Showing papers in "Engineering Optimization in 1985"
TL;DR: In the presented procedure, optimum structural design with fuzzy constraints is transformed into a set of ordinary optimum problems by a level cuts approach which results in a sequence of optimum design schemes with different design levels.
Abstract: It is pointed out that there exists a vast amount of fuzzy information in both objective and constraint functions of optimum design of structures (ODS) Thus, relatively reasonable optimum designs can only be obtained by fuzzy programming methods. While all fuzzy constraints enclose a fuzzy feasible region in decision-making space, the fuzzy optimum solution will be a sequence of points in a small fuzzy optimum subregion. In the presented procedure, optimum structural design with fuzzy constraints is transformed into a set of ordinary optimum problems by a level cuts approach which results in a sequence of optimum design schemes with different design levels. The concept of optimum design level corresponding to the most suitable scheme among the obtained sequence is also advanced in this paper.
96 citations
TL;DR: In this paper, the selection of a minimum weight truss, out of a large set of candidate trusses, is treated, and an initial configuration is generated by connecting all the n nodal points with n(n−− 1)-2 truss members.
Abstract: The selection of a minimum weight truss, out of a large set of candidate trusses, is treated. An initial configuration is generated by connecting all the n nodal points with n(n − 1)\2 truss members. A feasible displacement field, satisfying displacement and stress constraints, is obtained from a static analysis of this truss, followed by a uniform scaling of all truss dimensions. The finite element formulation for the initial configuration is then reformulated to yield a linear programming problem. The solution to this leads to a new configuration which is further optimized by solving a small nonlinear programming problem. With the method proposed, trusses subject to one loading condition and subject to stress and displacement constraints can be selected and optimized using a modest computational effort. Three examples are given to demonstrate the usefulness of the proposed method.
70 citations
TL;DR: The rationale for using clustering methods to reduce the size of the Pareto optimal set whilst retaining its shape is explained and an implementation of the complete-linkage clustering method is described and its application is demonstrated.
Abstract: This paper describes the rationale for using clustering methods to reduce the size of the Pareto optimal set whilst retaining its shape. It proceeds lo describe an implementation of the complete-linkage clustering method and demonstrates its application. Finally, the method is incorporated into a Pareto optimal serial dynamic programming process to reduce the size of the Pareto optimal set generated at each stage of the optimization.
59 citations
TL;DR: In this paper, a quasi-Newton method was proposed for maximizing the bending strength of symmetric, laminated, fiber-reinforced plates. Butler et al. used the Rayleigh-Ritz technique to calculate plate deformations and applied it to a graphite/epoxy laminate having equal thickness layers.
Abstract: A procedure is proposed for maximizing the bending strength of symmetric, laminated, fiber-reinforced plates. Laminate strength is described by a failure criterion in strain space. Design variables include the fiber directions and/or the layer thicknesses. The Rayleigh-Ritz technique is used lo calculate plate deformations. Optimization is performed via a quasi-Newton method, with the initial point determined by a random jump technique. As an illustrative example, a graphite/epoxy laminate having equal thickness layers, resting on simple supports, and subject to a single concentrated force is considered. Application of the optimization procedure is found to result in a significant increase in failure load; in general, bending stiffness as well as strength is increased.
35 citations
TL;DR: In this article, a general overview of multilevel systems is presented and a step by step outline for optimal design of such systems and the sensitivity analysis of the resulting designs are presented.
Abstract: Multilevel hierarchical systems are commonplace in engineering design applications. “Optimal” design of multilevel systems is important and leads to cost effective designs. In this paper, a general overview of multilevel systems is presented. A step by step outline for optimal design of such systems and the sensitivity analysis of the resulting designs are presented. A simple example that illustrates the procedure is also included.
32 citations
TL;DR: A dynamic programming method for designing the least expensive network of sewers that will drain water from a number or discrete sources is presented in this article, where the positions of sewer junctions, the diameters and slopes of the sewers are all considered as variables.
Abstract: A dynamic programming method for designing the least expensive network of sewers that will drain water from a number or discrete sources is presented. The positions of sewer junctions, the diameters and slopes of the sewers are all considered as variables. Results of using the method for the design of three storm sewer networks are presented and discussed.
