The emptiness of the core of a voting game can be viewed as the failure of a society to select a stable alternative : every alternative can be vetoed by a winning coalition. To solve this problem, also known as the paradox of voting, Rubinstein (1980) introduces the stability set by a clause of prudence in the core dominance relation which amounts to assume that individuals are aware of possibl...

Hypervolume indicator is a commonly accepted quality measure for comparing Pareto approximation set generated by multi-objective optimizers. The best known algorithm to calculate it for n points in ddimensional space has a run time of O(n) with special data structures. This paper presents a recursive, vertex-splitting algorithm for calculating the hypervolume indicator of a set of n non-compara...

Pareto set generation methods are considered with respect to their application for multi criteria portfolio selection. Several such methods were compared experimentally including some recently proposed evolutionary methods and the method of adjustable weights. Test problems were based on standard portfolio quality criteria and data on stocks of 10 Lithuanian companies. The experimental data on ...

Many real-world problems involve the optimization of multiple, possibly conflicting objectives. Multi-objective reinforcement learning (MORL) is a generalization of standard reinforcement learning where the scalar reward signal is extended to multiple feedback signals, in essence, one for each objective. MORL is the process of learning policies that optimize multiple criteria simultaneously. In...

In optimization problems with at least two conflicting objectives, a set of solutions rather than a unique one exists because of the trade-offs between these objectives. A Pareto optimal solution set is achieved when a solution cannot be improved upon without degrading at least one of its objective criteria. This study investigated the application of multi-objective evolutionary algorithm (MOEA...

The paper investigates the notion of Pareto-Nash equilibrium as continuation of the works [2–4]. Problems and basic theoretical results are exposed. Method of intersection of graphs of best response mappings [3] is applied to solve the dyadic two-criteria games. Mathematics Subject Classification 2000: 91A05, 91A06, 91A10, 91A43, 91A44.

Many practical optimization problems usually have several conflicting objectives. In those multi-objective optimization, no solution optimizing all objective functions simultaneously exists in general. Instead, Pareto optimal solutions, which are “efficient” in terms of all objective functions, are introduced. In general we have many Pareto optimal solutions. Therefore, we need to decide a fina...

Multiobjective problems usually contain conflicting objectives. Therefore, there is no single best solution but a set of solutions that represent different tradeoffs between these objectives. Knowledge of this front can help in understanding the optimization problem better, as promising designs can be identified, and it can be seen what the achievable tradeoffs between the objective values are....

Evolutionary algorithms (EAs) have been well acknowledged as a promising paradigm for solving optimisation problems with multiple conflicting objectives in the sense that they are able to locate a set of diverse approximations of Pareto optimal solutions in a single run. EAs drive the search for approximated solutions through maintaining a diverse population of solutions and by recombining prom...

In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider multiobjective optimization problems that additionally depend on an external parameter λ ∈ R, so-called parametric...