Showing papers in "Engineering Optimization in 2004"
TL;DR: An improved particle swarm optimizer (PSO) for solving mechanical design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables is presented.
Abstract: This paper presents an improved particle swarm optimizer (PSO) for solving mechanical design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. A constraint handling method called the ‘fly-back mechanism’ is introduced to maintain a feasible population. The standard PSO algorithm is also extended to handle mixed variables using a simple scheme. Five benchmark problems commonly used in the literature of engineering optimization and nonlinear programming are successfully solved by the proposed algorithm. The proposed algorithm is easy to implement, and the results and the convergence performance of the proposed algorithm are better than other techniques.
382 citations
TL;DR: A new global optimization method for black-box functions is proposed, based on a novel mode-pursuing sampling method that systematically generates more sample points in the neighborhood of the function mode while statistically covering the entire search space.
Abstract: The presence of black-box functions in engineering design, which are usually computation-intensive, demands efficient global optimization methods. This article proposes a new global optimization method for black-box functions. The global optimization method is based on a novel mode-pursuing sampling method that systematically generates more sample points in the neighborhood of the function mode while statistically covering the entire search space. Quadratic regression is performed to detect the region containing the global optimum. The sampling and detection process iterates until the global optimum is obtained. Through intensive testing, this method is found to be effective, efficient, robust, and applicable to both continuous and discontinuous functions. It supports simultaneous computation and applies to both unconstrained and constrained optimization problems. Because it does not call any existing global optimization tool, it can be used as a standalone global optimization method for inexpensive probl...
205 citations
TL;DR: A cultural algorithm that uses domain knowledge to improve the performance of an evolutionary programming technique adopted for constrained optimization and builds a map of the feasible region to guide the search more efficiently is introduced.
Abstract: This paper introduces a cultural algorithm that uses domain knowledge to improve the performance of an evolutionary programming technique adopted for constrained optimization. The proposed approach extracts domain knowledge during the evolutionary process and builds a map of the feasible region to guide the search more efficiently. Additionally, in order to have a more efficient memory management scheme, the current implementation uses 2 n -trees to store this map of the feasible region. Results indicate that the approach is able to produce very competitive results with respect to other optimization techniques at a considerably lower computational cost.
181 citations
TL;DR: Smart Pareto sets as mentioned in this paper are a general approach to solving multiobjective optimization problems, which is based on generating a set of optimal solutions and then selecting the most attractive solution from this set as the final design.
Abstract: Multiobjective optimization is a powerful tool for resolving conflicting objectives in engineering design and numerous other fields. One general approach to solving multiobjective optimization problems involves generating a set of Pareto optimal solutions, followed by selecting the most attractive solution from this set as the final design. The success of this approach critically depends on the designer's ability to obtain, manage, and interpret the Pareto set—importantly, the size and distribution of the Pareto set. The potentially significant difficulties associated with comparing a significantly large number of Pareto designs can be circumvented when the Pareto set: (i) is adequately small, (ii) represents the complete Pareto frontier, (iii) emphasizes the regions of the Pareto frontier that entail significant tradeoff, and (iv) de-emphasizes the regions corresponding to little tradeoff. We call a Pareto set that possesses these four important and desirable properties a smart Pareto set. Specifically, ...
170 citations
TL;DR: The hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions is proposed and demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for multimodAL functions.
Abstract: This article proposes the hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions. The hybrid NM–PSO algorithm is very easy to implement, in practice, since it does not require gradient computation. This hybrid procedure performed the exploration with PSO and the exploitation with the NM simplex search method. In a suite of 17 multi-optima test functions taken from the literature, the computational results via various experimental studies showed that the hybrid NM–PSO approach is superior to the two original search techniques (i.e. NM and PSO) in terms of solution quality and convergence rate. In addition, the presented algorithm is also compared with eight other published methods, such as hybrid genetic algorithm (GA), continuous GA, simulated annealing (SA), and tabu search (TS) by means of a smaller set of test functions. On the whole, the new algorithm is demonstrated to be extremely effective and ef...
135 citations
TL;DR: The results indicate that the proposed algorithm to handle constraints of all types in a genetic algorithm used for global optimization is highly competitive with respect to penalty-based techniques and withrespect to other constraint-handling techniques which are considerably more complex to implement.
