Donald E. Grierson

Comparison among five evolutionary-based optimization algorithms

Evolutionary algorithms (EAs) are stochastic search methods that mimic the natural biological evolution and/or the social behavior of species. Such algorithms have been developed to arrive at near-optimum solutions to large-scale optimization problems, for which traditional mathematical techniques may fail. This paper compares the formulation and results of five recent evolutionary-based algorithms: genetic algorithms, memetic algorithms, particle swarm, ant-colony systems, and shuffled frog leaping. A brief description of each algorithm is presented along with a pseudocode to facilitate the implementation and use of such algorithms by researchers and practitioners. Benchmark comparisons among the algorithms are presented for both continuous and discrete optimization problems, in terms of processing time, convergence speed, and quality of the results. Based on this comparative analysis, the performance of EAs is discussed along with some guidelines for determining the best operators for each algorithm. The study presents sophisticated ideas in a simplified form that should be beneficial to both practitioners and researchers involved in solving optimization problems.

A modified shuffled frog-leaping optimization algorithm: applications to project management

Evolutionary algorithms, such as shuffled frog-leaping, are stochastic search methods that mimic natural biological evolution and/or the social behavior of species. Such algorithms have been developed to arrive at near-optimum solutions to complex and large-scale optimization problems which cannot be solved by gradient-based mathematical programming techniques. The shuffled frog-leaping algorithm draws its formulation from two other search techniques: the local search of the ‘particle swarm optimization’ technique; and the competitiveness mixing of information of the ‘shuffled complex evolution’ technique. A brief description of the original algorithm is presented along with a pseudocode and flowchart to facilitate its implementation. This paper then introduces a new search-acceleration parameter into the formulation of the original shuffled frog-leaping algorithm to create a modified form of the algorithm. A number of simulations are carried out for two continuous optimization problems (known as benchmark test problems) and two discrete optimization problems (large scale problems in the project management domain) to illustrate the positive impact of this new parameter on the performance of the shuffled frog-leaping algorithm. A range of ‘best’ usable values for the search-acceleration parameter is identified and discussed.

Push-over analysis for performance-based seismic design

Abstract The paper presents a simple computer-based push-over analysis technique for performance-based design of building frameworks subject to earthquake loading. The technique is based on the conventional displacement method of elastic analysis. Through the use of a ‘plasticity-factor’ that measures the degree of plastification, the standard elastic and geometric stiffness matrices for frame elements (beams, columns, etc.) are progressively modified to account for nonlinear elastic–plastic behavior under constant gravity loads and incrementally increasing lateral loads. The behavior model accounts for material inelasticity due to both single and combined stress states, and provides the ability to monitor the progressive plastification of frame elements and structural systems under increasing intensity of earthquake ground motion. The proposed analysis technique is illustrated for two building framework examples.

Mathematical programming methods for deformation analysis at plastic collapse

Abstract A variety of alternative mathematical programming procedures for first-order elastoplastic analysis at the collapse-load level for discrete structures described by piecewise-linear elastic-perfectly plastic constitutive laws are formulated and then assessed with respect to their relative computational merit. An iterative Linear Programming, three Quadratic Programming and two Restricted Basis Linear Programming procedures are developed in detail. In addition, Parametric Linear Complementarity and Parametric Quadratic Programming methods are briefly discussed. The governing relations for analysis and the various formulations are initially developed for a trusslike structure, and are then shown to apply, without formal alteration, to a broad range of frameworks and continua discretized into finite elements. The unbounded nature of deformations at plastic collapse of elastic-perfectly plastic structures is considered, as is the possibility that there may be a multiplicity of (bounded) deformation responses to a single load path prior to plastic collapse, and several devices to overcome related difficulties are illustrated. Two example structures are each analyzed by six of the procedures presented.

Pareto multi-criteria decision making

The paper concerns design governed by multiple objective criteria, which are conflicting in the sense of competing for common resources to achieve variously different performance objectives (financial, functional, environmental, esthetical, etc.). A multi-criteria decision making (MCDM) strategy is proposed that employs a tradeoff-analysis technique to identify compromise designs for which the competing criteria are mutually satisfied in a Pareto-optimal sense. The MCDM strategy is initially developed for the case of design governed by n=2 objective criteria. It is then extended to design governed by n>2 objective criteria, by introducing the concept of primary and aggregate criteria. It is proved that, from among the theoretically infinite number of feasible designs forming the Pareto front for a design problem governed by n independent objective criteria, there exists a unique Pareto-compromise design that represents a mutually agreeable tradeoff between all n criteria. This remarkable result is illustrated for a flexural plate design governed by n=2 criteria, a bridge maintenance-intervention protocol design governed by n=3 criteria, and a media centre envelop design governed by n=11 criteria.

