M.P. Saka

Adaptive Harmony Search Method for Structural Optimization

This paper presents an adaptive harmony search algorithm for solving structural optimization problems. The harmony memory considering rate and pitch adjusting rate are conceived as the two main parameters of the technique for generating new solution vectors. In the standard implementation of the technique appropriate constant values are assigned to these parameters following a sensitivity analysis for each problem considered. The success of the optimization process is directly related on a chosen parameter value set. The adaptive harmony search algorithm proposed here incorporates a new approach for adjusting these parameters automatically during the search for the most efficient optimization process. The efficiency of the proposed algorithm is numerically investigated using two large-scale steel frameworks that are designed for minimum weight according to the provisions of ASD-AISC specification. The solutions obtained are compared with those of the standard algorithm as well as of the other metaheuristic search techniques. It is shown that the proposed algorithm improves performance of the technique and it renders unnecessary the initial selection of the harmony search parameters.

Optimum Geometry Design of Geodesic Domes Using Harmony Search Algorithm

The optimum geometry design of geodesic domes presents difficulty due to the fact that the height of the dome keeps on changing during the design process. This in turn makes it necessary to automate the computation of the coordinates of joints in the dome when the height of crown changes. The algorithm presented in this study carries out the optimum geometry design of single layer geodesic domes. It treats the height of the crown as design variable in addition to the cross-sectional designations of members. A procedure is developed that calculates the joint coordinates automatically for a given height of the crown. The serviceability and strength requirements are considered in the design problem as specified in BS5950–2000. This code makes use of limit state design concept in which structures are designed by considering the limit states beyond which they would become unfit for their intended use. This new addition contains revisions adopting European and international standards for materials, processes and loading. BS 5950 is adopted by many commonwealth countries as their steel design code. The optimum solution of the design problem is obtained using harmony search algorithm. This numerical technique imitates the musical performance process that takes place when a musician searches for a better state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The design examples considered have shown that harmony search algorithm obtains the optimum height and sectional designations for members in relatively less number of searches.

Optimum design of nonlinear steel frames with semi-rigid connections using a genetic algorithm

Abstract The realistic modeling of beam-to-column connections plays an important role in the analysis and design of steel frames. A genetic algorithm based optimum design method is presented for nonlinear multistorey steel frames with semi-rigid connections. The design algorithm obtains a frame with the least weight by selecting appropriate sections from a standard set of steel sections such as wide flange sections of AISC or universal sections of British standard. The algorithm accounts for the serviceability and strength constraints as specified in BS5950. A nonlinear empirical model is used to include the moment–rotation relation of beam-to-column connections. Furthermore, the P – Δ effect is also accounted for in the analysis and design of the multistorey frame. The effective length factors for columns which are flexibly connected to beams are obtained from the solution of the nonlinear interaction equation. A number of frames with end plate without column stiffeners are designed to demonstrate the efficiency of the algorithm.

Genetic algorithm based optimum design of nonlinear planar steel frames with various semi- rigid connections

Abstract A genetic algorithm based optimum design method is presented for nonlinear multistorey steel frames with semi-rigid connections. The design algorithm obtains optimum frame by selecting appropriate sections from standard steel section tables while satisfying the serviceability and strength limitations specified in BS5950. The algorithm accounts for the effect of the flexibility of the connections and the geometric non-linearity of the members. The semi-rigid connections are modeled with the Frye–Morris polynomial model. The values of the coefficients, such as the diameter of bolts, the gauge and the geometric dimensions of angles used in the standardization constants are obtained by designing each connection in the frame during the optimum design cycles. The effective length factors for columns, which are flexibly connected to beams, are obtained from the solution of the nonlinear interaction equation. Several steel frames with different beam to column connections, such as extended end plate, and top and seat angle with and without web cleat, are designed using the algorithm. Each design is carried out twice, with and without considering the geometric non-linearity. Comparison of optimum frames has shown that consideration of geometric non-linearity results in greater economy. It is also noticed that taking the realistic behavior of beam–column connection into account produces more appropriate and in some cases even lighter designs.

Optimum design of pitched roof steel frames with haunched rafters by genetic algorithm

Abstract The pitched roof steel frames appear to be the simplest structural form used in single storey buildings. However, its design necessitates consideration of many different structural criteria that are required in the design of complex structures. In this paper, a genetic algorithm is used to develop an optimum design method for pitched roof steel frames with haunches for the rafters in the eaves. The algorithm selects the optimum universal beam sections for columns and rafters from the available steel sections tables. Furthermore, it determines the optimum depth of the haunch at the eaves and the length of the haunch required for reaching the most cost-effective form. Formulation of the design problem is based on the elastic design method. The serviceability and the strength constraints are included in the design problem as defined in BS 5950. Furthermore, the overall buckling of columns and rafters in the torsional mode between effective torsional restraints to both flanges is also checked. A pitched roof frame is designed by the algorithm developed to demonstrate its practical application.