Abstract: This paper proposes an algorithm based on a model of the immune system to handle constraints of all types (linear, nonlinear, equality, and inequality) in a genetic algorithm used for global optimization. The approach is implemented both in serial and parallel forms, and it is validated using several test functions taken from the specialized literature. Our results indicate that the proposed approach is highly competitive with respect to penalty-based techniques and with respect to other constraint-handling techniques which are considerably more complex to implement.
133 citations
TL;DR: Through comparison with other methods, it is found that the proposed methodology can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum in the presence of highly nonlinear constraints.
Abstract: For computation-intensive design problems, metamodeling techniques are commonly used to reduce the computational expense during optimization; however, they often have difficulty or even fail to model an unknown system in a large design space, especially when the number of available samples is limited. This article proposes an intuitive methodology to systematically reduce the design space to a relatively small region. This methodology entails three main elements: (1) constructing metamodels using either response surface or kriging models to capture unknown system behavior in the original large space; (2) calculating many inexpensive points from the obtained metamodel, clustering these points using the fuzzy c-means clustering method, and choosing an attractive cluster and its corresponding reduced design space; (3) progressively generating sample points to construct kriging models and identify the design optimum within the reduced design space. The proposed methodology is illustrated using the well-known ...
128 citations
TL;DR: In this article, a framework for performing reliability based multidisciplinary design optimization using approximations is developed, where the reliability constraints are formulated as constraints on the probability of failure corresponding to each of the failure modes or a single constraint on the system probability of failing.
Abstract: Traditionally, reliability based design optimization (RBDO) is formulated as a nested optimization problem. For these problems the objective is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure corresponding to each of the failure modes or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large scale multidisciplinary systems which are likewise computationally intensive. In this research, a framework for performing reliability based multidisciplinary design optimization using approximations is developed. Response surface approximations (RSA) of the limit state fu...
74 citations
TL;DR: The EAGA promises to be a flexible procedure for exploring alternative solutions that could assist when making decisions for real engineering optimization problems riddled with unmodeled or unquantified issues.
Abstract: Typically for a real optimization problem, the optimal solution to a mathematical model of that real problem may not always be the ‘best’ solution when considering unmodeled or unquantified objectives during decision-making. Formal approaches to explore efficiently for good but maximally different alternative solutions have been established in the operations research literature, and have been shown to be valuable in identifying solutions that perform expectedly well with respect to modeled and unmodeled objectives. While the use of evolutionary algorithms (EAs) to solve real engineering optimization problems is becoming increasingly common, systematic alternatives-generation capabilities are not fully extended for EAs. This paper presents a new EA-based approach to generate alternatives (EAGA), and illustrates its applicability via two test problems. A realistic airline route network design problem was also solved and analyzed successfully using EAGA. The EAGA promises to be a flexible procedure for explo...
64 citations
TL;DR: A stochastic integer programming model is proposed in which the objective is to maximize expected profits and on/off decisions for each generator are made in the first stage of this model.
Abstract: The unit commitment problem consists of determining the schedules for power generating units and the generating level of each unit. The decisions concern which units to commit during each time period and at what level to generate power to meet the electricity demand. The problem is a typical scheduling problem in an electric power system. The electric power industry is undergoing restructuring and deregulation. This article developes a stochastic programming model which incorporates power trading. The uncertainty of electric power demand or electricity price are incorporated into the unit commitment problem. It is assumed that demand and price uncertainty can be represented by a scenario tree. A stochastic integer programming model is proposed in which the objective is to maximize expected profits. In this model, on/off decisions for each generator are made in the first stage. The approach to solving the problem is based on Lagrangian relaxation and dynamic programming.
35 citations
TL;DR: An approach to engineering design of mixed-domain dynamic systems that generates engineering designs that satisfy predefined specifications in an automatic manner and a hierarchical fair competition model is adopted in this work.