28 citations
TL;DR: In this paper, the authors address the problem of maximizing the critical load of shallow space trusses of given configuration and volume by implicit differentiation of the nonlinear equilibrium equations and the stability criterion.
Abstract: This paper addresses the problem of the maximization of the critical load of shallow space trusses of given configuration and volume. Through implicit differentiation of the nonlinear equilibrium equations and the stability criterion, the sensitivity derivatives of the critical load parameter with respect to the design variables are developed. Optimum designs are generated using a projected Lagrangian technique known as the Variable Metric method for constrained optimization (VMCON).
22 citations
TL;DR: A modelling approach is presented which enables the determination of compromise solutions, using a goal programming formulation with boolean expressions and a weighted attainment function, which can be solved using standard mathematical programming software.
Abstract: The product range versatility of automated production systems provides scope for economic operations covering a wide range of feasible groups of orders. The selection of a particular group of orders which will facilitate the satisfactory fulfilment of possibly conflicting multiple performance goals requires the formulation of a flexible planning model, incorporating several special characteristics. This paper presents a modelling approach which enables the determination of compromise solutions, using a goal programming formulation with boolean expressions and a weighted attainment function. This can be solved using standard mathematical programming software. Consideration of the modular elements in the model formulation is followed by an example problem to illustrate its application.
19 citations
TL;DR: In this article, the problem of determining the optimal constant flow allowance for the CON due-date assignment method is considered and a linear programming formulation of the problem is proposed and the optimal due date is obtained by solving the LP dual problem.
Abstract: This paper considers the problem of determining the optimal constant flow allowance for the CON due-date assignment method. A linear programming formulation of the problem is proposed and the optimal due-date is obtained by solving the LP dual problem.
17 citations
TL;DR: The NISE method is extended to three-objective problems and an algorithm is applied to a problem drawn from the literature to produce numerical results.
Abstract: The noninferior set estimation (NISE) method is a powerful technique for the generation of the Pareto optimal set for multicriteria optimization problems with two dimensions. This paper extends the NISE method to three-objective problems. The concepts which allow this extension are presented and an algorithm described. The method is applied to a problem drawn from the literature to produce numerical results.
16 citations
TL;DR: In this paper, a highly nonlinear optimum design problem of reinforced concrete frames is treated in two levels corresponding to global constraints and local constraints respectively, with iterations in each level, with the optimum solution from the first level applied to construct bounds upon design variables.
Abstract: In this paper, a highly nonlinear optimum design problem of reinforced concrete frames is treated in two levels corresponding to global constraints and local constraints respectively, with iterations in each level. In the first level, the most flexible structure among those satisfying the global constraints such as displacement constraints, size constraints, etc., is sought under the most unfavourable horizontal loads. The optimum solution from the first level is applied to construct bounds upon design variables. In the second level, using these values from the first level, the most economical structure satisfying all local constraints such as those of strength, size, percentage of reinforcement, and all other code requirements is obtained. In fact, the subproblem associated with the first level is converted into a sequential linear programming problem, and that associated with the second level is a separable optimum design problem. In this paper, the heights and widths of member sections are all specifie...
TL;DR: The objective of this paper is to present a reliability-based optimization technique to design reinforced concrete frames that is iterative in nature and remarkably efficient for handling the uncertainities included in the formulation.
Abstract: Recent developments in probabilistic analysis combined with simultaneous rapid growth of computing power provide the necessary conditions for the application of reliability concepts in the optimum design of complete structures. In light of this design philosophy, which extends reliability optimization concepts from structural elements to complete structures, the objective of this paper is to present a reliability-based optimization technique to design reinforced concrete frames. Based on this technique, a computer program was prepared. The computer-based optimization technique is iterative in nature and remarkably efficient for handling the uncertainities included in the formulation. The application of this technique is illustrated on a reinforced concrete frame example.
TL;DR: In this paper, the design of the ride-rings or tyres of industrial rotary kilns is studied as a nonlinear programming problem, and a special-purpose algorithm for the location of the global optimum is presented.
