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The objective of this work is to build a useful-response-surface-based reliability design approach for solving stress-constrained optimization problems taking into consideration load uncertainty. To this end, a reliability optimization problem of minimizing the volume fraction while satisfying a global probabilistic stress constraint is formulated, in which a Kreisselmeier–Steinhauser-function-based aggregate approach with a correction parameter is introduced to ensure accurate approximation of the maximum stress. To avoid the expensive computational cost of calculating the sensitivity of the global maximum stress with respect to random loads in reliability evaluation, a response-surface-based global stress measure is established. Finally, several typical design instances are solved to prove the performance of the presented methodology. The importance of considering load uncertainty in stress-related topology optimization is also explained by comparing the results acquired by the presented reliability-based topology optimization methodology with deterministic designs. [ABSTRACT FROM AUTHOR]

Computationally expensive constrained optimization problems are challenging owing to their high complexity and computational cost. To solve these problems efficiently, a kriging-assisted bi-objective constrained global optimization (BOCGO) algorithm is developed, where three phases with three bi-objective subproblems are performed. In phase I, the constraints are searched locally and globally to find the feasible region. Once a feasible region has been located, the two terms of the constrained expected improvement function are utilized to exploit and explore the feasible region in phase II. As the kriging models are accurate enough in the concerned region, a local search is processed to improve the optimal solution in phase III. The capability of the BOCGO algorithm is demonstrated by comparison with two classical and two state-of-the-art algorithms on 20 problems and an engineering simulation problem. The results show that the BOCGO algorithm performs better in more than three-fifths of problems, illustrating its effectiveness and robustness. [ABSTRACT FROM AUTHOR]

The present work compares the performance of scientific law-inspired optimization algorithms for real-life constrained optimization applications. Ten such scientific law-inspired algorithms developed during the past decade are considered in this article. A constrained engineering application of the Stirling heat engine system is investigated with these algorithms. Four operating variables and two output constraints of the Stirling heat engine are considered for optimization. Comparative results are presented with statistical data to judge the performance of the algorithms and subsequently to identify the statistical significance and rank of each algorithm. The effects of various constraint handling methods on the performance of the algorithms are evaluated and presented. The behaviour of the constraint handling methods is analysed and presented. The effect of output constraints on the performance of the algorithms is also evaluated and presented. Finally, the convergence behaviour of the competitive algorithms is obtained and demonstrated. [ABSTRACT FROM AUTHOR]

The optimal placement of sensors is studied to construct a surveillance sensor network for a complicated stochastic system with random measurement errors. The problem is formulated as a joint problem of constrained black-box optimization for the fast detection of an anomaly event and spatio-temporal change-point detection for a low false alarm rate. An algorithm is proposed called Confidence-Set based Constrained Bayesian Optimization (CSCBO) that models performance measures as Gaussian Processes (GPs) and provides a flexible and easy-to-implement framework for handling noisy black-box constraints. As the decision variables of this problem are high-dimensional binary variables, the Wasserstein similarity metric is introduced as a distance measure among different solutions to capture the similarity among solutions properly. Finally, a newly proposed detection statistic for spatio-temporal surveillance is combined with CSCBO to identify the optimal sensor placement while controlling the false alarm rate. The combined procedure is applied to the Altamaha River. [ABSTRACT FROM AUTHOR]

This article presents design optimization based on swarm intelligence algorithms of a tubular linear voice coil motor (TLVCM). A magnetic equivalent circuit model is used, allowing a faster and more accurate evaluation of the initial design of the TLVCM. The design requirements are determined, and an initial design is formed based on the design requirements. The TLVCM design is considered a constrained optimization problem with complex linear and nonlinear constraints. The optimization process based on swarm intelligence algorithms is performed to find the optimal solution and improve the performance of the TLVCM. Finally, finite element analysis is used again to verify the optimized results, and different design outputs are compared. According to numerical experimental results, the average thrust is increased by 8.3% and the thrust ripple is reduced by 35.6%. Thus, a highly effective motor design meeting efficiency and performance requirements is achieved. [ABSTRACT FROM AUTHOR]