Abstract: This paper presents an approach to engineering design of mixed-domain dynamic systems. The approach aims at system-level design and has two key features: first, it generates engineering designs that satisfy predefined specifications in an automatic manner; second, it can design systems belonging to different or mixed physical domains, such as electrical, mechanical, hydraulic, pneumatic, thermal systems and/or a mixture of them. Two important tools are used in this approach, namely, bond graphs and genetic programming. Bond graphs are useful because they are domain independent, amenable to free structural composition, and are efficient for classification and analysis, allowing rapid determination of various types of acceptability or feasibility of candidate designs. Genetic programming, on the other hand, is a powerful tool for open-ended topological search. To prevent the premature convergence often encountered in evolutionary computation, a hierarchical fair competition model is adopted in this work. Ex...
TL;DR: In this article, a methodology and two example applications for finding the optimal layout of a detection system, taking explicitly into account the dilution and decay properties of the water quality constituents as distributed with flow, as well as the ability of the monitoring equipment to detect contaminant concentrations, are formulated and demonstrated.
Abstract: Water distribution systems are spatially diverse. As such, they are inherently vulnerable to accidental or deliberate physical, chemical, or biological threats. Efficient water quality monitoring is one of the most important tools to guarantee a reliable potable water supply. A methodology and two example applications for finding the optimal layout of a detection system, taking explicitly into account the dilution and decay properties of the water quality constituents as distributed with flow, as well as the ability of the monitoring equipment to detect contaminant concentrations, are formulated and demonstrated. The detection system outcome is aimed at capturing contaminant entries within a pre-specified level of service (LOS) defined as the maximum volume of polluted water exposure to the public at a concentration higher than a minimum hazard level. The proposed methodology couples hydraulic simulations with graph theory techniques to identify a minimum set of monitoring stations that ‘covers’ the entir...
TL;DR: In this article, the authors describe the methodology and application of a genetic algorithm scheme tailor-made to EPANET, for optimizing the operation of a water distribution system under unsteady water quality conditions.
Abstract: This paper describes the methodology and application of a genetic algorithm scheme tailor-made to EPANET, for optimizing the operation of a water distribution system under unsteady water quality conditions. The water distribution system consists of sources of different qualities, treatment facilities, tanks, pipes, control valves, and pumping stations. The objective is to minimize the total cost of pumping and treating the water for a selected operational time horizon, while delivering the consumers the required quantities at acceptable qualities and pressures. The decision variables for each of the time steps that encompass the total operational time horizon include: the scheduling of the pumping units, settings of the control valves, and treatment removal ratios at the treatment facilities. The constraints are: head and concentrations at the consumer nodes, maximum removal ratios at the treatment facilities, maximum allowable amounts of water withdrawals at the sources, and returning at the end of the o...
TL;DR: In this article, the authors used sequential quadratic programming (SQP) to find an optimum speed control hump geometric design to reduce the excessive shocks experienced by drivers when crossing the hump below the speed limit.
Abstract: The aim of the present paper is to find an optimum speed control hump geometric design by using the sequential quadratic programming method. Theoretical investigation of the dynamic behavior of the driver body components and the vehicle due to crossing speed control humps is presented. The vehicle–driver system represented as a mathematical model consists of 12 degrees of freedom (DOF). Seven DOFs are used for the human body model in the heave mode and the rest are for the vehicle body, suspension system and tires. An optimum design method for the hump geometry is proposed to reduce the excessive shocks experienced by drivers when crossing the hump below the speed limit, while being unpleasant when going over the speed limit. The pleasant or unpleasant ride, or what is called comfort criteria (CC), is modeled by calculating the driver's head acceleration. In this regard, the geometry of the hump will be controlled to match an optimum practical shape that can be implemented economically. Three types of hum...
TL;DR: In this paper, a multiobjective design optimization system of exhaust manifold shapes with tapered pipes for a car engine has been developed by using divided range multi-objective genetic algorithm (DRMOGA) to obtain more engine power as well as to produce less pollutant.
Abstract: A multiobjective design optimization system of exhaust manifold shapes with tapered pipes for a car engine has been developed by using divided range multiobjective genetic algorithm (DRMOGA) to obtain more engine power as well as to produce less pollutant. Although the present design problem is known to be highly non-linear, the exhaust manifold has been successfully designed to improve both objectives. A comparison of the results obtained by DRMOGA and MOGA was performed and DRMOGA was demonstrated to find better solutions than MOGA.
TL;DR: In this article, the geometrical dimensions of a counterflow natural draft wet cooling tower are optimized to obtain the minimum combined operational and capital cost compounded over the economic life of the cooling tower.
