Pareto Optimality Concept Research Articles

Feasibility and Pareto optimality for multiobjective nonlinear programming problems with fuzzy parameters

Abstract In this paper, we focus on multiobjective nonlinear programming problems with fuzzy parameters and extend the ordinary feasibility and Pareto optimality concepts based on the concepts of possibility and necessity for fuzzy numbers. Using the four indices for ranking two fuzzy numbers, four types of feasibility and Pareto optimality are defined and the relationships among them are examined in detail. These concepts can be viewed as quite generalized versions of the well-known feasibility and Pareto optimality concepts, and the generalized Pareto optimal solutions for the multiobjective nonlinear programming problems with fuzzy parameters may be obtained on the basis of the method of nonlinear programming.

A New Pareto Optimal Solution in a Lagrange Decomposable Multi-Objective Optimization Problem

In this paper a committee decision-making process of a convex Lagrange decomposable multi-objective optimization problem, which has been decomposed into various subproblems, is studied. Each member of the committee controls only one subproblem and attempts to select the optimal solution of this subproblem most desirable to him, under the assumption that all the constraints of the total problem are satisfied. This procedure leads to a new solution concept of a Lagrange decomposable multi-objective optimization problem, called a preferred equilibrium set. A preferred equilibrium point of a problem, for a committee, may or may not be a Pareto optimal point of this problem. In some cases, a non-Pareto optimal preferred equilibrium point of a problem, for a committee, can be considered as a special type of Pareto optimal point of this problem. This fact leads to a generalization of the Pareto optimality concept in a problem.

International Legal Policy and Efficient Resource Allocation

The impact of international interactions on the level and allocation of a nation's expenditures for police protection and law enforcement are discussed: A model is developed and used to analyze various types of international interactions such as crime spillovers from one nation to another, effective police action in one country against a crime organization active in a number of countries, and the assistance that one country offers another in the securing of information and evidence. The impacts of these interactions are then evaluated in terms of the concept of Pareto-optimality. International cooperation through police and legal institutions is discussed as a way of narrowing the gap between actual and optimal expenditures, and an international body is proposed to deal with criteria, coordination, and compensation for international discovery orders. In the final section the results of a number of studies are presented that suggest the importance of interjurisdictional interactions and cooperation. These results are used to evaluate the possible impacts of international interactions in crime, police protection and law enforcement.

Extended pareto optimality concept for multiobjective linear programming problems with fuzzy parameters and its properties

AbstractIn order to handle multiobjective linear programming problems containing fuzzy parameters, the authors have already proposed four kinds of α‐feasibility and β‐Pareto optimality, based on the four kinds of index introduced by Dubois et al. This paper discusses the proposed concepts of four kinds of β‐Pareto optimality in further detail, in order to indicate problems with β‐Pareto optimality. As a means of coping with those problems, four kinds of γ‐Pareto optimal solutions are introduced. Then the concept of (α, γ)‐Pareto optimal solution is introduced, by considering simultaneously the α‐feasibility and the γ‐Pareto optimality. It is shown that the set of (α, γ)‐Pareto optimal solutions, which can be regarded as the most optimistic and the most pessimistic, can be found using linear programming.

Optimal distributed control of a continuous beam with damping

Optimal control of a damped two-span beam is studied with the objective of minimizing its deflection and velocity in a given period of time with the minimum possible expenditure of force. The beam undergoes transient vibrations and is subject to given displacement and velocity initial conditions. The control is exercised by means of a transverse distributed force. The multiple objectives of the problem lead to a vector performance criterion which is reduced to a scalar one by using the concept of Pareto optimality. Necessary and sufficient conditions of optimality are expressed in the form of a maximum principle which leads to an explicit expression for the control force. The behaviour of the controlled beam is numerically studied which indicates that optimally controlled distributed forces are effective in damping out the dynamic response. Relations between various objectives are studied by means of optimal trade-off curves showing the best performance of the controlled beam.