Shape optimization is an effective tool for designing free-form structures for a variety of design objectives. Aiming at long-term structural performance, a computational framework is presented for performing shape optimization of free-form shells while considering material creep. The material creep model is incorporated into a gradient-based optimization algorithm using a viscoelastic finite element model. Non-uniform rational B-spline (NURBS) is employed to parameterize the free-form geometric shapes of shells. Optimization is conducted for minimizing the shell volume subject to constraints of specified maximum displacement. The results demonstrate that it is necessary to consider creep when designing shells made of viscoelastic materials for long-term performance. [ABSTRACT FROM AUTHOR]

Optimization problems are considered that involve the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete, optimization problems arise in applications from biology and materials science among others, and are known to be NP-hard for a special case of interest. The underlying structure of such optimization problems is analysed for two particular applications and, depending on the matrix family, compact-size mixed-integer linear or quadratically constrained quadratic programming reformulations are obtained that can be solved via commercial solvers. Finally, the results are presented of computational experiments that demonstrate the success of the author's approach compared to heuristic and enumeration methods predominant in the literature. [ABSTRACT FROM AUTHOR]

Considering stress constraints in multi-material topology optimization is of great importance from both theoretical and application perspectives. In this article, the stress-constrained multi-material topology optimization problem is considered under the framework of an alternating active-phase algorithm. A nodal variable strategy is employed. In addition, a material distribution-based cluster method is employed instead of a global stress constraint to improve control of the local stress level. The von Mises stresses of the elements are aggregated into several clusters using a p-norm function to represent the stress constraints. Numerical examples are presented, and the influences of key parameters are discussed. The effectiveness of the proposed approach is demonstrated through numerical results. [ABSTRACT FROM AUTHOR]

The Constrained Expected Improvement (CEI) criterion used in the so-called Constrained Efficient Global Optimization (C-EGO) algorithm is one of the most famous infill criteria for expensive constrained optimization problems. However, the standard CEI criterion selects only one point to evaluate in each cycle, which is time consuming when parallel computing architecture is available. This work proposes a new Parallel Constrained EGO (PC-EGO) algorithm to extend the C-EGO algorithm to parallel computing. The proposed PC-EGO algorithm is tested on sixteen analytical problems as well as one real-world engineering problem. The experiment results show that the proposed PC-EGO algorithm converges significantly faster and finds better solutions on the test problems compared to the standard C-EGO algorithm. Moreover, when compared to another state-of-the-art parallel constrained EGO algorithm, the proposed PC-EGO algorithm shows more efficient and robust performance. [ABSTRACT FROM AUTHOR]

Combined heat and power (CHP) generation is a competent configuration for simultaneous production of thermal and electric energy. The interdependency of heat and power outputs of CHP units presents complications and non-convexities in modelling and optimization. The nonlinear constrained economic dispatch optimization problem becomes more complex when one considers the pollution produced by generating units, transmission losses and valve-point effects of thermal units. This article uses the stochastic fractal search algorithm to solve the bi-objective combined heat and power economic dispatch (CHPED) problem. The CHPED problem has bounded feasible operating regions and many local minima. The compromise programming method is used to transform the two objective functions into an aggregated objective function. The results are compared with previous results obtained by many different methods reported in the literature. The results reveal that the proposed algorithm achieves a better near-global solution and compares favourably with other commonly used global optimization techniques. [ABSTRACT FROM AUTHOR]

This article considers a resource-constrained project scheduling problem with a single shared resource. In this model, multiple processors are required to complete jobs with a certain amount of shared resource. The supply of the resource is limited and must be shared between processors. A column-generation-based algorithm with some enhancement techniques, including stabilization, a mechanism to update the solution pool, and an approximate solution technique, is proposed. Finally, extensive computational experiments are conducted to evaluate the performance of the proposed method by comparing it with Lagrangian relaxation, CPLEX ® and a self-adapting genetic algorithm. The results prove the proposed method has an advantage in terms of the objective and CPU time. Numerical experiments are also conducted to verify the effectiveness of the proposed enhancements. [ABSTRACT FROM AUTHOR]