Abstract: The geometrical dimensions of a counterflow natural draft wet-cooling tower are optimized to obtain the minimum combined operational and capital cost compounded over the economic life of the cooling tower. Wet-cooling tower performance evaluation software is employed in conjunction with an optimization algorithm to obtain the optimum cooling tower geometry. It is shown that the inlet height of the cooling tower, which primarily determines the operational cost, is the most critical parameter influencing the total operational and capital cost of a cooling tower. The effects of the diameter of the cooling tower and the volume of the concrete have a less pronounced effect on the total operational and capital cost of a cooling tower. The results of the mathematical optimization algorithm are verified by a manual investigation of the solution domain.
TL;DR: The proposed approach is tested on problems from the literature, and it is shown that it improves significantly upon previous single objective approaches and provides the user with a Pareto optimal set of designs to examine further.
Abstract: This paper presents an evolutionary approach to design of capacitated networks considering cost, performance, and survivability. Traditionally, network performance and survivability have been considered independently. The approach presented in this paper is comprehensive where selecting network topology, assigning capacities for each link, and determining a route for each communicating node pair are simultaneously performed during optimization. Dual objectives of minimizing cost and minimizing delay are used, and the network design is subject to a survivability constraint. The proposed approach is tested on problems from the literature, and it is shown that it improves significantly upon previous single objective approaches and provides the user with a Pareto optimal set of designs to examine further. *E-mail: konak@psu.edu
TL;DR: In this article, the robustness of the solutions is discussed, based on the analysis of the range of model parameters for robustness measures, and a graphical representation of the meaningful parameter ranges is clearly defined with mathematical proofs.
Abstract: In this study, ranges of model parameters are analyzed for robustness measures. In particular, the properties of partial mean and worst-case cost in robust optimization are investigated. The robust optimization models are considered as multiobjective problems having two objectives, the expected performance (i.e. expected cost) and a robustness measure (Suh, M. and Lee, T. (2001) Robust optimization method for the economic term in chemical process design and planning. Industrial & Engineering Chemical Research, 40, 5950–5959). The robust partial mean model is defined with objectives of expected value and partial mean. The robust worst-case model is defined with the objective of expected value and worst-case. They are proved to guarantee Pareto optimality, which should be satisfied for multiobjective optimization problems. A graphical representation of the meaningful parameter ranges is clearly defined with mathematical proofs. The robustness of the solutions is discussed, based on the analysis of the range...
TL;DR: In this paper, a multi-objective extension of the shape annealing approach to conceptual design of bicycle frames is presented. And the results demonstrate the success of this approach in exploring a multiplicity of different design configurations and presenting the designer with a variety of Pareto-optimal concepts worthy of further consideration.
Abstract: Using the design of bicycle frames as a case study, this paper explores the potential of a multiobjective extension of the shape annealing approach to conceptual design. The key elements of this approach are a randomized search based optimization method (to simulate creativity), a generative structural shape grammar (to allow different configurations to be explored), and a multiobjective optimization approach (to identify competing concepts occupying different parts of the trade-off surface). The results presented demonstrate the success of this approach in exploring a multiplicity of different design configurations and presenting the designer with a variety of Pareto-optimal concepts worthy of further consideration.
TL;DR: In this paper, an integrated procedure for optimizing parameter settings in electroforming to improve stamper quality performance is proposed, which combines neural networks, desirability functions and tabu search to solve multi-response parameter design problems.
Abstract: In optical recordable media manufacturing, an electroforming process uses glass masters to produce metal shells which then act as stampers to replicate thousands of copies of a disc. The physical characteristics of stampers influence their life time significantly and, moreover, significantly affect the quality performance of the finished optical recordable media. Traditionally, engineers sought the optimal parameter settings in the electroforming process through trial and error, and thus serious losses were experienced owing to the low yield of stampers. This study proposes an integrated procedure for optimizing parameter settings in electroforming to improve stamper quality performance. The proposed procedure combines neural networks, desirability functions and tabu search to solve multi-response parameter design problems. The proposed procedure was applied at a Taiwanese optical recordable media manufacturer, and the implementation results demonstrated its feasibility and effectiveness. Through this wor...