Steady state multiobjective optimization of continuous copolymerization reactors

AbstractThe multiobjective nature of optimization problems related to homopolymerizaton and copolymerization processes implies a vector objective formulation for a correct approach. Two copolymerization systems, methyl methacrylate‐vinyl acetate (MMA‐VA) and styrene‐acrylonitrile (ST‐AN) are simulated, and some aspects of the steady state optimality of continuous operation are analyzed. The determination of non‐inferior sets through the concept of Pareto optimality permits a clear decision on trade‐offs related to operating conditions and product specifications.

The Regulation of Regulation

The controversy over the level and nature of regulatory activities in the economy is shaped by both the methodology of analysis and its perspective. Most of the tools used to evaluate specific portions of the regulatory system are embedded in neoclassical economic theory. Further, these tools are applied from the perspective of questioning only the efficiency aspects of the regulations. These neoclassical tools and perspectives constrain the analysis to an evaluation limited to government activities in the regulatory matrix. The analysis compares the effects of regulation to equilibrium in a competitive market system. The criteria of evaluation are based on efficiency, while equity considerations may have been the impetus for creating the regulation. This process limits the range of conscious alternatives that policy makers have. If the neoclassical concepts of Pareto optimality and the theory of second best are applied in a strict sense, the conclusion will usually be for the status quo. Pareto optimality tends to prevent the development and evolution of new policies in two ways. First, in the political sphere there is nearly always some interest group or person that will insist that their welfare will be reduced by any change in the existing rule structure. Secondly, it can be shown that when any new policy is evaluated using efficient prices and values generated by an existing set of policies, there is a bias in favor of the existing policy. This bias has been called conservative reinforcement.' The theory of second best holds that the correction of one defect

Multiobjective Design of an Antisymmetric Angle-Ply Laminate by Nonlinear Programming

An antisymmetrically laminated angle-ply plate is optimized with the objectives of minimizing the maximum dynamic deflection, maximizing the natural frequencies and/or maximizing the buckling load. The design variables are the fiber orientation and the thickness of individual layers and are computed by using the methods of nonlinear programming. The concept of Pareto optimality is used in formulating the design problem and in reducing the multiple objectives into a single performance index. Numerical results are presented in the form of optimal tradeoff curves which allow the designer to assess the various possibilities open to him before deciding on a certain design. In this sense, the present design is an interactive process.

Pareto optimal design of beams subjected to support motions

The optimal design of a clamped-hinged beam is determined with the objectives of minimizing the maximum deflection, maximum normal and shearing stresses and of maximizing the fundamental eigenfrequency. The design variable is the area function of the beam which is approximated by linear splines in order to convert the continuous problem into a finite dimensional one. The multi-objective design problem is formulated by using the concept of Pareto optimality. The design algorithm consists of successive stages of analysis and optimization. Each analysis is carried out by iteratively solving an equivalent integral equation formulation of the original problem. Mathematical programming techniques are employed for optimization. The numerical results for a number of design examples are presented in the form of graphs of optimal trade-off curves which give the optimum performance of the structure with respect to specified objectives.