Abstract: The design of the ride-rings, or tyres, of industrial rotary kilns is studied as a nonlinear programming problem. The method of monotonicity analysis is employed to obtain results of sufficient generality and utility to the designer. A special-purpose algorithm for the location of the global optimum is presented. A parametric study provides design charts showing the range of criticallity for the various design requirements. The article represents the type of modeling analysis and subsequent solution, suitable for design problems which must be solved many times with parameter changes larger than those handled with the usual sensitivity analysis.
TL;DR: In this paper, a methodology for preliminary design of cable-stayed bridges using optimization techniques is presented, which enables the designer to vary the arrangement and size of stay cables and cross-sectional dimensions of the longitudinal deck girder.
Abstract: A methodology for preliminary design of cable-stayed bridges using optimization techniques is presented. A simple model of the bridge, comprising beam elements for the longitudinal deck girder and lower and truss elements for stay cables, is used. The computer program SADDLE is used for optimization. Constraints are placed on stresses, displacements and member sizes under multiple loading conditions. The methodology enables the designer to vary the arrangement and size of stay cables and cross-sectional dimensions of the longitudinal deck girder. Consequently an aesthetically pleasing as well as an economical and feasible design of a cable-stayed bridge can be obtained quickly and efficiently.
TL;DR: In this paper, the optimum design of beams in multi-storey steel frames using the recently proposed LRFD criteria was investigated and compared with those obtained using the conventional plastic design criteria.
Abstract: This paper deals with the optimum design of beams in multi-storey steel frames using the recently proposed LRFD criteria. The results are compared with those obtained using the conventional plastic design criteria. The optimization problems which are nonlinear in nature are either solved using an appropriate nonlinear optimization technique or linearized and solved by the simplex method. Numerical examples presented consider the design of three-bay 9 storey, 17 storey and 26 storey frames.
TL;DR: In this paper, the optimal load flow problem is formulated as a stochastic programming problem, where the electricity demand at each node is treated as a random variable with a given probability distribution function.
Abstract: The optimal load flow problem is to determine the allocation of electricity demand among the committed generating units to minimize the total operating costs subject to various physical and technological constraints. If only the real power generation is to be determined and the reactive power generation is assumed fixed, then the problem is known as the economic dispatch problem, It is extensively used in the real time management of electrical power systems. In the existing formulations of the economic dispatch problem, the electricity demands at nodes of the transmission network are treated as given, that is, the point estimates of demand values are used. In this paper, the electricity demand at each node is treated as a random variable with a given probability distribution function. This assumption leads to a stochastic programming model which consists of minimization of a convex objective function subject to upper and lower bounds on decision variables. The development of this model is presented in the...
TL;DR: In this paper, the authors proposed three different measures of structure stiffness in the nonlinear range and proceed to optimize these measures using the simple optimally criterion approach in one case and mathematical programming in the other two cases.
Abstract: The authors propose three different measures of structure stiffness in the nonlinear range and proceed to optimize these measures. Optimization is performed using the simple optimally criterion approach in one case and mathematical programming in the other two cases. It is found that although the three measures can lead to identical designs in the linear case the same is definitely not true in the nonlinear case. For the purposes of illustration a highly flexible centrally loaded clamped beam is chosen.
TL;DR: In this paper, two strategies are developed for optimizing the operation and tariff negotiation of a cogeneration plant in association with electricity purchase under a maximum demand tariff under varying load conditions.
Abstract: Two strategies arc developed for optimizing the operation and tariff negotiation of a cogeneration plant in association with electricity purchase under a maximum demand tariff. A mathematical model of the major plant items is used to make decisions on the choice of the amount of local generation under varying load conditions and hence the maximum demand for purchased power and, optionally, the size of installed generating capacity. The choices are based on the opportunity costs for the different sources of energy under varying conditions. Of four different approaches tried, two have proved effective. They are a heuristic method specific to this problem and an application of linear programming following a monotonicity analysis. Each has advantages when applied to a certain class of problems.
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TL;DR: In this article, the optimality of flexureless orthogonal archgrids is investigated and an efficient and simple iterative method for obtaining the optimal solution is proposed, considering the load proportions carried by arches as independent variables.
