A parallel genetic algorithm (GA) was used to generate, in a single run, a family of aerodynamically efficient, low-noise rotor blade designs representing the Pareto optimal set. The n-branch tournament, uniform crossover genetic algorithm operates on twenty design variables, which constitute the control points for a spline representing the airfoil surface. The GA takes advantage of available c...

This paper addresses the short-term scheduling of chemical process with uncertainty considerations. A multiobjective robust optimization method is proposed to identify Pareto optimal solutions, where Normal boundary intersection (NBI) technique is utilized in order to trace the Pareto optimal surface in the objective space, on which each point represents a trade-off between the various objectiv...

Design is a multi-objective decision-making process considering manufacturing, cost, aesthetics, usability among many other product attributes. The set of optimal solutions, the Pareto set, indicates the tradeoffs between objectives. Decision-makers generally select their own optima from the Pareto set based on personal preferences or other judgements. However, uncertainties from manufacturing ...

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...

Solvent–steam mixture is a key factor in controlling the economic efficiency of the solvent-aided thermal injection process for producing bitumen in a highly viscous oil sands reservoir. This paper depicts a strategy to quickly provide trade-off operating conditions of the Expanding Solvent–Steam Assisted Gravity Drainage (ES-SAGD) process based on Pareto-optimality. Response surface models are...

In this paper, the concepts of Pareto H -eigenvalue and Pareto Z -eigenvalue are introduced for studying constrained minimization problem and the necessary and sufficient conditions of such eigenvalues are given. It is proved that a symmetric tensor has at least one Pareto H -eigenvalue (Pareto Z -eigenvalue). Furthermore, theminimumPareto H -eigenvalue (or Pareto Z -eigenvalue) of a symmetric ...

This paper deals with the problem of existence of compromise decisions and conditions for a compromise decision to be weakly Pareto-optimal, i.e., to be a weak Pareto-maximizer, Pareto-maximizer, or strong Pareto-maximizer. The concept of compromise decision is generalized by adopting triangular norms. Further, a concept of fuzzy interval is introduced. Suucient conditions for the existence of ...

the fisher information matrix for a mixture of two pareto distributions is derived. numericaltabulations of the matrix are also provided for practical purposes. the work is motivated by a real-lifeexample.

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale [Global analysis and economics. I. Pareto optimum and a generalization of Morse theory, in Dynamical Systems, Academic Press, New York, 1973, pp. 531–544]. The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by mean...