Finding optimum conditions for process factors in an engineering optimization problem with response surface functions requires structured data collection using experimental design. When the experimental design space is constrained owing to external factors, its design space may form an asymmetrical and irregular shape and thus standard experimental design methods become ineffective. Computer-generated optimal designs, such as D-optimal designs, provide alternatives. While several iterative exchange algorithms for D-optimal designs are available for a linearly constrained irregular design space, it has not been clearly understood how D-optimal design points need to be generated when the design space is nonlinearly constrained and how response surface models are optimized. This article proposes an algorithm for generating the D-optimal design points that satisfy both feasibility and optimality conditions by using piecewise linear functions on the design space. The D-optimality-based response surface design models are proposed and optimization procedures are then analysed. [ABSTRACT FROM AUTHOR]

Temperature-constrained topology optimization for thermo-mechanical coupled problems under a design-dependent temperature field considering the thermal expansion effect remains an open problem. A temperature-constrained topology optimization method is proposed for thermo-mechanical coupled problems. In this article, the temperature values at the heat sources are constrained. The numerical results reveal that the temperature constraints play an important role in topology optimization of thermo-mechanical coupled problems. The optimized structure obtained by the presented method not only has certain strength but also decreases the temperature significantly compared with structures obtained by other methods without considering temperature constraints. The proposed method is applied to the design of the cooling system of a battery package. Numerical examples verify the efficiency of the presented method. [ABSTRACT FROM AUTHOR]

This article concerns a proximal-point algorithm with time penalization. The case where the cost of moving from one position to a better one is penalized by the time taken by the agent for the decision-making is studied and the restriction employing the penalty method is incorporated. It is shown that the method converges monotonically with respect to the minimal weighted norm to a unique minimal point under mild assumptions. The gradient method is employed for solving the objective function, and its convergence is proven. The rate of convergence of the method is also estimated by computing the optimal parameters. The effectiveness of the method is illustrated by a numerical optimization example employing continuous-time Markov chains. [ABSTRACT FROM AUTHOR]

This article deals with the optimization of energy resource management of industrial districts, with the aim of minimizing customer energy expenses. A model of the district is employed, whose optimization gives rise to a nonlinear constrained optimization problem. Here the focus is on its numerical solution. Two different methods are considered: a sequential linear programming method and a particle swarm optimization method. Efficient implementations of both approaches are devised and the results of the tests performed on several energetic districts are reported, including a real case study. [ABSTRACT FROM AUTHOR]

Sequential optimization and reliability analysis (SORA) is an efficient approach to reliability-based design (RBD). It decouples the double-loop structure of RBD into a serial cycle of deterministic optimization and reliability analysis. The first order approximation is used in SORA for reliability analysis owing to its good balance between accuracy and efficiency. However, it may result in a large error when a constraint function is highly nonlinear. This study proposes a new numerical method so that second order approximations for the reliability analysis can be used for higher accuracy. To minimize the increased computational cost due to second order approximations, this study also develops an efficient algorithm for searching for an equivalent reliability index with the help of the saddlepoint approximation. The efficiency and accuracy of the proposed method are verified through numerical examples. [ABSTRACT FROM AUTHOR]

Material flow in a chemical processing plant often follows complicated control laws and involves plant capacity constraints. Importantly, the process involves discrete scenarios which when modelled in a programming format involves if-then-else statements. Therefore, a formulation of an optimization problem of such processes becomes complicated with nonlinear and non-differentiable objective and constraint functions. In handling such problems using classical point-based approaches, users often have to resort to modifications and indirect ways of representing the problem to suit the restrictions associated with classical methods. In a particular gold processing plant optimization problem, these facts are demonstrated by showing results from MATLAB R® 's well-known fmincon routine. Thereafter, a customized evolutionary optimization procedure which is capable of handling all complexities offered by the problem is developed. Although the evolutionary approach produced results with comparatively less variance over multiple runs, the performance has been enhanced by introducing derived heuristics associated with the problem. In this article, the development and usage of derived heuristics in a practical problem are presented and their importance in a quick convergence of the overall algorithm is demonstrated. [ABSTRACT FROM AUTHOR]