Abstract: Treated in this work is the optimality of flexureless orthogonal archgrids. Various features of fully stressed arches and archgrids are highlighted and an efficient and simple iterative method for obtaining the optimal solution is proposed. Considering the load proportions carried by arches as independent variables, the optimality of the archgrid is ensured by imposing the conditions of equal elevation at nodal intersections and individual optimality of component arches. Computational effort, is reduced by using a simple updating procedure during repetitive calculations. The convergence of the solution is aptly tested by the convergence of elevations and compressive forces in arches. It is shown that the optimal solutions for some skew archgrid systems can be obtained by solving equivalent orthogonal archgrids.
TL;DR: This paper investigates the relative merits of declarative programming and procedural programming languages for optimization problems through an example taken from the field of multicriteria decision making.
Abstract: This paper investigates the relative merits of declarative programming and procedural programming languages for optimization problems through an example taken from the field of multicriteria decision making. The results obtained from this work are presented and discussed.
TL;DR: In this paper, an application of the goal programming technique is described to take care of such a conflicting situation, and experiments were conducted to establish functional relationships between the dressing variables and the surface roughness as well as specific grinding energy under reciprocating plunge surface grinding conditions.
Abstract: The dressing depth of cut and the dressing lead arc the two important dressing variables which significantly affect the surface roughness and specific grinding energy. Normally, to ensure good grinding performance, it is desirable to have, among other things, low surface roughness and, at the same time, low specific grinding energy. A finely dressed wheel gives low surface roughness but at the same time, a higher specific grinding energy, and vice versa. Therefore, both criteria of good grinding performance are in conflict and cannot be achieved simultaneously. To take care of such a conflicting situation, an application of the goal programming technique is described in this paper which determines optimal values of the dressing variables. For this purpose, experiments were conducted to establish functional relationships between the dressing variables and the surface roughness as well as specific grinding energy under reciprocating plunge surface grinding conditions. A sensitivity analysis is carried out t...
TL;DR: In this article, the minimum-weight design of elastic members which are acted upon simultaneously by transverse forces and concentrated moments and by an axial compressive force is studied, and a general optimality condition applicable to members of sandwich and solid construction and having homogeneous fixity conditions is derived.
Abstract: The paper presents analytical expressions for the minimum-weight design of elastic members which are acted upon simultaneously by transverse forces and concentrated moments and by an axial compressive force. The design has to be such that the compliance of the transverse forces and concentrated moments achieves a prescribed value. A general optimality condition applicable to members of sandwich and solid construction and having homogeneous fixity conditions is derived. Several examples illustrate the use of this optimality condition.
TL;DR: In this article, the minimum-weight design of elastic plates subjected to harmonically varying dynamic loading, under a deflection constraint, was studied, and the optimality condition was derived using a generalized form of the principle of stationary mutual potential energy including the inertial force.
Abstract: This paper is concerned with the minimum-weight design of elastic plates subjected to harmonically varying dynamic loading, under a deflection constraint. In the derivation of the optimality condition a generalized form of the principle of stationary mutual potential energy including the inertial force has been used. Numerical results are presented for simply supported circular plates under rotationally symmetric loading.
TL;DR: In this paper, the authors generalized Duncan's model for the economic design of an X¯-control chart using the Edgewarth approximation to the normal distribution and proposed a simplified scheme for selecting the design parameters so that the expected loss-cost is minimal for a specified level of consumer's risk.
Abstract: In this paper Duncan's model for the economic design of an X¯-control chart is generalized using the Edgewarth approximation to the normal distribution. A single assignable cause process model is considered and its expected loss-cost function is presented. An improved version of the existing approximate analytical solution procedure to obtain the value of the design parameters (i.e., sample size n, sampling interval S. control limits coefficient k), is provided. Also, an oplimization technique based on Hooke and Jeeves's pattern search is developed and is employed on the loss-cost function to obtain the optimal design parameter values. Furthermore, a simplified scheme is proposed for selecting the design parameters so that the expected loss-cost is minimal for a specified level of consumer's risk. The proposed simplified scheme can be easily handled by a quality control practitioner at the workshop level.
TL;DR: In this article, the optimal structural design parameters of an Intze type overhead water tank for minimum material content have been considered using nonlinear optimization techniques to solve the problem of finding the minimum material consumption of an Inize type water tank.
