Pareto-optimality conditions are crucial when dealing with classic multi-objective optimization problems because we need to find out a set of optimal solutions rather than only one optimal solution to optimization problem with a single objective. Extensions of these conditions to the fuzzy domain have been discussed and addressed in recent literature. This work presents a novel approach based o...

This paper deals with the estimation of the lognormal-Pareto and the lognormal-Generalized Pareto distributions, for which a general result concerning asymptotic optimality of maximum likelihood estimation cannot be proved. We develop a method based on probability weighted moments, showing that it can be applied straightforwardly to the first distribution only. In the lognormal-Generalized Pare...

For multi-objective optimal reactive power dispatch (MORPD), a new approach is proposed where simultaneous minimization of the active power transmission loss, the bus voltage deviation and the voltage stability index of a power system are achieved. Optimal settings of continuous and discrete control variables (e.g. generator voltages, tap positions of tap changing transformers and the number of...

Design of control systems is characterised by many targets, therefore the methods enabling optimisation of several objectives have received more and more attention over the past years. When dealing with multi-objective optimisation problems the notion of the scalar function optimality was extended. The most common approach was originally proposed in 19th century by Edgeworth and later generalis...

The representation of data quality within established high-dimensional data visualization techniques such as scatterplots and parallel coordinates is still an open problem. This work offers a scale-invariant measure based on Pareto optimality that is able to indicate the quality of data points with respect to the Pareto front. In cases where datasets contain noise or parameters that cannot easi...

We consider a vector minimax Boolean programming problem. The problem consists in finding the set of Pareto optimal solutions. When the problem’s parameters vary then the optimal solution of the problem obtained for some initial parameters may appear non-optimal. We calculate the maximal perturbation of parameters which preseves the optimality of a given solution of the problem. The formula for...

In this paper, we consider the problem of Pareto optimal allocation in a general framework, involving preference functionals defined on a general real vector space. The optimization problem is equivalent to a modified sup-convolution of the different agents’ preference functionals. The results are then applied to a multi-period setting and some further characterization of Pareto optimality for ...

In this paper the authors point out that the Pareto Optimality is unfair, unreasonable and imperfect for Many-objective Optimization Problems (MOPs) underlying the hypothesis that all objectives have equal importance. The key contribution of this paper is the discovery of the new definition of optimality called ε-optimality for MOP that is based on a new conception, so called ε-dominance, which...

Swarm Intelligence (SI) is a relatively new paradigm being applied in a host of research settings to improve the management and control of large numbers of interacting entities such as communication, computer and sensor networks, satellite constellations and more. Attempts to take advantage of this paradigm and mimic the behavior of insect swarms however often lead to many different implementat...