Constrained Design Optimization Research Articles

Constrained efficient global multidisciplinary design optimization using adaptive disciplinary surrogate enrichment

Constrained efficient global multidisciplinary design optimization using adaptive disciplinary surrogate enrichment

Development and Statistical Optimization of Flakes from Selected Local Food Ingredients

Flakes are instant breakfast meals, primarily produced from mono-cereals (corn, wheat, rice, and/or oats), processed with added flavor and fortified with vitamins and minerals. They are one of the several forms of cold cereals that are consumed immediately after mixing with milk, yogurt, or fruit. In this study, value-added instant flakes were developed, characterized and optimized; from blends of corn, millet, and soybean. A three-component constrained optimal (custom) mixture experimental design, with 30 randomized experimental runs, was employed for the formulation. The formulation design constraints were: corn flour (30% - 45%), millet flour (10% - 25%), and soybean flour (5% - 20%). Other components of the formulation, which were kept constant, were: water (19%), sugar (8%), malt (2%), egg (3%), sweet potato extract (3%), ginger (2%), and moringa seed powder (3%). The formulated flakes were analyzed and evaluated for the proximate, physicochemical and sensory characteristics using standard procedures. The result of the numerical optimization gave optimized instant flakes with an overall desirability index of 0.637, based on the set optimization goals and individual quality desirability indices. The optimal instant flake was obtained from 30.5 % corn flour, 11.2 % millet flour, 18.3 % soybean meal. The quality properties of this optimal instant flake were: 1.83 % moisture content, 9.05 % fat content, 1.74 % ash content, 2.66 % crude fibre, 38.0 % crude protein, 46.7 % carbohydrate, 420 kcal energy value and 6.28 overall acceptability. The result of the study showed that the formulated instant flakes were of high quality and that improving the nutritional quality of flakes is possible through grain-to-grain composite formulation. It is recommended that further study be carried out on the formulation of nutritionally improved instant flakes using other nutritionally rich grains and legumes such as groundnut, sesame seed, melon seed etc. Enrichment of flakes with protein-rich sources will result in flakes product with improved nutrient quality that meets the consumer’s dietary needs.

Optimum-pursuing method for constrained optimization and reliability-based design optimization problems using Kriging model

This paper proposes a new active learning method named as optimum-pursuing method (OPM) from the viewpoint of optimization theory, which aims to provide an effective tool for solving constrained optimization and reliability-based design optimization (RBDO) problems with low computation cost. It uses the cheap Kriging metamodel to replace the expensive physical response. The novelty of the proposed OPM primarily lies in two aspects. First, the OPM utilizes the advantage of the optimization theory rather than sampling technology. By using the augmented Lagrangian approach, it comprehensively considers the objective, constraints, and their relations, thereby automatic identification of important region in the vicinity of the optimum. Second, the accordingly optimum-pursuing function consists of three parts: Kriging mean, Kriging standard deviation, and merit function. Also, the target reliability surface is further considered to enhance the local accuracy of the reliability analysis. The performance of OPM is tested for both deterministic optimization and problems, in which two mathematical and three real-world engineering examples are selected to showcase the feasibility and validity. The results demonstrate that OPM is promising for solving both deterministic optimization and RBDO problems by comparing with the well-known active learning methods.

Optimal allocation with known covariates into two treatments under generalized linear model through Hybrid VNS algorithm

The problem of optimal allocation of experimental units with known covariates into several treatment groups under linear ANCOVA model has already been discussed by the same authors and the optimal allocation design has been derived through an efficient algorithm named as hybrid variable neighborhood search (VNS) algorithm. In this work, we have addressed the same issue with regard to D- and A-optimality under the generalized linear model (GLM) set-up, assuming the response variable to be count or binary. The issue of mean covariate balance is also addressed through a constrained optimal approach in which a compromise between balance and optimality is maintained. The performance of the optimal and constrained optimal allocation design obtained through the hybrid VNS algorithm, under various GLM frameworks, has been investigated through simulation studies and real-life example.