Abstract: In this paper the possibility of using nonlinear optimization techniques to determine the optimal structural design parameters of an Intze type overhead water tank for minimum material content has been considered. A least-squares algorithm of Mohan and Muzahim-Bani-Tahir13 for solving nonlinear optimization problems has been used on the structural model formulated by Rao and Raghavan.12 to determine the optimal structural design parameters for various overhead tanks whose capacities lie in the range 200 KL to 2500 KL. The optimal parameters for Inize type tanks obtained in this paper require less material than that required by structures based on conventionally used design parameters as well as the design parameters suggested by Rao and Raghavan.12 Based on the results of these computations a working rule to determine the optimal design parameters of a tank of desired capacity in the range of 200 KL lo 2500 KL has also been proposed. The effects of small changes in the values of the obtained optimal desig...
TL;DR: In this article, an algorithm is presented for determining the minimum cost spanning tree for a flow network in which the are costs can be general non-linear functions of the are flows and lengths.
Abstract: An algorithm is presented for determining the minimum cost spanning tree for a flow network in which the are costs can be general non-linear functions of the are flows and lengths. Using dynamic programming the global optimum solution is achieved. An example is given to illustrate the efficiency of the solution method.
TL;DR: A procedure is proposed for optimizing devices or systems by “plugging in” existing library software modules that have been developed for optimization of components to provide an automatic best trade-off solution of the overall system.
Abstract: A procedure is proposed for optimizing devices or systems by “plugging in” existing library software modules that have been developed for optimization of components. The component modules are nested into a primary subsystem, by interfacing them through shared parameters or adjoint specifications. For every primary optimization, the secondaries are given a full optimization run, the results of which are fed into the primary and used for its current iteration. The availability of large disk storage computers in modern computer systems makes modular programming possible. The procedure will provide an automatic best trade-off solution of the overall system. Three examples are presented.
TL;DR: In this paper, a procedure is developed for selecting materials and thicknesses for the surface, base, and sub-base layers of flexible pavements, which is formulated in terms of a mathematical model.
Abstract: An adequate and economical design for a pavement structure is just as important as one for any other engineering structure. A procedure is developed for selecting materials and thicknesses for the surface, base, and sub-base layers of flexible pavements. The problem is formulated in terms of a mathematical model. The total pavement cost is minimised subject lo a set of constraints which specify minimum requirements of the design in terms of(a)u structural number or a minimum equivalent thickness of the pavement structure, (b) total thickness of the pavement structure, and (c) thickness for each individual layer of the structure. In order to determine the optimal materials and layer thicknesses of the flexible pavement the particular structure of the model is exploited and three major cases are identified and further subdivided into 18 subcases. For a given set of data, a systematic analysis is conducted to discard those subcases that are not appropriate. The developed mathematical model and linear program...
TL;DR: The ease with which empirical sensitivity analyses can be performed becomes apparent and is demonstrated through the performance of such analyses on the presented hydro-thermal system.
Abstract: A multi-stage optimization technique is proposed for solving large optimization problems. The primary advantages of this technique include the utilization of little computer memory and the preservation of much of the complexities inherent in the actual problems. A demonstration of the technique is presented via its application to a complex hydro-thermal scheduling problem faced by a particular company. With this technique this complex problem is seen to be broken down into a sequence of quadratic programming sub-problems. Further simplification of each of these sub-problems is seen to be possible through the reformulation of these problems with matrices. As a result, the ease with which empirical sensitivity analyses can be performed becomes apparent and is demonstrated through the performance of such analyses on the presented hydro-thermal system.
TL;DR: An approach to the optimization of thermal energy systems is described which is general in its structure and applicability and rigorously founded on functional insights into thermodynamics.
Abstract: An approach lo the optimization of thermal energy systems is described which is general in its structure and applicability, The method is rigorously founded on functional insights into thermodynamics. It allows any thermal energy system to be modelled in a standard form which is compatible with subsequent application of one or more of a range of suitable non-linear constrained optimizers. The formalism of the approach is such as to enable practising engineers, without special mathematical or optimization skills, to perform the necessary development. The modelling and calculation follow traditional engineering design procedures and use practical engineering insights to determine solution paths and methods. The technique of modelling is sequential modular and successive substitution is used where necessary. The modularity is extended to include the calculations of costs, handling of constraints and interfacing to optimization routines Optimizers successfully used are the generalized reduced gradient and the...