In this article, the genetic algorithm (GA) and fully informed particle swarm (FIPS) are hybridized for solving the multi-mode resource-constrained project scheduling problem (MRCPSP) with minimization of project makespan as the objective subject to resource and precedence constraints. In the proposed hybrid genetic algorithm–fully informed particle swarm algorithm (HGFA), FIPS is a popular variant of the particle swarm optimization algorithm. A random key and the related mode list representation schemes are used as encoding schemes, and the multi-mode serial schedule generation scheme (MSSGS) is considered as the decoding procedure. Furthermore, the existing mode improvement procedure in the literature is modified. The results show that the proposed mode improvement procedure remarkably improves the project makespan. Comparing the results of the proposed HGFA with other approaches using the well-known PSPLIB benchmark sets validates the effectiveness of the proposed algorithm to solve the MRCPSP. [ABSTRACT FROM AUTHOR]

In this article, models and methods for solving a real-life frequency assignment problem based on scheduling theory are investigated. A realistic frequency assignment problem involving cumulative interference constraints in which the aim is to maximize the number of assigned users is considered. If interferences are assumed to be binary, a multiple carrier frequency assignment problem can be treated as a disjunctive scheduling problem since a user requesting a number of contiguous frequencies can be considered as a non-preemptive task with a processing time, and two interfering users can be modelled through a disjunctive constraint on the corresponding tasks. A binary interference version of the problem is constructed and a disjunctive scheduling model is derived. Based on the binary representation, two models are proposed. The first one relies on an interference matrix and the second one considers maximal cliques. A third, cumulative, model that yields a new class of scheduling problems is also proposed. Computational experiments show that the case-study frequency assignment problem can be solved efficiently with disjunctive scheduling techniques. [ABSTRACT FROM AUTHOR]

This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented. [ABSTRACT FROM AUTHOR]

This study presents a model for valve setting in water distribution networks (WDNs), with the aim of reducing the level of leakage. The approach is based on the harmony search (HS) optimization algorithm. The HS mimics a jazz improvisation process able to find the best solutions, in this case corresponding to valve settings in a WDN. The model also interfaces with the improved version of a popular hydraulic simulator, EPANET 2.0, to check the hydraulic constraints and to evaluate the performances of the solutions. Penalties are introduced in the objective function in case of violation of the hydraulic constraints. The model is applied to two case studies, and the obtained results in terms of pressure reductions are comparable with those of competitive metaheuristic algorithms (e.g.genetic algorithms). The results demonstrate the suitability of the HS algorithm for water network management and optimization. [ABSTRACT FROM AUTHOR]

A collection of intersecting sets of operations is considered. These sets of operations are performed successively. The operations of each set are activated simultaneously. Operation durations can be modified. The cost of each operation decreases with the increase in operation duration. In contrast, the additional expenses for each set of operations are proportional to its time. The problem of selecting the durations of all operations that minimize the total cost under constraint on completion time for the whole collection of operation sets is studied. The mathematical model and method to solve this problem are presented. The proposed method is based on a combination of Lagrangian relaxation and dynamic programming. The results of numerical experiments that illustrate the performance of the proposed method are presented. This approach was used for optimization multi-spindle machines and machining lines, but the problem is common in engineering optimization and thus the techniques developed could be useful for other applications. [ABSTRACT FROM AUTHOR]

The design of water distribution systems is a large class of combinatorial, nonlinear optimization problems with complex constraints such as conservation of mass and energy equations. Since feasible solutions are often extremely complex, traditional optimization techniques are insufficient. Recently, metaheuristic algorithms have been applied to this class of problems because they are highly efficient. In this article, a recently developed optimizer called the mine blast algorithm (MBA) is considered. The MBA is improved and coupled with the hydraulic simulator EPANET to find the optimal cost design for water distribution systems. The performance of the improved mine blast algorithm (IMBA) is demonstrated using the well-known Hanoi, New York tunnels and Balerma benchmark networks. Optimization results obtained using IMBA are compared to those using MBA and other optimizers in terms of their minimum construction costs and convergence rates. For the complex Balerma network, IMBA offers the cheapest network design compared to other optimization algorithms. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms are robust optimization methods that have been used in many engineering applications. However, real-world fitness evaluations can be computationally expensive, so it may be necessary to estimate the fitness with an approximate model. This article reviews design and analysis of computer experiments (DACE) as an approximation method that combines a global polynomial with a local Gaussian model to estimate continuous fitness functions. The article incorporates DACE in various evolutionary algorithms, to test unconstrained and constrained benchmarks, both with and without fitness function evaluation noise. The article also introduces a new evolution control strategy called update-based control that estimates the fitness of certain individuals of each generation based on the exact fitness values of other individuals during that same generation. The results show that update-based evolution control outperforms other strategies on noise-free, noisy, constrained and unconstrained benchmarks. The results also show that update-based evolution control can compensate for fitness evaluation noise. [ABSTRACT FROM AUTHOR]

