Showing papers in "Engineering Optimization in 1991"
TL;DR: An algorithm for solving non-linear programming problems containing integer, discrete and continuous variables is presented and penalties on integer and/or discrete violations are imposed on the objective function to force the search to converge upon standard values.
Abstract: An algorithm for solving non-linear programming problems containing integer, discrete and continuous variables is presented. Based on a commonly employed optimization algorithm, penalties on integer and/or discrete violations are imposed on the objective function to force the search to converge upon standard values. Examples are included to illustrate the practical use of this algorithm in the area of engineering design.
148 citations
TL;DR: By considering any Steiner tree as a disjoint union of paths, it is shown it is possible to define a neighbourhood structure on the set of feasible solutions which can be used in a k-opt exchange heuristic.
Abstract: This paper considers the use of local optimization or improvement heuristics on the Steiner problem in graphs. By considering any Steiner tree as a disjoint union of paths we show it is possible to define a neighbourhood structure on the set of feasible solutions which can be used in a k-opt exchange heuristic. These ideas are then extended to a simulated annealing method. Computational experience, comparing these new methods with one of the best existing heuristics is presented.
61 citations
TL;DR: In this paper, a model for optimal multi-period operation of a multi-reservoir system with uncertain inflows and water demands is formulated and solved by the Finite Generation Algorithm.
Abstract: A model for optimal multi-period operation of a multi-reservoir system with uncertain inflows and water demands is formulated and solved by the Finite Generation Algorithm. Uncertainties are considered in chance constraints and in penalties due to deviations from meeting demand and reservoir level targets. The penalty functions are linear-quadratic, can be imposed on deviations in one or both directions from the target, and are easily fitted to data by selection of parameters. The stochastic variables are assigned discrete probability distributions. The primal (optimal operation) problem is solved by formulating the dual and then finding its optimum (which is proven to be global for the conditions specified) via a sequence of linear-quadratic deterministic optimization problems of controlled size. The method is demonstrated for a three-reservoir two-period problem. Sensitivity analysis with respect to parameter values is presented. Stochastic simulation is used, to augment the information given by the opt...
41 citations
TL;DR: A decomposition technique is suggested for optimal design of water supply networks and a novel form of the pump equation, based on dimensional analysis, is presented and used as part of the optimization model.
Abstract: A decomposition technique is suggested for optimal design of water supply networks. The general mathematical model is decomposed into two submodels which are solved iteratively. The flow variables are solved in the first submodel for a fixed value of the head variables, using a minimum concave cost flow algorithm. The head variables are solved in the second submodel for a fixed value of the flow variable using LP. The solution is usually obtained after 2 iterations, and is proven to be a local optimum. A novel form of the pump equation, based on dimensional analysis, is also presented and used as part of the optimization model.
40 citations
TL;DR: In this paper, the problem of choosing the types of pressure control elements and locating them in order to minimize leakage in water supply networks is formulated as a non-linear mixed-integer programming problem.
Abstract: The problem of choosing the types of pressure-control elements and locating them in order to minimize leakage in water supply networks is formulated as a non-linear mixed-integer programming problem. This problem is then relaxed by linearizing the pressure-flow relationships to yield a linear mixed-integer programming problem, which is solved by a branch and bound procedure. The relaxed problems at each node of the decision tree are solved by separable programming. Results of case studies to assess the efficacy and computational efficiency of the proposed models are presented and discussed.
38 citations
TL;DR: In this article, the authors focus on the application of MINLP (Mixed Integer Non Linear Programming) for the utility network management problem, which is important for mechanical and chemical engineers, and choose MINLP for the sake of application.
Abstract: This paper will focus on the application of MINLP (Mixed Integer Non Linear Programming). For the sake of application, we have chosen the utility network management problem which is important lo mechanical and chemical engineers.
32 citations
TL;DR: In this paper, a simple procedure for selecting the optimal economic design of a control chart for a single assignable cause system is presented, which consists only of solving an explicit equation for h (sampling interval) in terms of n (sample size) and L (control limit factor).
Abstract: A simple procedure for selecting the optimal economic design of a control chart for a single assignable cause system is presented. The procedure consists only of solving an explicit equation for h (sampling interval) in terms of n (sample size) and L (control limit factor). We conclude that our model is not only more accurate, more applicable, and more flexible, but also simpler to solve than Lorenzen and Vance's Model3.