TL;DR: It is argued that the synthesis of circuits using bottom–up procedures (such as GP) is at least as powerful as any top–down method, and that this is possible by means of the replication of a single element: the binary multiplexer.
Abstract: This article introduces the circuit design problem as a synthesis procedure. An evolutionary technique denominated Genetic Programing (GP) is proposed as the main engine for the synthesis of logic circuits. This article argues that the synthesis of circuits using bottom–up procedures (such as GP) is at least as powerful as any top–down method, and that this is possible by means of the replication of a single element: the binary multiplexer. The properties of this device are described as a sound basis for the synthesis of logic circuits using GP. Several circuits are synthesized and contrasted against two design methods: the standard implementation of logic functions using multiplexers, and ordered binary decision diagrams.
TL;DR: Fast and reliable numerical algorithms, based on the conjugate gradient method, are presented for normal as well as for Poisson traffic demands, and the Poisson case is linked with entropy maximization.
Abstract: This paper presents numerical methods for dynamic traffic demand estimation between N zones in a network, where the zones are disjoint subsets of nodes of the network. Traffic is assumed to be generated or absorbed only in the zones and nowhere else in the network. Traffic volumes between zones over a fixed period of time are modeled as independent random variables with unknown means which it is desired to estimate. For each zone, the volume of all incoming and outgoing traffic is counted on a regular basis but no information about the origin or destination of the observed traffic is used. Procedures are suggested for a regular update of estimates of the N(N - 1) mean traffic demands between the zones on the basis of an incoming stream of the 2N traffic counts. The procedures are based on an exponential smoothing scheme and are reminiscent of the expectation maximization (EM) algorithm if smoothing is removed. Fast and reliable numerical algorithms, based on the conjugate gradient method, are presented fo...
TL;DR: In this paper, a comparison of two methods for design improvement: genetic algorithms (GA) and model-based robust engineering design (RED) is presented, and the benefits of each method are discussed.
Abstract: Modern engineering design contains both creative and analytic components. This paper discusses the design process and illustrates links between design optimization and conceptual design through the re-design of a cardiovascular stent. A comparison is presented of two methods for design improvement: genetic algorithms (GA) and model-based robust engineering design (RED). Computational fluid dynamics (CFD) models are used to generate measurements of the quality of competing designs based on the concept of dissipated power. Alternative performance measures are also discussed. Environmental noise is introduced into the analysis and consideration is given to the treatment of discrete and continuous design parameters. Improved designs are identified using both methods and verified with further CFD analyses, and the benefits of each method are discussed.
TL;DR: In this paper, a co-evolutionary method for solving pursuit-evasion games with consideration of non-zero lethal radii is proposed, which can handle both the final time problem and the miss distance problem simultaneously, by adopting a separated payoff function.
Abstract: This study suggests a co-evolutionary method for solving pursuit-evasion games with consideration of non-zero lethal radii. The proposed method has three key features. First, it can handle both the final time problem and the miss distance problem simultaneously, by adopting a separated payoff function. Second, the Stackelberg equilibrium instead of the security strategy solution is employed to consider the maximin characteristics of an open-loop solution. Finally, an additional evolving group is introduced to treat an unprescribed final time. Numerical simulations are performed to verify the proposed method by comparing it with the gradient-based method. In addition, the effect of lethal radius is discussed based on the numerical results.
TL;DR: In this article, the problem of the optimal design of simply supported columns under loadings controlled by displacements is investigated and the optimal solutions for different constraints of minimal and maximal cross-sectional area and various elastic foundations are presented.
Abstract: In this article, the problem of the optimal design of simply supported columns under loadings controlled by displacements is investigated. It seeks a cross-sectional area, varying along the axis of the column, which leads to the maximal axial displacement caused by compression before the structure buckles. The uni-modal and bi-modal problems are considered. The optimal solutions for different constraints of minimal and maximal cross-sectional area and various elastic foundations are presented in this article. The results are obtained by solving an analytical formulation of the optimization problem and by using numerical optimization methods, namely the method of moving asymptotes and the simulated annealing method.
TL;DR: Experimental results on configuration design problems: the design of parity checker and adder circuits, demonstrate the performance gains from the approach and show that the system learns to take less time to provide quality solutions to a new design problem as it gains experience from solving other similar design problems.