Chance constrained optimization problems in engineering applications possess highly nonlinear process models and non-convex structures. As a result, solving a nonlinear non-convex chance constrained optimization (CCOPT) problem remains as a challenging task. The major difficulty lies in the evaluation of probability values and gradients of inequality constraints which are nonlinear functions of stochastic variables. This article proposes a novel analytic approximation to improve the tractability of smooth non-convex chance constraints. The approximation uses a smooth parametric function to define a sequence of smooth nonlinear programs (NLPs). The sequence of optimal solutions of these NLPs remains always feasible and converges to the solution set of the CCOPT problem. Furthermore, Karush–Kuhn–Tucker (KKT) points of the approximating problems converge to a subset of KKT points of the CCOPT problem. Another feature of this approach is that it can handle uncertainties with both Gaussian and/or non-Gaussian distributions. [ABSTRACT FROM PUBLISHER]

Three-degrees-of-freedom (3-DOF) parallel manipulators have many advantages such as simple structure, fewer actuators, and lower maintenance cost. However, parasitic motions may degrade the positioning accuracy of the platforms. In order to design 3-DOF parallel manipulators which can fulfil specified workspace requirements and exhibit minimum parasitic motions, the design problem is formulated into a minimax problem with workspace constraints. Then, an interval-based method is exploited to determine the feasible solution set which is derived as a union of many scattered parameter intervals (boxes). Then, a new approach based on region mapping and a powerful optimizer (namely differential evolution) is proposed to solve the optimization problem over scattered search regions. Benchmark tests show the superiority of the proposed approach. Then, the approach and interval analysis are used to solve a real-world design problem involving a 3-DOF manipulator. Numerical results demonstrate the effectiveness and advantages of the proposed design method. [ABSTRACT FROM AUTHOR]

Metamodelling techniques are widely used to approximate system responses of expensive simulation models. In association with the use of metamodels, objective-oriented sequential sampling methods have been demonstrated to be effective in balancing the need for searching an optimal solution versus reducing the metamodelling uncertainty. However, existing infilling criteria are developed for deterministic problems and restricted to one sampling point in one iteration. To exploit the use of multiple samples and identify the true robust solution in fewer iterations, a multi-point objective-oriented sequential sampling strategy is proposed for constrained robust design problems. In this article, earlier development of objective-oriented sequential sampling strategy for unconstrained robust design is first extended to constrained problems. Next, a double-loop multi-point sequential sampling strategy is developed. The proposed methods are validated using two mathematical examples followed by a highly nonlinear automotive crashworthiness design example. The results show that the proposed method can mitigate the effect of both metamodelling uncertainty and design uncertainty, and identify the robust design solution more efficiently than the single-point sequential sampling approach. [ABSTRACT FROM AUTHOR]

Constraint handling is an important aspect of evolutionary constrained optimization. Currently, the mechanism used for constraint handling with evolutionary algorithms mainly assists the selection process, but not the actual search process. In this article, first a genetic algorithm is combined with a class of search methods, known as constraint consensus methods, that assist infeasible individuals to move towards the feasible region. This approach is also integrated with a memetic algorithm. The proposed algorithm is tested and analysed by solving two sets of standard benchmark problems, and the results are compared with other state-of-the-art algorithms. The comparisons show that the proposed algorithm outperforms other similar algorithms. The algorithm has also been applied to solve a practical economic load dispatch problem, where it also shows superior performance over other algorithms. [ABSTRACT FROM AUTHOR]

