On the Relationship Between the Value Function and the Efficient Frontier of a Mixed Integer Linear Optimization Problem

In this paper, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related single-objective MILP. We demonstrate that the EF of the multiobjective MILP is comprised of points on the boundary of the epigraph of the RVF so that any description of the EF suffices to describe the RVF and vice versa. In the first part of the paper, we describe the mathematical structure of the RVF, including characterizing the set of points at which it is differentiable, the gradients at such points, and the subdifferential at all nondifferentiable points. Because of the close relationship of the RVF to the EF, we observe that methods for constructing so-called value functions and methods for constructing the EF of a multiobjective optimization problem, each of which have been developed in separate communities, are effectively interchangeable. By exploiting this relationship, we propose a generalized cutting plane algorithm for constructing the EF of a multiobjective MILP based on a generalization of an existing algorithm for constructing the classical value function. We prove that the algorithm is finite under a standard boundedness assumption and comes with a performance guarantee if terminated early

Multiobjective Trajectory Optimization and Model Semiregularization

The typical formulation of an optimal control or dynamic optimization problem is to optimize a scalar performance functional; less frequently, also vectors of performance functionals are considered in multiobjective optimization. However, there are practical problems -- mostly related to the use of dynamic control models in economic planning -- where the objectives are stated in terms of desirable trajectories. If the goal would be to approximate the desired trajectory from both sides, then the problem could be equivalently stated as a typical approximation problem. However, in many cases the desired trajectories have the meaning of aspiration levels: if possible, they should be exceeded. The paper presents a mathematical formulation of a multiobjective trajectory optimization problem, various theoretical approaches to this problem -- including interpretations as a generalized Lagrangian functional approach and as a semi-regularization procedure for ill-posed problems, a review of possible computational approaches and examples of actual computations

Stable and total Fenchel duality for DC optimization problems in locally convex spaces

Author name used in this publication: X. Q. Yang.2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Interactive Decision Analysis; Proceedings of an International Workshop on Interactive Decision Analysis and Interpretative Computer Intelligence, Laxenburg, Austria, September 20-23, 1983

An International Workshop on Interactive Decision Analysis and Interpretative Computer Intelligence was held at IIASA in September 1983. The Workshop was motivated, firstly, by the realization that the rapid development of computers, especially microcomputers, will greatly increase the scope and capabilities of computerized decision-support systems. It is important to explore the potential of these systems for use in handling the complex technological, environmental, economic and social problems that face the world today. Research in decision-support systems also has another, less tangible but possibly more important, motivation. The development of efficient systems for decision support requires a thorough understanding of the differences between the decision-making processes in different nations and cultures. An understanding of the different rationales underlying decision making is not only necessary for the development of efficient decision-support systems, but it is also an important factor in encouraging international understanding and cooperation. The Proceedings of the Workshop which are contained in this volume are divided in four main sections. The first section consists of an introductory lecture in which a unifying approach to the use of computers and computerized mathematical models for decision analysis and support is described. The second section is concerned with approaches and concepts in interactive decision analysis and section three is devoted to methods and techniques for decision analysis. The final section contains descriptions of a wide range of applications of interactive techniques, covering the fields of economics, public policy planning, energy policy evaluation, hydrology and industrial development

Search-based system architecture development using a holistic modeling approach

This dissertation presents an innovative approach to system architecting where search algorithms are used to explore design trade space for good architecture alternatives. Such an approach is achieved by integrating certain model construction, alternative generation, simulation, and assessment processes into a coherent and automated framework. This framework is facilitated by a holistic modeling approach that combines the capabilities of Object Process Methodology (OPM), Colored Petri Net (CPN), and feature model. The resultant holistic model can not only capture the structural, behavioral, and dynamic aspects of a system, allowing simulation and strong analysis methods to be applied, it can also specify the architectural design space. Both object-oriented analysis and design (OOA/D) and domain engineering were exploited to capture design variables and their domains and define architecture generation operations. A fully realized framework (with genetic algorithms as the search algorithm) was developed. Both the proposed framework and its suggested implementation, including the proposed holistic modeling approach and architecture alternative generation operations, are generic. They are targeted at systems that can be specified using object-oriented or process-oriented paradigm. The broad applicability of the proposed approach is demonstrated on two examples. One is the configuration of reconfigurable manufacturing systems (RMSs) under multi-objective optimization and the other is the architecture design of a manned lunar landing system for the Apollo program. The test results show that the proposed approach can cover a huge number of architecture alternatives and support the assessment of several performance measures. A set of quality results was obtained after running the optimization algorithm following the proposed framework --Abstract, page iii

Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems, part 1

The proceedings of the workshop are presented. Some areas of discussion are as follows: modeling, systems identification, and control of flexible aircraft, spacecraft, and robotic systems

IIASA Reports, 3(2):237-474 (Completing Volume 3) (April-June 1981)

This volume, which completes Volume 3, contains five papers on IIASA research, as well as an overview of "Energy in a Finite World," IIASA's study of global energy supply and demand through 2030. The five papers are: -- N.S.S. Narayana and K.S. Parikh, "Estimation of Farm Supply Response and Acreage Allocation: A Case Study of Indian Agriculture;" -- M. Breitenecker and H.-R. Gruemm, "Economic Evolutions and Their Resilience: A Model;" -- H.-D. Haustein, H. Maier, and L. Uhlmann, "Innovation and Efficiency;" -- L. Bergman and L. Ohlsson, "Changes in Comparative Advantages and Paths of Structural Adjustment and Growth in Sweden, 1975-2000;" -- A. Propoi and I. Zimin, "Dynamic Linear Programming Models of Energy, Resource, and Economic Development Systems.

Multi-Agent Systems

A multi-agent system (MAS) is a system composed of multiple interacting intelligent agents. Multi-agent systems can be used to solve problems which are difficult or impossible for an individual agent or monolithic system to solve. Agent systems are open and extensible systems that allow for the deployment of autonomous and proactive software components. Multi-agent systems have been brought up and used in several application domains