Abstract: Genetic algorithms (GAs) augmented with a case-based memory of past design problem-solving attempts are used to obtain better performance over time on sets of similar design problems. Rather than starting anew on each design, a GA's population is periodically injected with appropriate intermediate design solutions to similar, previously solved design problems. Experimental results on configuration design problems: the design of parity checker and adder circuits, demonstrate the performance gains from the approach and show that the system learns to take less time to provide quality solutions to a new design problem as it gains experience from solving other similar design problems.
TL;DR: The paper reviews the development of the cluster-oriented genetic algorithm (COGA) strategy from the initial approach to more recent advances which significantly improve the performance of COGA in both the search capabilities and the consistency of the generated design solutions.
Abstract: The paper reviews the development of the cluster-oriented genetic algorithm (COGA) strategy from the initial approach to more recent advances which significantly improve the performance of COGA in both the search capabilities and the consistency of the generated design solutions. COGAs are specifically designed to identify high-performance (HP) regions of complex, multi-variable design spaces whilst also achieving good set cover in terms of solutions across these regions. The objective is to extract information from such regions relating to the nature of the problem space in addition to providing the designer with a succinct collection of HP design options. The application of COGA to a number of real-world design tasks is discussed, and also its integration within a graphical user interface and the interactive evolutionary design system.
TL;DR: These formulations lead to rapid implementation of the model by introducing the idea of a candidate set of median machines, which consists of the machines that have a high possibility of serving as medians or seed machines for grouping and can attack large-size MPGPs efficiently.
Abstract: This article develops efficient p-median mathematical formulations for solving the machine-part grouping problem (MPGP) in group technology manufacturing and compares the performance of the formulations with that of existing p-median ones. In spite of the successful applications of MPGP that have been reported in the literature, existing p-median formulations have been restricted to small to medium-sized MPGP since they attempt to find the optimal solution over the entire feasible region of the constraint set without any prior knowledge about the median machines. Our formulations lead to rapid implementation of the model by introducing the idea of a candidate set of median machines, which consists of the machines that have a high possibility of serving as medians or seed machines for grouping. The candidate set of median machines plays the role of medians known in advance and enables the model to be implemented with the feasible region of a reduced constraint set. Furthermore, our alternative formulation ...
TL;DR: The algorithm is used to determine the optimal combination of input parameter values of an automated manufacturing system and it is shown that under suitable conditions on the boundaries, the algorithm converges almost surely to an optimum solution.
Abstract: Developing efficient methods for solving discrete simulation optimization problems is an important area of research, especially in the field of engineering design problems. This paper presents a sequential stochastic comparison search algorithm for solving a discrete stochastic optimization problem where the objective function does not have an analytical form, but has to be measured or estimated, for instance through Monte Carlo simulation. The optimization algorithm in this paper uses a binary hypothesis test. At each iteration of the algorithm, two neighboring configurations are compared and the one that appears to be better is passed on to the next iteration. The algorithm uses a sequential sampling procedure with increasing boundaries as the number of iterations increases. It is shown that under suitable conditions on the boundaries, the algorithm converges almost surely to an optimum solution. The algorithm is used to determine the optimal combination of input parameter values of an automated manufac...
TL;DR: In this article, a multidisciplinary optimization procedure is described to delay the occurrence of store-induced flutter of an aircraft wing/tip store configuration in the transonic Mach number regime.
Abstract: In this research, a multidisciplinary optimization procedure is described to delay the occurrence of store-induced flutter of an aircraft wing/tip store configuration. A preliminary design procedure was developed to enhance the performance characteristics of an aircraft wing model in the transonic Mach number regime. A wing/tip store configuration with the store center of gravity (c.g.) located at the 50% aerodynamic tip chord was chosen for structural optimization. The aircraft wing structural weight was chosen as the objective function with constraints on natural frequency, stress and flutter. Automated Structural Optimization System and Computational Aeroelasticity Program-Transonic Small-Disturbance were the computational tools employed to perform the structural optimization and subsequent aeroelastic (mutual interaction between the aerodynamics and structural deformation) analysis in the transonic regime. This work showed that an improved store-induced flutter speed was obtained by increasing the sep...