Externality, efficiency and the pareto principle

This paper discusses the nature of, and relation between, the concepts of Externality and Pareto-Efficiency. The importance of these concepts in economic theory needs no introduction. The relevance of this analysis to ‘the law’ is essentially two-fold: 1. In so far as the economic analysis of the law depends upon such concepts. 2. In so far as the legal and institutional framework is often instrumental in creating what has been termed ‘market failure’ and that changes in that framework are often proposed as remedies. Coase’s seminal paper-1 developed in detail the relation between externality and the legal and institutional framework and a considerable body of literature has developed since that time. These relations are therefore not dwelt upon here, the concern being to examine the basic concepts. Morgenstern noted that Pareto Optimality was: ‘a basic concept of contemporary economic theory which has not been sufficiently explored’.2 It is argued here that different conceptions of Pareto Optimality (often implicit) are instrumental in generating different theoretical structures and different policy conclusions;3 inadequate concepts can very easily generate misleading policy prescription. It is frequently argued that a separation can be made between the positive and normative parts of theory; the ‘New’ Welfare Economics sought to build a theoretical structure from ‘minimal’ basic value judgments which were then conjoined with positive theory to provide policy recommendations. It is argued here that this is incorrect and that additional or more complex value judgments must always be made; the classical Pareto principle per se is seen to be fundamentally inoperable. The approach used is to examine the writings of the Pigovian, Paretian and so called neo-institutionahsts on ‘Externality’ with the purpose of defining, comparing, contrasting and criticizing their concepts of ‘optimality’ and ‘externality.’ Section II discusses the neo-classical concept of externality and relates it to the concept of Pareto Optimality; III examines the status of the classical Pareto principle; IV introduces the neo-institutionalist analysis of Externality; V the neoinstitutionalist concept of ‘Objective Cost’ and VI draws together the conclusions, focusing in particular upon the implications of the analysis for the practical approach to policy.

Tradeoff diagrams for the integrated design of the physical environment in buildings

Although computer programs providing very detailed simulations of a building's performance in a number of environmental components are now available, the information they offer is necessarily evaluative rather than prescriptive. As a method of investigating alternatives at the early stages of design, such programs are inefficient because they require the user to operate by trial and error. They also fail to provide any direct information on the relationship between different environmental components, information which is central to the concept of integrated environmental design. This paper describes the form and application of environmental tradeoff diagrams as an alternative computer aid for the design of the physical environment in buildings. Environmental tradeoff diagrams utilize the concepts of Pareto optimality in multi-criterion decision making to offer a designer prescriptive quantitative information which relates the performance achievable in different environmental components both to the building design and to each other. They are generated using a mathematical model of building/environment behaviour imbedded within an optimization problem formulation.

A note on Pareto optimality in mutual reinsurance

Abstract A theorem of Borch on changing reinsurances on a reciprocal basis is considered with the classical concept of Pareto optimality.

Intertemporal and intergenerational Pareto efficiency

Efficiency conditions are derived for both private and public goods which provide benefits over time. In deriving these conditions, the paper extends the notion of efficiency to an intertemporal Pareto-optimal concept requiring the maximization of the ith individual's utility at a point of time subject to the constancy of his utility in all future periods and that of all other individuals during the relevant time span. By permitting births and deaths, a generalization of the basic model recasts the analysis into an intergenerational setting. Additional extensions involve learning by doing and perpetual public goods. The paper concludes that several of the conventional practices in public expenditure analysis do not conform to our definition of intertemporal Pareto efficiency.

A Dynamic Disequilibrium Model of Residential Location

Operational models of residential location have followed two separate lines of development. The gravity and maximum entropy models are characterized by operational simplicity and adaptability to disaggregated data; they remain, however, descriptive in nature. The theoretical microeconomic models, on the other hand, have delineated the concepts of competitive equilibrium and Pareto optimality in an aggregate and deterministic way. There has been an implicit need, since the development of maximum entropy models by Wilson, to bridge the gap between the descriptive and the theoretical models. As Wilson himself has asserted: “The models will only become significantly better when they are extended to incorporate a detailed knowledge of preference structures and utility functions …” (Wilson, 1969b). The present paper is a development in this direction.

On Pareto optimal decisions for a coalition of a subset of players

The concept of Pareto optimality and the concept of max-inf condition are used to give a new definition of optimality for a coalition of players. A necessary condition and a sufficient condition are proven for a class of topological games by using the approach of the theory of reachability for perturbed systems.

Biological externalities

The concepts of externality and Pareto optimality were originally developed for economic analysis. This article demonstrates that they can be applied to ecological problems as well as economic problems. If there are two or more species in an area which have effects on each other, then these effects are classical externalities. Standard economic reasoning indicates that these externalities would lead to a nonoptimal situation. It would always be possible to increase all of the species in a given area by appropriate management. The analysis is mainly carried out in terms of a simple two-species example, but its generalization to many species is reasonably straightforward.