This article develops two new algorithms for constrained expensive black-box optimization that use radial basis function surrogates for the objective and constraint functions. These algorithms are called COBRA and Extended ConstrLMSRBF and, unlike previous surrogate-based approaches, they can be used for high-dimensional problems where all initial points are infeasible. They both follow a two-phase approach where the first phase finds a feasible point while the second phase improves this feasible point. COBRA and Extended ConstrLMSRBF are compared with alternative methods on 20 test problems and on the MOPTA08 benchmark automotive problem (D.R. Jones, Presented at MOPTA 2008), which has 124 decision variables and 68 black-box inequality constraints. The alternatives include a sequential penalty derivative-free algorithm, a direct search method with kriging surrogates, and two multistart methods. Numerical results show that COBRA algorithms are competitive with Extended ConstrLMSRBF and they generally outperform the alternatives on the MOPTA08 problem and most of the test problems. [ABSTRACT FROM AUTHOR]

Economic dispatch is the short-term determination of the optimal output from a number of electricity generation facilities to meet the system load while providing power. As such, it represents one of the main optimization problems in the operation of electrical power systems. This article presents techniques to substantially improve the efficiency of the canonical coordinates method (CCM) algorithm when applied to nonlinear combined heat and power economic dispatch (CHPED) problems. The improvement is to eliminate the need to solve a system of nonlinear differential equations, which appears in the line search process in the CCM algorithm. The modified algorithm was tested and the analytical solution was verified using nonlinear CHPED optimization problems, thereby demonstrating the effectiveness of the algorithm. The CCM methods proved numerically stable and, in the case of nonlinear programs, produced solutions with unprecedented accuracy within a reasonable time. [ABSTRACT FROM AUTHOR]

In fluid mechanics, topology optimization is used for designing flow passages, connecting predefined inlets and outlets, with optimal performance based on selected criteria. In this article, the continuous adjoint approach to topology optimization in incompressible ducted flows with heat transfer is presented. A variable porosity field, to be determined during the optimization, is the means to define the optimal topology. The objective functions take into account viscous losses and the amount of heat transfer. Turbulent flows are handled using the Spalart–Allmaras model and the proposed adjoint is exact,i.e.the adjoint to the turbulence model equation is formulated and solved, too. This is an important novelty in this article which extends the porosity-based method to account for heat transfer flow problems in turbulent flows. In problems such as the design of manifolds, constraints on the outlet flow direction, rates and mean outlet temperatures are imposed. [ABSTRACT FROM AUTHOR]

Constrained optimization is a computationally difficult task, particularly if the constraint functions are nonlinear and non-convex. As a generic classical approach, the penalty function approach is a popular methodology which degrades the objective function value by adding a penalty proportional to the constraint violation. However, the penalty function approach has been criticized for its sensitivity to the associated penalty parameters. Since its inception, evolutionary algorithms have been modified in various ways to solve constrained optimization problems. Of them, the recent use of a bi-objective evolutionary algorithm in which the minimization of the constraint violation is included as an additional objective has received significant attention. In this article, a combination of a bi-objective evolutionary approach with the classical penalty function methodology is proposed, in a manner complementary to each other. The evolutionary approach provides an appropriate estimate of the penalty parameter, while the solution of an unconstrained penalized function by a classical method induces a convergence property to the overall hybrid algorithm. The working of the procedure on a number of standard numerical test problems and an engineering design problem is demonstrated. In most cases, the proposed hybrid methodology is observed to take one or more orders of magnitude fewer function evaluations to find the constrained minimum solution accurately than some of the best reported existing methodologies. [ABSTRACT FROM AUTHOR]