Novel approaches to predict the Marshall parameters of basalt fiber asphalt concrete

Experimental approach for evaluating the Marshall Stability (MS) and Marshall Flow (MF) of basalt fiber asphalt concrete (BFAC) is time-consuming and expensive. This study employed the Extreme Gradient Boost (XGB) algorithm in conjunction with two novel optimization algorithms, namely Sailfish Optimizer (SFO) and Aquila Optimizer (AO), to construct novel and enhanced prediction models for MS and MF of BFAC. Two databases were compiled from 18 experimental investigations with 128 and 89 experimental samples, respectively for MS and MF. Ten input parameters covering the mixture components were considered for MS and MF modeling. In addition, cross-validation was applied to evaluate the generalizability of the trained XGB model. The obtained findings demonstrated that the XGB model has an excellent and consistent predictive capacity, thereby demonstrating the model's stability in predicting MS and MF. In addition, the SFO optimization algorithm was applied for a constrained design optimization problem regarding the composition mixture for BFAC. The results were discussed considering existing design standards.

Applying Numerical Optimization Technique in the Development of Valueadded Powdered Custard

Custard powder is a relatively shelf-stable, fine textured, dry-formulated, carbohydrate-rich breakfast food product primarily made from corn starch with the addition of salt, flavoring, and coloring agents and with or without the inclusion of egg yolk solids, vitamins, and minerals. The aim of this study was to formulate, characterize, and optimize value-added custard from millet, soybean, and tigernut. A three-component constrained optimal (custom) mixture experimental design, with 69 randomized experimental runs, was employed. The formulation design constraints were: millet (10% - 70%), soybean (10% - 70%), and tigernut (10% - 70%). Other constant components of the formulation were sweet potato extract (3%), date (2 %), clove (1%), cinnamon (1%), turmeric (1%), and ginger (2%). The formulated samples were analyzed and evaluated for quality and sensory characteristics using standard procedures. The result of the optimization gave optimized custard with an overall desirability index of 0.535, based on the set optimization goals and individual quality desirability indices. The optimal formulated value-added custard was obtained from 10.0 % millet flour, 49.3 % soybean meal, and 30.7 % tigernut. The quality properties of this optimal custard are 3.78 % ash content, 28.5 % crude protein, 10.1 % moisture content, 20.1 % fat content, 4.43 % crude fibre, 33.9 % carbohydrate, and 5.79 overall acceptability. The result of the study showed that the formulated value-added custard was found to be of higher quality than the traditional custard which is produced from monocereals. Improving the nutritional quality of food and tackling nutrient deficiencies, particularly protein energy malnutrition in populations, is possible through the application of numerical optimization technique in development new, dietary-based food products.

Optimization design of crude oil distillation unit using bi-level surrogate model

Crude Oil Distillation Unit (CDU) is one of the most important separation installations in the petroleum refinery industries. In this work, a Bi-level Surrogate column model Aided Constrained Optimization Design (Bi-SACOD) is proposed for time-consuming objectives and constraints in the evolutionary optimization design of CDUs. The main components of Bi-SACOD include bi-level surrogate model construction (Bi-SMC), bi-level model management (Bi-MM), and particle swarm optimization (PSO) mixed-integer constrained evolutionary (PSO-MICE) search. Bi-SMC implements surrogate column model construction and feasible domain identification. Bi-MM combines surrogate column models with rigorous CDU simulations to perform model management, and PSO-MICE implements optimum search works. The optimization results of the CDUs indicate that Bi-SACOD outperforms the single-level surrogate column model approaches, and are more consistent with the rigorous CDU model optimization approach, whereas the evaluation numbers of the time-consuming rigorous models are significantly reduced.

Optimization and Decision-Making Framework for Small Unmanned Aircraft Systems Fleet Design

Many unmanned aircraft applications require or benefit from deploying a fleet to perform a mission. Technology innovations such as rapid prototyping and microelectronics enable the use of unmanned aircraft systems (UAS) at lower costs, so the ability to design a bespoke UAS for a specific mission is an additional advantage. The problem of designing the new UAS and allocating the fleet of these aircraft is a challenging optimization problem. Using constrained multi-objective design optimization with an interactive multicriteria decision-making method, which involves the mission customer, the approach in this paper generates UAS designs and fleet allocations and determines preferential solutions for the customer. The paper presents a case study involving a UAS weather profiling mission for the aircraft sizing and fleet allocation and uses inputs from meteorological subject-matter experts acting as customers to demonstrate the functionality of the approach.