18 citations
TL;DR: In this article, the problem of rigid-plastic framed structures subjected to load pulses of arbitrary form, and of intensity such that substantial plastic deformation takes place, is treated by approximate means.
Abstract: The problem of rigid-plastic framed structures subjected to load pulses of arbitrary form, and of intensity such that substantial plastic deformation takes place, is treated by approximate means. Mesh and nodal descriptions of the kinetic and kinematic laws are given under the restriction of small displacements, while the structural material is assumed rigid, perfectly plastic and strain rate insensitive. The vectorial relations of the finite element representation of the structure are integrated numerically by means of Newmark's method. For each increment of time, there emerges a linear complementarity problem which can be solved by a variant of Wolfe's algorithm.
13 citations
TL;DR: The physical approach developed in this paper could be one of the better methods of the future to solve the approximate optimization problem of shape optimum design by finite element.
Abstract: Because of increasing CAD requirements in industry, shape optimum design by finite element is an important field of research and development. The global solution of this problem involves two main aspects: the first one is the availability of powerful and robust optimizers and the second one is the necessity of producing the best sensitivity analysis for the approximate problem concerned by optimization. Nowadays, several good softwares or computer programs are available in order to solve a well stated approximate optimization problem. For sensitivity analysis the method using big design elements is quite successful but it appears that more general and powerful methods could be implemented. It is expected that the physical approach developed in this paper could be one of these better methods of the future.
11 citations
TL;DR: In this article, a structural optimization algorithm which includes global displacements as decision variables is presented, which addresses the possibility of using a universal procedure for obtaining optimal solutions independently of local code restrictions.
Abstract: A structural optimization algorithm which includes global displacements as decision variables is presented. The formulation addresses the possibility of using a universal procedure for obtaining optimal solutions independently of local code restrictions. A comparison of current ACI code safety requirements and reliability constraints with examples of optimal limit design techniques is presented. The flexural performance of the elements was evaluated as a function of the actual stress-strain diagrams of the materials. For the non-linear case, formation of fictitious rotational hinges was allowed and the equilibrium constraints were updated accordingly. The adequacy of the frames was guaranteed by imposing constraints, representing the maximum probability of failure of the members and the global displacements allowed, combined with a prescribed limited system probability of failure.
10 citations
TL;DR: In this paper, the authors considered both at the material level and at the structural level by using an internal variable formulation, in which a free energy and a dissipation function were considered.
Abstract: Stepwise holonomic elastic-plastic problems are considered both at the material level and at the structural level by using an internal variable formulation (in which a free energy and a dissipation function ptay a central role). Under convenient hypotheses concerning the material behaviour, some extremal properties are proved, which imply that the elastic-plastic response can be determined by solving non-linear (mostly unconstrained) programs. The paper also discusses the links with extremum theorems previously demonstrated by other authors on the basis of a different approach, which explicitly consider yield surfaces and sometimes plastic multipliers, leading lo non-linear constrained optimization problems. Finally, limit analysis and shakedown problems are briefly discussed within the context of the same internal variable formulation.
TL;DR: In this paper, the authors discuss the existence of solutions to problems of structural optimization which are of an iterative nature and possess explicit recurrence relationships for redesign, and discuss the fixed points, fully stressed designs and optimal solutions.
Abstract: This paper discusses the existence of solutions to problems of structural optimization which are of an iterative nature and possess explicit recurrence relationships for redesign. Five optimization problems are presented. These are the stress constrained truss, the stress constrained prestressed truss under two loading conditions, the natural frequency constrained truss, the overall stability constrained truss and the rigid frame. Common to the five problems is an “allowable stress” algorithm. Schauder's fixed point theorems are discussed and utilized to prove existence, fundamental to which is the scaling property of the individual mappings. A discussion on fixed points, fully stressed designs and optimal solutions follows.
TL;DR: In this article, the optimal level of hybridization and optimal closed-loop and open-loop control functions are determined for a symmetric, cross-ply laminate of hybrid construction, where the objectives of the optimization problem are to maximize the fundamental frequency (design objective) and to minimize the dynamic response to external disturbances (control objective) with minimum expenditure of control energy.