Optimum design of geometrically nonlinear space trusses

Abstract A structural optimization algorithm is developed for geometrically nonlinear three-dimensional trusses subject to displacement, stress and cross-sectional area constraints. The method is obtained by coupling the nonlinear analysis technique with the optimality criteria approach. The nonlinear behaviour of the space truss which was required for the steps of optimality criteria method was obtained by using iterative linear analysis. In each iteration the geometric stiffness matrix is constructed for the deformed structure and compensating load vector is applied to the system in order to adjust the joint displacements. During nonlinear analysis, tension members are loaded up to yield stress and compression members are stressed until their critical limits. The overall loss of elastic stability is checked throughout the steps of algorithm. The member forces resulted at the end of nonlinear analysis are used to obtain the new values of design variables for the next cycle. Number of design examples are presented to demonstrate the application of the algorithm. It is shown that the consideration of nonlinear behaviour of the space trusses in their optimum design makes it possible to achieve further reduction in the overall weight. The other advantage of the algorithm is that it takes into account the realistic behaviour of the structure, without which an optimum design might lead to erroneous result. This is noticed in one of the design example where a tension member changed into a compression one at the end of nonlinear analysis.

Metaheuristics in structural optimization and discussions on harmony search algorithm

Abstract Metaheuristic algorithms have provided efficient tools to engineering designers by which it became possible to determine the optimum solutions of engineering design optimization problems encountered in every day practice. Generally metaheuristics are based on metaphors that are taken from nature or some other processes. Because of their success of providing solutions to complex engineering design optimization problems the recent literature has flourished with a large number of new metaheuristics based on a variety of metaphors. Despite the fact that most of these techniques have numerically proven themselves as reliable and strong tools for solutions of design optimization problems in many different disciplines, some argue against these methods on account of not having mathematical background and making use of irrelevant and odd metaphors. However, so long as these efforts bring about computationally efficient and robust optimum structural tools for designers what type of metaphors they are based on becomes insignificant. After a brief historical review of structural optimization this article opens this issue up for discussion of the readers and attempts to answer some of the criticisms asserted in some recent publications related with the novelty of metaheuristics.

Optimum design of steel frames with stability constraints

Abstract Optimum design algorithms based on the optimality criteria approach are proven to be efficient and general. They have the flexibility of accomodating variety of design constraints such as displacement, stress, stability and frequency in the design problem. The design methods developed recently, although considering one or more of these constraints, lack the necessity of referring to any relevant design code. The algorithm presented for the optimum design of street frames implements the displacement and combined stress limitations according to AISC. The recursive relationship for design variables in the case of dominant displacement constraints is obtained by the optimality criteria approach. The combined stress inequalities which include in-plane and lateral buckling of members are reduced into nonlinear equations of design variables. The solution of these equations gives the values of bounds for the variables in the case where the stress constraints are dominant in the design problem. The use of effective length in the combined stress constraints makes it possible to study the effect of the end rigidities on the final designs. The design procedure is simple and easy to program which makes it particularly suitable for microcomputers. A number of design examples are considered to demonstrate the practical applicability of the method. It is also shown that the design procedure can be employed in selecting the optimum topology of steel frames.

Mathematical and Metaheuristic Applications in Design Optimization of Steel Frame Structures: An Extensive Review

The type of mathematical modeling selected for the optimum design problems of steel skeletal frames affects the size and mathematical complexity of the programming problem obtained. Survey on the structural optimization literature reveals that there are basically two types of design optimization formulation. In the first type only cross sectional properties of frame members are taken as design variables. In such formulation when the values of design variables change during design cycles, it becomes necessary to analyze the structure and update the response of steel frame to the external loading. Structural analysis in this type is a complementary part of the design process. In the second type joint coordinates are also treated as design variables in addition to the cross sectional properties of members. Such formulation eliminates the necessity of carrying out structural analysis in every design cycle. The values of the joint displacements are determined by the optimization techniques in addition to cross sectional properties. The structural optimization literature contains structural design algorithms that make use of both type of formulation. In this study a review is carried out on mathematical and metaheuristic algorithms where the effect of the mathematical modeling on the efficiency of these algorithms is discussed.

Optimum design of unbraced steel frames to LRFD-AISC using particle swarm optimization

Particle Swarm method based optimum design algorithm for unbraced steel frames is presented. The Particle Swarm method is a numerical optimization technique that simulates the social behavior of birds, fishes and bugs. In nature fish school, birds flock and bugs swarm not only for reproduction but for other reasons such as finding food and escaping predators. Similar to birds seek to find food, the optimum design process seeks to find the optimum solution. In the particle swarm optimization each particle in the swarm represents a candidate solution of the optimum design problem. In the optimum design algorithm presented the design constraints are imposed in accordance with LRFD-AISC (Load and Resistance Factor Design, American Institute of Steel Construction). In the design of beam-column members the combined strength constraints are considered that take into account the lateral torsional buckling of the member. The algorithm developed selects optimum W sections for beams and columns of unbraced frame from the list of 272W-sections list. This selection is carried out such that design constraints imposed by the LRFD are satisfied and the minimum frame weight is obtained. The efficiency of the algorithm is demonstrated considering a number of design examples.