Goal programming

About: Goal programming is a research topic. Over the lifetime, 4330 publications have been published within this topic receiving 117758 citations.

Goal programming models for multiple attribute decision making under linguistic setting

Abstract: In this paper,we study the multiple attribute decision making problems,in which the information about attribute weights is partly known and the attribute values take the form of linguistic variables or uncertain linguistic variables,and the decision maker has preferences on alternatives.We introduce the operation laws of linguistic variables and uncertain linguistic variables and a formula of possibility degree for the comparison between uncertain linguistic variables,and then define the concept of deviation degree between linguistic variables.We establish two goal programming models based on the concept of deviation degree under the situations where the attribute values are linguistic variables and uncertain linguistic variables respectively.By solving these two models, the attribute weights can be obtained.After that,when the attribute values are linguistic variables,we utilize the linguistic weighted averaging(LWA) operator to aggregate the given linguistic decision information,and then rank the alternatives and select the most desirable one(s);when the attribute values are uncertain linguistic variables,we utilize the uncertain linguistic weighted averaging(ULWA) operator to aggregate the given uncertain linguistic decision information and utilize the formula of possibility degree to construct a possibility degree matrix(or called complementary judgement matrix),and then utilize the priority formula of complementary judgement matrix to rank the alternatives and to select the most desirable one(s).Finally,an illustrative example is also given.

Goal Programming Approaches to Managing Consistency and Consensus for Intuitionistic Multiplicative Preference Relations in Group Decision Making

Abstract: Intuitionistic multiplicative preference relations (IMPRs), as an extension of multiplicative preference relations (MPRs), are suitable to capture hesitation and indeterminacy of the experts’ judgments. This paper aims to build several goal programming models to manage consistency and consensus of IMPRs and develop a consistency and consensus-based approach for dealing with group decision making (GDM) with IMPRs. First, the study offers a consistency index to quantify the consistency level for IMPRs as well as to define acceptably consistent IMPRs. For an IMPR, which is unacceptably consistent, several consistency-based programming models are developed to deal with the inconsistency and to establish an acceptable consistent IMPR. A consistency-based method to decision making with an IMPR is presented. Subsequently, considering the consensus in GDM, a consensus index is proposed for gauging the agreement degree among individual IMPRs. As to the individual IMPRs, which do not exhibit acceptable consistency or acceptable consensus, several goal programming models to derive new IMPRs with acceptable consistency and consensus are provided. Afterward, individual IMPRs are fused into a group IMPR by an aggregation operator that can guarantee the consistency of the obtained group IMPR. A consistency and consensus-based GDM method with a group of IMPRs is developed. Finally, two practical numerical examples are offered and a comparative analysis is presented.

Robustness Improvement of Actively Controlled Structures through Structural Modifications

Abstract: The parameter variations introduced by the analysis model, uncertain material properties, or optimization may adversely influence the stability and performance characteristics of a closed-loop controlled structure. The improvement of robustness of actively controlled structures through structural modifications is considered in this work. The stability and performance robustness indices are defined as measures of robustness of actively controlled structures. The integrated structural/control design problem is considered as a multiobjective optimization problem, in which three objectives—structural weight, stability robustness index, and performance robustness index—are considered for minimization. The utility function, lexicographic, and goal programming methods are applied to solve the multiobjective nonlinear programming problem. Two examples, a two-bar truss and two-bay truss, are considered to demonstrate the procedure. HERE has been a dramatic increase in the past decade in the use of active control systems to improve structural performance.1'2 The major challenge in the field of active control of structures is in the design of control systems for very large space structures. These structures are by nature distributed parameter systems with multiple inputs (controls) and a continuum of outputs (displacements). The finite-ele- ment method is commonly used for the description of these structures. This is a source of parameter errors and truncated (or reduced order) models in the system. In addition, the structural properties of large space structures cannot be tested before they are put into orbit and, hence, sizeable uncertain- ties exist in modal parameters. A great deal of research is currently in progress on develop- ing methods for the simultaneous (integrated) design of the structure and the control system. The weight of the structure was minimized, with constraints on the distribution of the eigenvalues and/or damping ratio of the closed-loop system by Khot et al.3 Miller and Shim4 considered the simultaneous minimization, in structural and control variables, of the sum of structural weight and the infinite horizon linear regulator quadratic control cost. The structure/control system optimiza- tion problem was formulated by Khot et al.,5 with constraints on the closed-loop eigenvalue distribution and the minimum Frobenious norm of the control gains. It can be seen that in all the above works the consideration of robustness of the control system has been ignored. The parameter variations introduced by the analysis model, uncertain material properties, or optimization may adversely influence the stability and performance characteristics of the control system. The robustness is an extremely important feature of a feedback control design. A robust control design is one that satisfactorily meets the system specifications, even in the presence of parameter uncertainties and other modeling errors. Since the system specifications could be in terms of