Abstract: Optimal level of hybridization and optimal closed-loop and open-loop control functions are determined for a symmetric, cross-ply laminate of hybrid construction. The objectives of the optimization problem are to maximize the fundamental frequency (design objective) and to minimize the dynamic response to external disturbances (control objective) with minimum expenditure of control energy. The design/control problem is formulated as a multiobjective optimization problem by employing a performance index which combines the design and control objectives in a weighted sum. The control energy is limited by taking a quadratic functional of the control force as a penalty term in this performance index. The plate is constructed as a sandwich hybrid laminate with outer layers of a high-stiffness material. Hybridization refers to the relative amounts of high and low stiffness fibers. Comparative numerical results are given for hybrid and non-hybrid laminates which indicate that although the hybrid laminate ...
TL;DR: The use of non-linear programming methods in grid definition allows greater flexibility in selecting the form and relative importance of criteria employed for grid adaptation and refinement, which in the present formulation is treated as a nested optimization problem.
Abstract: The paper examines the use of boundary element methods in optimal shape synthesis from the standpoint of an integrated formulation. A set of linear equations obtained from the boundary element analysis are treated as equality constraints in the mathematical programming optimization problem. Requirements of computational efficiency mandate the inclusion of grid refinement and grid adaptation in boundary element analysis, which in the present formulation is treated as a nested optimization problem. Two strategies for the solution of this optimization problem, one based on a variational approach and another employing non-linear programming methods, are presented in the paper. The use of non-linear programming methods in grid definition allows greater flexibility in selecting the form and relative importance of criteria employed for grid adaptation and refinement.
TL;DR: In this article, a semi-automated rotordynamic balancing procedure using nonlinear programming (NLP) techniques is presented, which does not require the use of trial runs, but a valid mathematical model of the system dynamics is required.
Abstract: A systematic procedure for balancing flexible rotordynamic systems using nonlinear programming (NLP) techniques is presented. The procedure does not require the use of trial runs, but a valid mathematical model of the system dynamics is required. The rotor response to balance corrections obtained from an optimal search process is then simulated using this model. The objective is to determine the particular correction distribution which will minimize the difference between simulated and experimental results. The effort and expense of trial runs are eliminated, however, this is replaced by the time and expense of generating a valid mathematical model. An example is presented to explore the feasibility and potential of this semi-automated balancing procedure. The results are encouraging and the procedure appears to be a viable alternative to conventional balancing procedures for applications where accurate rotordynamic mathematical models are available.
TL;DR: In this article, the use of duality theory in the plastic limit analysis and shakedown analysis of structures is examined and both primal and dual formulations of the above problems are given.
Abstract: The paper examines the use of duality theory in the plastic limit analysis and shakedown analysis of structures. Classical results are reviewed and both primal and dual formulations of the above problems are given. The use of formulations and the information which can be derived from them are studied with the aid of an example.
TL;DR: In this paper, a minimum weight strut formulation for composite laminated struts is given, which satisfies failure criteria of local buckling, overall buckling and maximum strain or maximum stress.
Abstract: A formulation for minimum weight optimization of composite laminated struts is given. The minimum weight strut satisfies failure criteria of local buckling, overall buckling and maximum strain or maximum stress. Seven types of strut shapes, six composite materials and aluminium alloy are considered. The formulation requires the evaluation of the buckling coefficient, K, for both ends and one side simply supported and one side free for composite laminated plates of high aspect ratio, and the method of evaluation is also given. A computer program OPTSTRUT for carrying out the optimization procedure is described. Examples of strut design are carried out using this program and compared with existing designs. It was found that these results compared well with those from past investigators.
TL;DR: The relevant features and methodological approaches of a DSS (Decision Support System) for dynamic planning of rural telecommunication networks and the attempt to integrate AI techniques and specialized heuristics, aiming at obtaining solutions of better quality.
Abstract: In this work we present the relevant features and methodological approaches of a DSS (Decision Support System) for dynamic planning of rural telecommunication networks. We outline the complexities and difficulties of the formulation and of the planning process. A relevant feature of the model is the attempt to integrate AI techniques and specialized heuristics (using mathematical programming algorithms for particular sub-problems), aiming at obtaining solutions of better quality. The structure of the DSS is presented and justified as well as the main procedures of the model, regarded from the point of view of the decision environment.
