Jörg Fliege We present a novel response surface method for global optimisation of an expensive and noisy (black-box) objective function, where error bounds on the deviation of the observed noisy function values from their true counterparts are available. The method is based on the well-established RBF method by Gutmann (2001a,c) for minimising an expensive and deterministic objective … Read more
A number of first-order methods have been proposed for smooth multiobjective optimization for which some form of convergence to first order criticality has been proved. Such convergence is global in the sense of being independent of the starting point. In this paper we analyze the rate of convergence of gradient descent for smooth unconstrained multiobjective … Read more
In this paper, we introduce the Glider Routing and Trajectory Optimisation Problem (GRTOP), the problem of finding simultaneously optimal routes and trajectories for a fleet of gliders with the aim of surveying a set of locations. We propose a novel Mixed-Integer Nonlinear Programming (MINLP) formulation for the GRTOP, which simultaneously optimises the routes as well … Read more
Unmanned Aerial Vehicles (UAVs) are becoming increasingly popular over the past few years. The complexity of routing UAVs has not been fully investigated in the literature. In this survey, we aim to review recent contributions in UAV trajectory optimisation, UAV routing and contributions addressing these two problems simultaneously. A unified framework is introduced to describe … Read more
We propose an SQP type method for constrained nonlinear multiobjective optimization. The proposed algorithm maintains a list of nondominated points that is improved both for spread along the Pareto front and optimality by solving singleobjective constrained optimization problems. Under appropriate differentiability assumptions we discuss convergence to local optimal Pareto points. We provide numerical results for … Read more
In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multiobjective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such … Read more
We propose an extension of Newton’s Method for unconstrained multiobjective optimization (multicriteria optimization). The method does not scalarize the original vector optimization problem, i.e. we do not make use of any of the classical techniques that transform a multiobjective problem into a family of standard optimization problems. Neither ordering information nor weighting factors for the … Read more
We present a new primal-dual algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Results of this algorithm when applied on a three-criteria real-world power plant optimization problem are reported, thereby illustrating the feasibility of … Read more
Suppose that for a given optimisation problem (which might be multicriteria problem or a single-criteron problem), an additional objective function is introduced. How does the the set of solutions, i.~e.\ the set of efficient points change when instead of the old problem the new multicriteria problem is considered? How does the set of properly efficient … Read more
In multicriteria optimization, several objective functions, conflicting with each other, have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multiobjective programming problem, where the objective functions involved are arbitary convex functions and the set of feasible points is convex. The method is based on generating warm-start … Read more