Solving Fractional Geometric Programming Problems via Relaxation approach

In the optimization literature , Geometric Programming problems play a very important role rather than primary in engineering designs. The geometric programming problem is a nonconvex optimization problem that has received the attention of many researchers in the recent decades. Our main focus in this issue is to solve a Fractional Geometric Programming(FGP) problem via linearization technique[1]. Linearizing separately both the numerator and denominator of the fractional geometric programming problem in the objective function, causes the problem to be reduced to a Fractional Linear Programming problem (FLPP) and then the transformed linearized FGP is solved by Charnes and Cooper method which in fact gives a lower bound solution to the problem. To illustrate the accuracy of the final solution in this approach, we will compar our result with the LINGO software solution of the initial FGP problem and we shall see a close solution to the globally optimum. A numerical example is given in the end to illustrate the methodology and efficiency of the proposed approach

The Encyclopedia of Neutrosophic Researchers - vol. 1

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry

Decision-making and problem-solving methods in automation technology

The state of the art in the automation of decision making and problem solving is reviewed. The information upon which the report is based was derived from literature searches, visits to university and government laboratories performing basic research in the area, and a 1980 Langley Research Center sponsored conferences on the subject. It is the contention of the authors that the technology in this area is being generated by research primarily in the three disciplines of Artificial Intelligence, Control Theory, and Operations Research. Under the assumption that the state of the art in decision making and problem solving is reflected in the problems being solved, specific problems and methods of their solution are often discussed to elucidate particular aspects of the subject. Synopses of the following major topic areas comprise most of the report: (1) detection and recognition; (2) planning; and scheduling; (3) learning; (4) theorem proving; (5) distributed systems; (6) knowledge bases; (7) search; (8) heuristics; and (9) evolutionary programming

An Integrated Engineering-Computation Framework for Collaborative Engineering: An Application in Project Management

Today\u27s engineering applications suffer from a severe integration problem. Engineering, the entire process, consists of a myriad of individual, often complex, tasks. Most computer tools support particular tasks in engineering, but the output of one tool is different from the others\u27. Thus, the users must re-enter the relevant information in the format required by another tool. Moreover, usually in the development process of a new product/process, several teams of engineers with different backgrounds/responsibilities are involved, for example mechanical engineers, cost estimators, manufacturing engineers, quality engineers, and project manager. Engineers need a tool(s) to share technical and managerial information and to be able to instantly access the latest changes made by one member, or more, in the teams to determine right away the impacts of these changes in all disciplines (cost, time, resources, etc.). In other words, engineers need to participate in a truly collaborative environment for the achievement of a common objective, which is the completion of the product/process design project in a timely, cost effective, and optimal manner. In this thesis, a new framework that integrates the capabilities of four commercial software, Microsoft Excel™ (spreadsheet), Microsoft Project™ (project management), What\u27s Best! (an optimization add-in), and Visual Basic™ (programming language), with a state-of-the-art object-oriented database (knowledge medium), InnerCircle2000™ is being presented and applied to handle the Cost-Time Trade-Off problem in project networks. The result was a vastly superior solution over the conventional solution from the viewpoint of data handling, completeness of solution space, and in the context of a collaborative engineering-computation environment

An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives

This article proposes a framework to handle multiattribute group decision making problems with incomplete pairwise comparison preference over decision alternatives where qualitative and quantitative attribute values are furnished as linguistic variables and crisp numbers, respectively. Attribute assessments are then converted to interval-valued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in the evaluation process. Group consistency and inconsistency indices are introduced for incomplete pairwise comparison preference relations on alternatives provided by the decision-makers (DMs). By minimizing the group inconsistency index under certain constraints, an auxiliary linear programming model is developed to obtain unified attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS). Attribute weights are subsequently employed to calculate distances between alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method

An Inventory Model under Space Constraint in Neutrosophic Environment: A Neutrosophic Geometric Programming Approach

In this paper, an inventory model is developed without shortages where the production cost is inversely related to the set up cost and production quantity. In addition, the holding cost is considered time dependent. Here impreciseness is introduced in the storage area. The objective and constraint functions are defined by the truth (membership) degree, indeterminacy (hesitation) degree and falsity (non-membership) degree. Likewise, a non-linear programming problem with a constraint is also considered. Then these are solved by Neutrosophic Geometric Programming Technique for linear membership, hesitation and non-membership functions. Also the solution procedure for Neutrosophic Non-linear Programming Problem is proposed by using additive operator and Geometric Programming method. Numerical examples are presented to illustrate the models using the proposed procedure and the results are compared with the results obtained by other optimization techniques

Suppliers Selection In Manufacturing Industries And Associated Multi-Objective Desicion Making Methods: Past, Present And The Future

Nowadays, many manufacturing companies have decided to use other companies’ competencies and outsource part of their manufacturing processes and business to suppliers globally in order to reduce costs, improve quality of products, explore or expand new markets, and offer better services to customers, etc. The decisions have rendered manufacturing organizations with new challenges. Organizations need to evaluate their suppliers' performance, and take account of their weakness and strength in order to win and survive in highly competitive global marketplaces. Hence, suppliers evaluation and selection are taken as an important strategy for manufactring enterprises. This paper aims to provide a comprehensive and critical review on suppliers selection and the formulation of different criteria for suppliers selection, the associated multi-objctive decision makings, selecion algorithms, and their implementation and application perspectives. Furthermore, individual and integrated suppliers selection approaches are presented, including Analytic hierarchy process (AHP), Analytic network process (ANP), and Mathematical programming (MP). Linear programming (LP), Integer programming (IP), Data envelopment analysis (DEA) and Goal programming (GP) are discussed with in-depth. The paper concludes with further discussion on the potential and application of suppliers selection approach for the broad manufacturing industry