TL;DR: In this article, the problem of minimizing the cost of a structural control system subject to displacement, stress, and side constraints is stated in a linear programming (LP) form, where the control variables are either control forces or control displacements and the objective function represents the magnitude and the number of variables.
Abstract: The problem of minimizing the cost of a structural control system subject to displacement, stress and side constraints is stated in a linear programming (LP) form. The control variables are either control forces or control displacements and the objective function represents the magnitude and the number of variables. It is shown that equivalent stress distributions can be achieved by various control systems. The displacements, on the other hand, depend on the location of the control variables. Some relationships between control forces, control displacements, stiffness and flexibility method formulations are derived. The LP formulation provides effective solutions of the presented problem. An alternative solution procedure is proposed for problems where the main object is to minimize the number of control variables.
TL;DR: The chance-constrained approach provides a natural and more flexible model for the operation of the Dam.
Abstract: This paper analyzes the problem of the operation of Aswan High Dam. A chance-Constrained Model (CCM) is developed for the operation of the Dam. The model optimizes total benefits from the discharged water while incorporating all physical and operational constraints. Zero-order decision rules are used to obtain the model deterministic equivalent. The model operating policy is compared with the current operation policy derived from a heuristic rule and an alternative policy derived from a dynamic programming model developed earlier for the operation of the Aswan High Dam. The chance-constrained approach provides a natural and more flexible model for the operation of the Dam.
TL;DR: In order to handle the large computational demand of the method, the system has been implemented on a distributed memory transputer array, using an event parallelization scheme.
Abstract: An optimization strategy for the improvement of membrane structure stress distribution by way of planar cutting pattern variation is presented. In order to handle the large computational demand of the method, the system has been implemented on a distributed memory transputer array, using an event parallelization scheme. The method is applied to a test problem to demonstrate its essential features.
TL;DR: In this article, a regular perturbation expansion of the pre-buckling equilibrium state of the structure in terms of the imperfection magnitude is proposed for both simple and compound buckling.
Abstract: The erosion of the optimal design of structures with buckling constraints, due to the presence of small structural imperfections, is studied. A simple algebraic formula is developed for the imperfection effect on such structures, which is valid for both simple and compound buckling. The formula is based on a regular perturbation expansion of the pre-buckling equilibrium state of the structure in terms of the imperfection magnitude. The developed formula is applied to the reliability-based optimization of a simple structure in a stochastic environment. The strong effect of small structural imperfections in such cases, which may completely invalidate the optimal design of an imperfection sensitive structure, is clearly demonstrated.
TL;DR: In this paper, a new approach based on graph theory for the machine-component grouping problem in a cellular manufacturing system is proposed, where the objective is to form components into part families such that the degree of interrelations is high among components within the same part family and low between components of different part families.
Abstract: This paper proposes a new approach based on graph theory for the machine-component grouping problem in a cellular manufacturing system. The objective is to form components into part families such that the degree of interrelations is high among components within the same part family and low between components of different part families. Since finding an optimal solution through total enumeration is prohibitive in terms of time and efforts even for problems with a moderate number of components, a heuristic algorithm is proposed. The algorithm is hierarchical and divisive in nature and illustrated with numerical examples.
TL;DR: A fairly detailed description is provided of the optimum design problem of finding the minimum cost modifications of the supporting profile along a submarine pipeline, and their connections with variational inequalities and solution algorithms.
Abstract: In the late 1960s complementarity systems have been recognized to be natural models for some problems in structural mechanics. Complementarity systems are known to arise also as stationarity conditions in optimization problems. This paper, after a short survey of complementarity systems, their connections with variational inequalities and solution algorithms, deals with some recent nonconventional applications in structural engineering. Precisely, a fairly detailed description is provided of the optimum design problem of finding the minimum cost modifications of the supporting profile along a submarine pipeline. In this engineering optimization problem a complementary system is included among the constraints. Mathematically similar problems arise in the area of sluctural identification and optimization. All these problems are related to analysis problems (unilateral contact, elastoplasticity) which are amenable to complementarity systems or non-linear convex (often quadratic) programming. The present purp...
