A new adaptive algorithm for convex quadratic multicriteria optimization

We present a new adaptive 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. Numerical results show that this technique is faster than a standard method used for this problem

Glider Routing and Trajectory Optimisation in disaster assessment

In this paper, we introduce the Glider Routing and Trajectory Optimisation Problem (GRTOP), the problem of finding optimal routes and trajectories for a fleet of gliders with the mission of surveying a set of locations. We propose a novel MINLP formulation for the GRTOP. In our approach, we consider the gliders' flight dynamics during the definition of the routes. In order to achieve better convergence, we linearise the gliders' dynamics and relax the dynamic constraints of our model, converting the proposed MINLP into a MISOCP. Several different discretisation techniques and solvers are compared. The formulation is tested on 180 randomly generated instances. In addition, we solve instances inspired by risk maps of flooding-prone cities across the UK

Reliability-as-a-Service for bearing risk assessment investigated with advanced mathematical models

As a key player in bearing service life, the lubricant chemistry has a profound effect on bearing reliability. To increase the reliability of bearings, an Industrial Analytics solution is proposed for proactive condition monitoring and this is delivered via a Reliability-as-a-Service application. The performance predictions of bearings rely on customized algorithms with the main focus on digitalizing lubricant chemistry; the principles behind these processes are outlined in this study. Subsequently, independent testing is performed to confirm the ability of the presented Industrial Analytics solution for such predictions. By deciphering the chemical compounds of lubricants and characteristics of the interface, the Industrial Analytics solution delivers a precise bearing reliability assessment a priori to predict service life of the operation. Bearing tests have shown that the classification system of this Industrial Analytics solution is able to predict 12 out of 13 bearing failures (92%). The described approach provides a proactive bearing risk classification that allows the operator to take immediate action in reducing the failure potential during smooth operation - preventing any potential damage from occurring. For this purpose, a mathematical model is introduced that derives a set of classification rules for oil lubricants, based on linear binary classifiers (support vector machines) that are applied to the chemical compound's mixture data.</p

Finding and verifying the nucleolus of cooperative games

The nucleolus offers a desirable payoff-sharing solution in cooperative games, thanks to its attractive properties—it always exists and lies in the core (if the core is non-empty), and it is unique. The nucleolus is considered as the most ‘stable’ solution in the sense that it lexicographically minimizes the dissatisfactions among all coalitions. Although computing the nucleolus is very challenging, the Kohlberg criterion offers a powerful method for verifying whether a solution is the nucleolus in relatively small games (i.e. with the number of players n≤ 15). This approach, however, becomes more challenging for larger games because of the need to form and check a criterion involving possibly exponentially large collections of coalitions, with each collection potentially of an exponentially large size. The aim of this work is twofold. First, we develop an improved version of the Kohlberg criterion that involves checking the ‘balancedness’ of at most (n- 1) sets of coalitions. Second, we exploit these results and introduce a novel descent-based constructive algorithm to find the nucleolus efficiently. We demonstrate the performance of the new algorithms by comparing them with existing methods over different types of games. Our contribution also includes the first open-source code for computing the nucleolus for games of moderately large sizes. © 2020, The Author(s)

Stochastic programming with multivariate second order stochastic dominance constraints with applications in portfolio optimization

In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component of vectors can be interpreted as the uncertain outcome of a given criterion. We propose a penalization scheme for the multivariate second order stochastic dominance constraints. We solve the penalized problem by the level function methods, and a modified cutting plane method and compare them to the cutting surface method proposed in the literature. The proposed numerical schemes are applied to a generic budget allocation problem and a real world portfolio optimization problem

The effects of adding objectives to an optimisation problem on the solution set

Suppose that an additional objective function is introduced into a (multicriteria or singlecriterion) optimisation problem. The following questions are considered: How does the set of (properly, weakly, or strictly) efficient points changes when instead of the old problem the new problem is considered? What happens in the value space