Pareto-Optimal Conceptual Design of the Structural Layout of Buildings Using a Multicriteria Genetic Algorithm

This article presents a computational procedure for multicriteria optimal conceptual design of the structural layout of buildings subject to given specifications and requirements. Two objective criteria are considered for evaluating alternative designs. The first objective concerns minimizing the building project cost through minimization of a function defining the combined costs of the building structural system and the land for the building site. The second objective concerns optimizing the flexibility of floor space usage, which is a qualitative criterion that is given a quantitative form through minimization of an exponential function that relates tributary load area to the spacing of columns. A multicriteria genetic algorithm (MGA) is applied to solve the biobjective conceptual building layout design problem using Pareto optimization theory . The MGA process is shown to be similar to that of the simple genetic algorithm, except that the fitness evaluation of candidate designs is based on a distance metric related to the Pareto-optimal set. A variable-mutation technique is introduced to maintain genetic diversity and to accelerate the stochastic search for the global optimum. An example conceptual building layout design is presented using the MGA, and the applicability and efficiency of the developed computational conceptual design procedure are discussed.

Optimal Synthesis of Steel Frameworks Using Standard Sections

ABSTRACT This paper presents a computer-based method for optimally sizing members of planar steel frameworks using commercially available standard sections. For first-order behavior and static loads, a minimum-weight structure is found while simultaneously ensuring stress and displacement performance conditions under applied service loads. Architectural conditions are imposed on section sizes to satisfy fabrication requirements related to member continuity and structure symmetry. The design method presented is iterative in nature and remarkably efficient. The number of iterations is generally quite small and almost totally independent: of the complexity of the structure. Designs are presented for two steel frameworks that are typical of those encountered in professional practise.

Influence of Semi‐Rigid Connections and Local Joint Damage on Progressive Collapse of Steel Frameworks

Abstract: Semi-rigidly connected steel frames are more vulnerable than rigidly connected frames to resist progressive collapse due to abnormal loading events. This article extends the threat-independent method for progressive-failure analysis of rigid frames to analysis accounting for semi-rigid connections. The influence of joint damage caused by disengagement of member(s) is also considered in the analysis, and the degree of damage is modeled by a health index. A compound element model is employed to include the contributions of nonlinear behavior of beam-to-column connections, connection and member-end damage, member inelasticity, member shear deformation, and geometrical nonlinearity to structural response. Four beam collapse modes are illustrated for the progressive collapse analysis associated with debris loading generated when disengaged structural components fall onto lower parts of the structure. The impact effect is taken into account for the quasi-static nonlinear analysis by utilizing an impact amplification factor according to GSA and DoD guidelines. Any progressive collapse occurring thereafter involves a series of collapse events associated with topological changes of the frame. The analysis procedure is illustrated for the progressive collapse behavior of two planar steel frames. The results demonstrate that the proposed method is potentially an effective tool for the progressive collapse analysis of semi-rigid steel frames under abnormal loading events.

Optimal synthesis of frameworks under elastic and plastic performance constraints using discrete sections

ABSTRACT A computer-based method is presented for minimum-weight design of planar frameworks under service and ultimate performance conditions using discrete member sections. Service-load conditions ensure acceptable elastic stresses and displacements, and ultimate-load conditions ensure adequate safety against plastic collapse. The sizes of the discrete sections, which can be of any type; e.g., WF, HSS, etc., may be constrained to satisfy fabrication requirements related to member continuity and structure symmetry. The design method is iterative in nature and remarkably efficient. The number of iterations is generally small and almost totally independent of the complexity of the structure. Several comparative designs for simple truss and frame structures are presented to illustrate features of the method.

Synthesis under service and ultimate performance constraints

Abstract A Method is developed for the minimum weight design of structural systems subject to performance constraints imposed at both the service and ultimate loading levels. The service-load constraints ensure acceptable elastic stresses and displacements, while the ultimate-load constraints ensure adequate safety against plastic collapse. Both sets of constraints are explicitly and simultaneously accounted for by the design process. The minimum weight design is achieved through an iterative process. For each design stage, the results of elastic and plastic analyses are employed in conjunction with approximation techniques to formulate the performance constraints. An improved (lower weight) design is found using optimization techniques, and the process is repeated until weight convergence occurs after a number of design stages. The method is developed for structural systems for which stiffness and strength properties are linear functions of the transverse sizes of the elements (thin-walled structures composed of bar, membrane and shear-panel elements). Several simple truss examples are presented to illustrate the theory.