Detecting Non-Overlapping Signals with Dynamic Programming

This paper studies the classical problem of detecting the locations of signal occurrences in a one-dimensional noisy measurement. Assuming the signal occurrences do not overlap, we formulate the detection task as a constrained likelihood optimization problem and design a computationally efficient dynamic program that attains its optimal solution. Our proposed framework is scalable, simple to implement, and robust to model uncertainties. We show by extensive numerical experiments that our algorithm accurately estimates the locations in dense and noisy environments, and outperforms alternative methods.

A Sequential Sampling Approach for Multi-Fidelity Surrogate Modeling-Based Robust Design Optimization

Abstract Multi-fidelity surrogate modeling has been extensively used in engineering design to achieve a balance between computational efficiency and prediction accuracy. Sequential sampling strategies have been investigated to improve the computational efficiency of surrogate-assisted design optimization. The existing sequential sampling approaches, however, are dedicated to either deterministic multi-fidelity design optimization or robust design under uncertainty using single-fidelity models. This paper proposes a sequential sampling method for robust design optimization based on multi-fidelity modeling. The proposed method considers both design variable uncertainty and interpolation uncertainty during the sequential sampling. An extended upper confidence boundary (EUCB) function is developed to determine both the sampling locations and the fidelity levels of the sequential samples. In the EUCB function, the cost ratio between high- and low-fidelity models and the sampling density are considered. Moreover, the EUCB function is extended to handle constrained robust design optimization problems by combining the probability of feasibility. The performance of the proposed approach is verified using two analytical examples and an engineering case. Results show that the proposed sequential approach is more efficient than the one-shot sampling method for robust design optimization problems.

A comparator-based constraint handling technique for evolutionary algorithms

Constraint handling is a key task for the successful optimization of design parameters in industrial design problems. This paper proposes a comparator-based constraint handling technique, called the More Less-Violations Method (MLVM), for solving real constrained optimization problems using evolutionary algorithms. The structure of the MLVM is simple and it can easily be integrated into conventional evolutionary algorithms. In the proposed method, constraint weights represent the level of importance of each constraint, enabling evolutionary compliance prioritization. Moreover, an acceptable region formed by the constraint tolerances allows trade-offs between objectives and constraints while preserving diverse solutions and improving optimization performance. These elements enable the appropriate design of industrial optimization problems. An application of this method to problems without constraint tolerances is also proposed. The JAXA/Mazda benchmark problem, developed on a real-world constrained design optimization dataset, is used to assess the performance of the MLVM. The results indicate that the MLVM realizes encouraging optimization performance.

A Fast Optimization Method for High-Speed Link Inverse Design With SVR-AS Algorithm

A fast constrained design optimization technique is introduced for the inverse design of high-speed links. The proposed method makes use of the support-vector-regression-based active subspace (SVR-AS) method to generate a lower dimensional space of active variables as a linear weighted combination of the higher dimensional design space to help simplify the optimization problem. This newly developed technique successfully transforms the complex nonlinear constraint optimization problem into a linear constraint minimization problem and provides a directly solvable function for the optimal results associated with each active variable. Furthermore, the proposed optimization algorithm can be utilized for the optimization problem with equality and inequality constraints, which contain one- and multidimensional active variables generated from the SVR-AS method. Studies of two high-speed links with channel design parameters for nonreturn-to-zero pulse and IBIS-AMI equalization settings for four-level pulse amplitude modulation, respectively, are utilized to verify the efficiency of the method. The sensitivity analysis ability of the SVR-AS method is also presented for both the one- and multidimensional active variable cases.

Asymptotic Bayesian Optimization: A Markov sampling-based framework for design optimization

This paper presents a Markov sampling-based framework, called Asymptotic Bayesian Optimization, for solving a class of constrained design optimization problems. The optimization problem is converted into a unified two-phase sample generation problem which is solved by an effective Markov chain Monte Carlo simulation scheme. First, an exploration phase generates designs distributed over the feasible design space. Based on this information, an exploitation phase obtains a set of designs lying in the vicinity of the optimal solution set. The proposed formulation can handle continuous, discrete, or mixed discrete-continuous design variables. Appropriate adaptive proposal distributions for the continuous and discrete design variables are suggested. The set of optimal solutions provides valuable sensitivity information of the different quantities involved in the problem with respect to the design variables. Representative examples including an analytical problem involving nonlinear benchmark functions, a classical engineering design problem, and a performance-based design optimization problem of a structural system under stochastic excitation are presented to show the effectiveness and potentiality of the proposed optimization scheme. Validation calculations show that the scheme is a flexible, efficient and competitive choice for solving a wide range of classical and complex engineering design problems.

