Distributed convex optimization via proportional-integral-differential algorithm

This paper studies the distributed convex optimization problem, where the global utility function is the sum of local cost functions associated to the individual agents. Only using the local information, a novel continuous-time distributed algorithm based on proportional-integral-differential (PID) control strategy is proposed. Under the assumption that the global utility function is strictly convex and local utility functions have locally Lipschitz gradients, the exponential convergence of the proposed algorithm is established with undirected and connected graph among these agents. Finally, numerical simulations are presented to illustrate the effectiveness of theoretical results.

AXIOMATIZATIONS AND FACTORIZATIONS OF SUGENO UTILITY FUNCTIONS

In this paper we consider a multicriteria aggregation model where local utility functions of different sorts are aggregated using Sugeno integrals, and which we refer to as Sugeno utility functions. We propose a general approach to study such functions via the notion of pseudo-Sugeno integral (or, equivalently, pseudo-polynomial function), which naturally generalizes that of Sugeno integral, and provide several axiomatizations for this class of functions.Moreover, we address and solve the problem of factorizing a Sugeno utility function as a composition q(φ1(x1),…,φn(xn)) of a Sugeno integral q with local utility functions φi, if such a factorization exists.

Towards a Consistent Preference Representation in Engineering Design

Multiattribute utility theory is commonly used to define and represent the decision-maker’s preferences under conditions of uncertainty and risk. A major issue in implementing this approach deals with the identification and generation of appropriate utility functions, especially in an often nonlinear and complex engineering design environment. Typically, the decision-maker’s preferences are provided through lottery questions rather than based on deductive reasoning to reflect the nonlinear tradeoffs among the attributes. The use of such an intuitive procedure can lead to inconsistent and inexact preference information that may result in inaccuracy and rank reversal problems. Alternatively, this paper presents an Interactive Preference-Modeling (IPM) method towards a consistent preference representation in engineering design. Focusing on the preference orientation by implicitly articulating the designer’s priorities, this method provides a methodical framework to check and eliminate inconsistency in preference information, and to accurately express preferences through rational pairwise comparisons. The development of IPM method and its utilization in the determination of the system utility function from a consistent set of local utility functions are presented in the context of a beam design problem and the results are discussed.

Multiple Objective Design Optimization by Estimating Local Utility Functions

This paper presents the application of an interactive multiple objective decision making (MODM) procedure to design synthesis. This procedure is composed of an interactive step trade-off method (ISTM) and the estimation of local utility functions. The ISTM method is used as a preference learning process to assist a designer (decision maker or DM) in generating a representative sub-set of efficient designs (solutions). In this learning process, the DM is expected to compare the generated solutions in a pairwise manner to express his preferences. A set of additive local utility functions are then estimated to help the DM search for his best compromise solution. A multiple objective design synthesis problem is examined using the procedure.