The use of evolutionary algorithms (EAs) to solve problems with multiple objectives (known as Multi-objective Optimization Problems (MOPs)) has attracted much attention recently. Being population based approaches, EAs offer a means to find a group of pareto-optimal solutions in a single run. Differential Evolution (DE) is an EA that was developed to handle optimization problems over continuous ...

Many real-world control applications, from economics to robotics, are characterized by the presence of multiple conflicting objectives. In these problems, the standard concept of optimality is replaced by Pareto–optimality and the goal is to find the Pareto frontier, a set of solutions representing different compromises among the objectives. Despite recent advances in multi–objective optimizati...

One of the most important tasks in multi-objective optimization is "trade-off analysis" which aims to make the total balance among objective functions. The trade-off relation among alternatives can be shown as Pareto frontier. In cases with two or three objective functions, the set of Pareto optimal solutions in the objective function space (i.e., Pareto frontier) can be depicted relatively eas...

We study retrading via reopening of trading posts in a market game where the static Nash equilibria yield Pareto suboptimal allocations whenever endowments are Pareto suboptimal. We show that there are allocations on the Pareto frontier that can be approximated arbitrarily closely along some Subgame Perfect Equilibrium path of retrading. The approximation result can also be proved when traders ...

where x is an n-dimensional vector of variables, A is an m × n matrix, b is the RHS vector and the vectors ci (i = 1, ...,m) represent the coefficients of the objective functions (criteria). Let’s denote yi = fi(x), i = 1, ...,m, and let y = (y1, ..., ym) be a vector in the criteria space. The set Y ⊂ Rm composed by all possible criterion vectors y = f(x) when x ∈ X, is known as Feasible Criter...

A visualization methodology is presented in which a Pareto Frontier can be visualized in an intuitive and straightforward manner for an n-dimensional performance space. Based on this visualization, it is possible to quickly identify ‘good’ regions of the performance and optimal design spaces for a multi-objective optimization application, regardless of space complexity. Visualizing Pareto solut...

This paper is about learning a continuous approximation of the Pareto frontier in Multi–Objective Markov Decision Problems (MOMDPs). We propose a policy–based approach that exploits gradient information to generate solutions close to the Pareto ones. Differently from previous policy–gradient multi–objective algorithms, where n optimization routines are used to have n solutions, our approach per...

This paper is about learning a continuous approximation of the Pareto frontier in Multi–Objective Markov Decision Problems (MOMDPs). We propose a policy–based approach that exploits gradient information to generate solutions close to the Pareto ones. Differently from previous policy–gradient multi–objective algorithms, where n optimization routines are use to have n solutions, our approach perf...

This paper investigates the use of a multi-objective approach for evolving artificial neural networks that act as controllers for the legged locomotion of a 3-dimensional, artificial quadruped creature simulated in a physics-based environment. The Pareto-frontier Differential Evolution (PDE) algorithm is used to generate a pareto optimal set of artificial neural networks that optimizes the conf...

A multiobjective optimization problem is considered in a general formulation. It is well known that the solution of the problem is not unique and represented in the objective space by a Pareto frontier. In an engineering design it can be important to provide a discrete representation of the entire Pareto surface. Meanwhile, the obtaining of a single Pareto solution may be time-consuming. Moreov...