Constrained optimal filter design for multi-channel active noise control via convex optimization.

In many practical multi-channel active noise control (ANC) applications, various constraints need to be satisfied, such as stability, enhancement, etc. One way to enforce these constraints is to add a regularization term to the Wiener filter formulation, which, by tuning only a single parameter, can over satisfy many constraints and degrade the ANC performance. Another approach for non-adaptive ANC filter design that can produce better ANC performance is to directly solve the constrained optimization problem formulated based on the H2/H∞ control framework. However, such a formulation does not result in a convex optimization problem and its practicality can be limited by the significant computation time required in the solving process. In the presented work, the H2/H∞ formulation is convexified and a global minimum is guaranteed. It is then further reformulated into a cone programming problem which can be solved using specialized algorithms. Results show that the proposed method can produce better noise control performance than the regularization method. Compared with the traditional H2/H∞ formulation, the proposed method is more reliable and the computation time can be reduced by several orders, which, practically, provides a potential to extend its application to adaptive control.

Comparison of metaheuristic optimization algorithms for solving constrained mechanical design optimization problems

Determining the solution for real mechanical design problems is a challenging task when using the newly developed and efficient swarm intelligence algorithms. There are so many difficulties to be addressed, including but not limited to mixed decision variables, diverse constraints, inherent errors, conflicting objectives, and numerous locally optimal solutions. This work analyzes the behavior of nine metaheuristic algorithms, namely, salp swarm algorithm (SSA), multi-verse optimizer (MVO), moth-flame optimizer (MFO), atom search optimization (ASO), ecogeography-based optimization (EBO), queuing search algorithm (QSA), equilibrium optimizer (EO), evolutionary strategy (ES) and hybrid self-adaptive orthogonal genetic algorithm (HSOGA). The efficiency of these algorithms is evaluated on eight mechanical design problems using the solution quality and convergence analysis, which verifies the wide applicability of these algorithms to real-world application problems.

Constrained Mixed-Variable Design Optimization Based on Particle Swarm Optimizer with a Diversity Classifier for Cyclically Neighboring Subpopulations

In this research, an easy-to-use particle swarm optimizer (PSO) for solving constrained engineering design problems involving mixed-integer-discrete-continuous (MIDC) variables that adopt two kinds of diversity-enhancing mechanisms to achieve superior reliability and validity was developed. As an initial diversity-boosting tool, the local neighborhood topology of each particle is set up such that information exchange is restricted to a limited number of consecutively numbered particles. This topological mechanism forces each particle to move in the search space while interacting only with its neighboring subpopulation. The second diversity-enhancing task is to ensure that the exploration behavior of each particle in the search space is governed such that it follows the diversity classifier decision applied to its subpopulation. This diversity classification iteratively adjusts the three-phase velocity-related mechanism of each particle such that it approaches or retreats from its previous best position/the current best position among the subpopulation. In summary, this PSO tool not only introduces the social interaction of the particle within its cyclically neighboring subpopulation but also exploits the three-phase velocity behavior law governed by the distributed diversity measures categorized for each neighboring subpopulation. This scheme has superior reliability, as well as high practicality for engineering optimization problems involving MIDC variables, which are handled by the widely adopted straightforward rounding-off technique used in most swarm-inspired metaheuristic search technologies.

