On D-Optimality Based Trust Regions for Black-Box Optimization Problems

In this paper we show how techniques from response surface methodology and mathematical programming can be combined into a new sequential derivative-free approach for solving unconstrained deterministic black-box optimization problems.In this sequential derivative-free optimization approach local approximations of the underlying objective function are optimized within a trust region framework.If the points that determine the local approximations are located in such away that the approximations become bad, a geometry improving iteration is carried out instead of an objective improving iteration.We incorporate the D-optimality criterion, well-known in design of experiments, in our approach in two different ways.Firstly, it is used to define a trust region that adapts its shape to the locations of the points in which the objective function has been evaluated.Secondly, it determines an optimal geometry improving point.An attractive feature of our approach is that it is insensitive to affine transformations

On D-Optimality Based Trust Regions for Black-Box Optimization Problems

In this paper we show how techniques from response surface methodology and mathematical programming can be combined into a new sequential derivative-free approach for solving unconstrained deterministic black-box optimization problems.In this sequential derivative-free optimization approach local approximations of the underlying objective function are optimized within a trust region framework.If the points that determine the local approximations are located in such away that the approximations become bad, a geometry improving iteration is carried out instead of an objective improving iteration.We incorporate the D-optimality criterion, well-known in design of experiments, in our approach in two different ways.Firstly, it is used to define a trust region that adapts its shape to the locations of the points in which the objective function has been evaluated.Secondly, it determines an optimal geometry improving point.An attractive feature of our approach is that it is insensitive to affine transformations.D-optimality;trust region;derivative free;optimization;affine transformations

Approximation of System Components for Pump Scheduling Optimisation

© 2015 The Authors. Published by Elsevier Ltd.The operation of pump systems in water distribution systems (WDS) is commonly the most expensive task for utilities with up to 70% of the operating cost of a pump system attributed to electricity consumption. Optimisation of pump scheduling could save 10-20% by improving efficiency or shifting consumption to periods with low tariffs. Due to the complexity of the optimal control problem, heuristic methods which cannot guarantee optimality are often applied. To facilitate the use of mathematical optimisation this paper investigates formulations of WDS components. We show that linear approximations outperform non-linear approximations, while maintaining comparable levels of accuracy

Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201