A general branch-and-bound framework for continuous global multiobjective optimization

Constraint Optimization Techniques for MultiObjective Branch and Bound Search

A General Framework for Convexity Analysis and an Alternative to Branch and Bound in Deterministic Global Optimization

To date, complete search in deterministic global optimization has been based on branch and bound techniques, with the bounding often done with linear or convex relaxations of the original non-convex problem. Here, we present an alternative, inspired by talks of Ch. Floudas. In this alternative, a set of non-convex variables, chosen from the intermediate variables in the expressions for the obje...

A branch and bound method for stochastic global optimization

A stochastic version of the branch and bound method is proposed for solving stochastic global optimization problems. The method, instead of deterministic bounds, uses stochastic upper and lower estimates of the optimal value of subproblems, to guide the partitioning process. Almost sure convergence of the method is proved and random accuracy estimates derived. Methods for constructing random bo...

A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and ...

A general framework for evolutionary multiobjective optimization via manifold learning

Under certain mild condition, the Pareto-optimal set (PS) of a continuous multiobjective optimization problem, with m objectives, is a piece-wise continuous (m 1)-dimensional manifold. This regularity property is important, yet has been unfortunately ignored in many evolutionary multiobjective optimization (EMO) studies. The first work that explicitly takes advantages of this regularity propert...