On Phase Shifting and Diversified Coil-Pitch for Enhanced Multiobjective Winding Design Optimization

In electric rotating machines, the stator winding design plays a crucial role on their overall performance. Novel approaches for winding design optimization, including multilayer configurations, stator shifting, and phase shifting, have been presented in recent studies. Most of them focus on a single strategy, which is generally applied to one winding topology only. In this paper, a unified and generalized methodology is proposed to solve a two-objective constrained winding design optimization problem, which can be applied to polyphase winding configurations with any number of slots per pole. The novelty concerns the combination of the phase shifting concept with an enhanced end-winding connection strategy, enabled by multiple coil pitches. The framework developed allows for the customization of the objective functions and constraints to the characteristics of the study. Two application examples are provided for validation purposes of the methodology, where time-step finite-element analysis simulations of a three-phase squirrel-cage induction motor and a six-phase permanent-magnet synchronous motor were carried out. The proposed methodology is capable of generating novel winding designs that can potentially improve the machine efficiency and reduce the amount of copper in the stator windings.

A general two-phase Markov chain Monte Carlo approach for constrained design optimization: Application to stochastic structural optimization

This contribution presents a general approach for solving structural design problems formulated as a class of nonlinear constrained optimization problems. A Two-Phase approach based on Bayesian model updating is considered for obtaining the optimal designs. Phase I generates samples (designs) uniformly distributed over the feasible design space, while Phase II obtains a set of designs lying in the vicinity of the optimal solution set. The equivalent model updating problem is solved by the transitional Markov chain Monte Carlo method. The proposed constraint-handling approach is direct and does not require special constraint-handling techniques. The population-based stochastic optimization algorithm generates a set of nearly optimal solutions uniformly distributed over the vicinity of the optimal solution set. The set of optimal solutions provides valuable sensitivity information. In addition, the proposed scheme is a useful tool for exploration of complex feasible design spaces. The general approach is applied to an important class of problems. Specifically, reliability-based design optimization of structural dynamical systems under stochastic excitation. Numerical examples are presented to evaluate the effectiveness of the proposed design scheme.

Constrained optimal design of seismic base absorbers based on an extended KDamper concept

In this paper, an extended KDamper (EKD) concept is proposed, for implementation as a seismic base absorber. The complexity of the EKD renders the conventional minmax (H∞) approaches ineffective. For this reason, a dedicated constrained optimization problem is proposed for the selection of the optimal system parameters. The EKD is designed according to seismic design codes and the constraints and limitations of the EKD components are evaluated based on engineering criteria. In order to better observe the efficiency of the proposed configuration, an acceleration filter is placed, as an additional constraint. Therefore, each set of optimized parameters of the EKD refers to the maximum structure acceleration, expressed as a percentage of PGA. A database of artificial accelerograms, compatible with the EC8 response spectra is generated. Sensitivity analysis is performed, and the effect of detuning is observed. Subsequently, the EKD is implemented as a seismic base absorber in a multi-story building. The performance of the proposed control strategy is compared not only to the original structure but also to the cases of conventional and highly damped base isolation systems, as well as to the KDamper. The EKD presents an improved superstructure dynamic behavior, comparable with a base isolated system. At the same time, the base relative displacement is drastically reduced, in the order of a few centimeters, rendering the implementation of the EKD feasible using conventional structural elements, without the need for special types of bearings. In addition, the base shear is reduced, as compared to the original structure, with the implementation of the proposed configuration, and thus, EKD can be considered a possible retrofitting option for seismic protection.

Evolutionary Algorithm Embedded With Bump-Hunting for Constrained Design Optimization

Abstract Real-world design optimization problems commonly entail constraints that must be satisfied for the design to be viable. Mathematically, the constraints divide the search space into feasible (where all constraints are satisfied) and infeasible (where at least one constraint is violated) regions. The presence of multiple constraints, constricted and/or disconnected feasible regions, non-linearity and multi-modality of the underlying functions could significantly slow down the convergence of evolutionary algorithms (EA). Since each design evaluation incurs some time/computational cost, it is of significant interest to improve the rate of convergence to obtain competitive solutions with relatively fewer design evaluations. In this study, we propose to accomplish this using two mechanisms: (a) more intensified search by identifying promising regions through “bump-hunting,” and (b) use of infeasibility-driven ranking to exploit the fact that optimal solutions are likely to be located on constraint boundaries. Numerical experiments are conducted on a range of mathematical benchmarks and empirically formulated engineering problems, as well as a simulation-based wind turbine design optimization problem. The proposed approach shows up to 53.48% improvement in median objective values and up to 69.23% reduction in cost of identifying a feasible solution compared with a baseline EA.