TL;DR: In this article, a mathematical programming technique is described which minimizes the total average volume of steel reinforcement of a reinforced concrete frame for a specified failure probability, where the structural material is assumed to exhibit a perfectly-plastic behaviour so that plastic collapse is the only possible failure mode.
Abstract: A mathematical programming technique is described which minimizes the total average volume of steel reinforcement of a reinforced concrete frame for a specified failure probability. The structural material is assumed to exhibit a perfectly-plastic behaviour so that plastic collapse is the only possible failure mode. It consists of solving alternatively a reliability assessment problem, which incorporates recent developments in large-scale constrained concave quadratic programming and an optimal sizing problem (convex minimization) until the best reliability-based design against collapse is found.
TL;DR: In this article, the cow model of Meijer describes a mathematical relation between the predicted daily milk production and the corresponding feed intake needed for lactating cows, and an optimization problem is obtained, which consists of one highly non-linear equality constraint, together with several linear inequality constraints.
Abstract: The cow model of Meijer describes a mathematical relation between the predicted daily milk production and the corresponding feed intake needed for lactating cows. The milk production is a function of several parameters defined for each cow. Used in least cost calculations of daily rations, an optimization problem is obtained, which consists of one highly non-linear equality constraint, together with several linear inequality constraints. Their number required in the optimization can vary and depends on the user's choice. The cost function itself gives a linear relation between the prices of the different forages mixed in the optimal blend. The optimization result has been implemented with the aid of Augmented Lagrange Functions with a view to apply the program in the feedmill industry.
TL;DR: In this paper, a minimal cost pumpage strategy for groundwater decontamination is found as the solution of a non-linearly constrained optimization problem, where the exact gradient of the constrains is computed at a minimum cost through the introduction of the discrete sensitivity equations or the discrete adjoint sensitivity equations.
Abstract: The contaminant distribution into an aquifer is simulated through steady state groundwater flow and transient convective-dispersive transport. A minimal cost pumpage strategy for groundwater decontamination is found as the solution of a non-linearly constrained optimization problem. The exact gradient of the constrains is computed at a minimal cost through the introduction of the discrete sensitivity equations or the discrete adjoint sensitivity equations. We propose a new initialization procedure of the Lagrangian function Hessian for the Sequential Quadratic Programming method (SQP). For this peculiar application, it appears to be very efficient when combined with the SQP implementation of Schittkowski and the discrete gradient compulation. Numerical experiments with problems with up to thirty-five extraction wells have been solved in a computer time equivalent to less than one hundred state equations simulations.
TL;DR: In this paper, the application of the aggregation-optimization-disaggregation systems approach to a multi-reservoir system composed of reservoirs in different river basins has been developed.
Abstract: Hydroelectric power plants associated with reservoirs in different river basins supplying an interconnected systems should be modeled as a whole for the efficient satisfaction of energy demand. Yet, as the number of reservoirs in the system increases, the mathematical model becomes increasingly complex, consuming too much computer time to be solved. With the aggregation-optimization-disaggregation systems approach, a system of reservoirs in different river basins can be aggregated into an equivalent reservoir model which can be optimized to determine optimal operation rules. As a final step, the optimal operation rules of the resulting system can be disaggregated into decisions for the multi-reservoir system again by the use of optimization techniques. In this study, the application of the aggregation-optimization-disaggregation systems approach to a multi-reservoir system composed of reservoirs in different river basins has been developed. As an example, optimization techniques which can be used...
TL;DR: The paper describes operations planning methods for power generation used by Electricite de France by means of Lagrangian dual methods and current research into developing their accuracy and efficiency.
Abstract: The paper surveys operations planning methods for power generation used by Electricite de France. Decomposition of the generation system into sub-units and the coordination of the sub-units is planned by means of Lagrangian dual methods. The paper describes these methods and current research into developing their accuracy and efficiency.
TL;DR: A stochastic model is presented which describes the interactions of individual fibres and is inspired by the spin flip process used in statistical mechanics to seek an approximate solution of a minimal cut problem.
Abstract: Drafting is an important process taking place at several stages of yarn manufacturing. We present a stochastic model which describes the interactions of individual fibres and is inspired by the spin flip process used in statistical mechanics. Simulating on the basis of such a model amounts to seeking an approximate solution of a minimal cut problem which is the formulation of a deterministic approach in term of friction forces.