Andrzej P. Wierzbicki

Bio: Andrzej P. Wierzbicki is an academic researcher from Japan Advanced Institute of Science and Technology. The author has contributed to research in topics: Decision support system & Decision analysis. The author has an hindex of 28, co-authored 142 publications receiving 5247 citations. Previous affiliations of Andrzej P. Wierzbicki include Warsaw University of Technology & International Institute for Applied Systems Analysis.

The Use of Reference Objectives in Multiobjective Optimization - Theoretical Implications and Practical Experience

Abstract: The paper presents a survey of known results and some new developments in the use of reference objectives -- that is, any reasonable or desirable point in the objective space -- instead of weighting coefficients in multiobjective optimization. The main conclusions are as follows: (1) Any point in the objective space -- no matter whether it is attainable or not, ideal or not -- can be used instead of weighting coefficients to derive scalarizing functions which have minima at Pareto points only. Moreover, entire basic theory of multiobjective optimization -- necessary and sufficient conditions of optimality and existence of Pareto-optimal solutions, etc. -- can be developed with the help of reference objectives instead of weighting coefficients or utility functions. (2) Reference objectives are very practical means for solving a number of problems such as Pareto-optimality testing, scanning the set of Pareto-optimal solutions, computer-man interactive solving of multiobjective problems, group assessment of solutions of multiobjective optimization or cooperative game problems, or solving dynamic multiobjective optimization problems.

The Use of Reference Objectives in Multiobjective Optimization

Abstract: The paper presents a survey of known results and some new developments in the use of reference objectives—that is, any reasonable or desirable point in the objective space—instead of weighting coefficients or utility (value) functions in multiobjective optimization. The main conclusions are as follows: Any point in the objective space—no matter whether it is attainable or not, ideal or not—can be used instead of weighting coefficients to derive scalarizing functions which have minima at Pareto points only. Moreover, entire basic theory of multiobjective optimization--necessary and sufficient conditions of optimality and existence of Pareto-optimal solutions, etc.—can be developed with the help of reference objectives instead of weighting coefficients or utility (value) functions. Reference objectives are very practical means for solving a number of problems such as Pareto-optimality testing, scanning the set of Pareto-optimal solutions, computer-man interactive solving of multiobjective problems, group assessment of solutions of multiobjective optimization or cooperative game problems, or solving dynamic multiobjective optimization problems.

On the completeness and constructiveness of parametric characterizations to vector optimization problems

Abstract: Motivated by recent reviews of characterizations of optimal solutions to vector optimization problems and by applications to decision support systems, this paper presents a methodological approach to comparing such characterizations. After specifying attributes of constructiveness, alternative classes of characterizations are reviewed. Characterization theorems are quoted or presented in more detail in cases that supplement those given in recent reviews. One of alternative classes of characterizations -- by aspiration levels and order-consistent achievement functions -- is discussed in more detail. An impossibility theorem of complete and robustly computable characterization of efficient (as opposed to weakly or properly efficient) solutions to vector optimization problems is presented. Angeregt durch neuere Ubersichten der Charakterisierung von optimalen Losungen von Vektoroptimierungsproblemen und durch Anwendungen auf Entscheidungsunterstutzungssysteme wird in diesem Beitrag ein methodischer Ansatz zum Vergleich solcher Charakterisierungen dargestellt. Nach der Spezifizierung von Attributen der Konstruktivitat werden alternative Klassen von Charakterisierungen betrachtet. Charakterisierungstheoreme werden entweder zitiert oder, in Erganzung neuerer Ubersichten, dargestellt. Eine der alternativen Klassen der Charakterisierungen wird naher diskutiert. Ein Unmoglichkeitstheorem einer vollstandigen und robust berechenbaren Charakterisierung von effizienten (im Gegensatz zu schwach oder streng effizienten) Losungen der Vektoroptimierungsprobleme wird dargelegt.

Introduction to Multiobjective Optimization: Noninteractive Approaches

Abstract: We give an introduction to nonlinear multiobjective optimization by covering some basic concepts as well as outlines of some methods. Because Pareto optimal solutions cannot be ordered completely, we need extra preference information coming from a decision maker to be able to select the most preferred solution for a problem involving multiple conflicting objectives. Multiobjective optimization methods are often classified according to the role of a decision maker in the solution process. In this chapter, we concentrate on noninteractive methods where the decision maker either is not involved or specifies preference information before or after the actual solution process. In other words, the decision maker is not assumed to devote too much time in the solution process.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

The knowledge-creating company : how Japanese companies create the dynamics of innovation

Abstract: How has Japan become a major economic power, a world leader in the automotive and electronics industries? What is the secret of their success? The consensus has been that, though the Japanese are not particularly innovative, they are exceptionally skilful at imitation, at improving products that already exist. But now two leading Japanese business experts, Ikujiro Nonaka and Hiro Takeuchi, turn this conventional wisdom on its head: Japanese firms are successful, they contend, precisely because they are innovative, because they create new knowledge and use it to produce successful products and technologies. Examining case studies drawn from such firms as Honda, Canon, Matsushita, NEC, 3M, GE, and the U.S. Marines, this book reveals how Japanese companies translate tacit to explicit knowledge and use it to produce new processes, products, and services.

Evolutionary algorithms for solving multi-objective problems

Abstract: List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.

Survey of multi-objective optimization methods for engineering

Abstract: A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints

Abstract: Having developed multiobjective optimization algorithms using evolutionary optimization methods and demonstrated their niche on various practical problems involving mostly two and three objectives, there is now a growing need for developing evolutionary multiobjective optimization (EMO) algorithms for handling many-objective (having four or more objectives) optimization problems. In this paper, we recognize a few recent efforts and discuss a number of viable directions for developing a potential EMO algorithm for solving many-objective optimization problems. Thereafter, we suggest a reference-point-based many-objective evolutionary algorithm following NSGA-II framework (we call it NSGA-III) that emphasizes population members that are nondominated, yet close to a set of supplied reference points. The proposed NSGA-III is applied to a number of many-objective test problems with three to 15 objectives and compared with two versions of a recently suggested EMO algorithm (MOEA/D). While each of the two MOEA/D methods works well on different classes of problems, the proposed NSGA-III is found to produce satisfactory results on all problems considered in this paper. This paper presents results on unconstrained problems, and the sequel paper considers constrained and other specialties in handling many-objective optimization problems.