMA-ES and DE with the ones of PSwarm [18], [19], [20], which is a deterministic variant of the Particle Swarm Optimization (PSO) algorithm; in particular, PSwarm assures a convergence to secondarystationary points if the conditions for pattern-search convergence are met.…”