This article presents the DYCORS (DYnamic COordinate search using Response Surface models) framework for surrogate-based optimization of HEB (High-dimensional, Expensive, and Black-box) functions that incorporates an idea from the DDS (Dynamically Dimensioned Search) algorithm. The iterate is selected from random trial solutions obtained by perturbing only a subset of the coordinates of the current best solution. Moreover, the probability of perturbing a coordinate decreases as the algorithm reaches the computational budget. Two DYCORS algorithms that use RBF (Radial Basis Function) surrogates are developed: DYCORS-LMSRBF is a modification of the LMSRBF algorithm while DYCORS-DDSRBF is an RBF-assisted DDS. Numerical results on a 14-D watershed calibration problem and on eleven 30-D and 200-D test problems show that DYCORS algorithms are generally better than EGO, DDS, LMSRBF, MADS with kriging, SQP, an RBF-assisted evolution strategy, and a genetic algorithm. Hence, DYCORS is a promising approach for watershed calibration and for HEB optimization. [ABSTRACT FROM AUTHOR]

This article proposes a new constrained optimization method using a multipoint type chaotic Lagrangian method that utilizes chaotic search trajectories generated by Lagrangian gradient dynamics with a coupling structure. In the proposed method, multiple search points autonomously implement global search using the chaotic search trajectory generated by the coupled Lagrangian gradient dynamics. These points are advected to elite points (which are chosen by considering their objective function values and their feasibility) by the coupling in order to explore promising regions intensively. In this way, the proposed method successfully provides diversification and intensification for constrained optimization problems. The effectiveness of the proposed method is confirmed through application to various types of benchmark problem, including the coil spring design problem, the benchmark problems used in the special session on constrained real parameter optimization in CEC2006, and a high-dimensional and multi-peaked constrained optimization problem. [ABSTRACT FROM PUBLISHER]

Many real-world optimization problems comprise objective functions that are based on the output of one or more simulation models. As these underlying processes can be time and computation intensive, the objective function is deemed expensive to evaluate. While methods to alleviate this cost in the optimization procedure have been explored previously, less attention has been given to the treatment of expensive constraints. This article presents a methodology for treating expensive simulation-based nonlinear constraints alongside an expensive simulation-based objective function using adaptive radial basis function techniques. Specifically, a multiquadric radial basis function approximation scheme is developed, together with a robust training method, to model not only the costly objective function, but also each expensive simulation-based constraint defined in the problem. The article presents the methodology developed for expensive nonlinear constrained optimization problems comprising both continuous and integer variables. Results from various test cases, both analytical and simulation-based, are presented. [ABSTRACT FROM AUTHOR]

An efficient optimization algorithm called teaching–learning-based optimization (TLBO) is proposed in this article to solve continuous unconstrained and constrained optimization problems. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The algorithm is tested on 25 different unconstrained benchmark functions and 35 constrained benchmark functions with different characteristics. For the constrained benchmark functions, TLBO is tested with different constraint handling techniques such as superiority of feasible solutions, self-adaptive penalty, ϵ-constraint, stochastic ranking and ensemble of constraints. The performance of the TLBO algorithm is compared with that of other optimization algorithms and the results show the better performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This article discusses the benefits of different infill sampling criteria used in surrogate-based constrained global optimization. A new method which selects multiple updates based on Pareto optimal solutions is introduced showing improvements over a number of existing methods. The construction of surrogates (also known as meta-models or response surface models) involves the selection of a limited number of designs which are analysed using the original expensive functions. A typical approach involves two stages. First the surrogate is built using an initial sampling plan; the second stage updates the model using an infill sampling criterion to select further designs that offer improvement. Selecting multiple update points at each iteration, allowing distribution of the expensive function evaluations on several processors offers large potential for accelerating the overall optimization process. This article provides a comparison between different infill sampling criteria suitable for selecting multiple update points in the presence of constraints. [ABSTRACT FROM PUBLISHER]

In this article, a robust method is presented for handling constraints with the Nelder and Mead simplex search method, which is a direct search algorithm for multidimensional unconstrained optimization. The proposed method is free from the limitations of previous attempts that demand the initial simplex to be feasible or a projection of infeasible points to the nonlinear constraint boundaries. The method is tested on several benchmark problems and the results are compared with various evolutionary algorithms available in the literature. The proposed method is found to be competitive with respect to the existing algorithms in terms of effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

The present study aims to develop a new genetic algorithm utilizing population recombination and elitist refinement. Population recombination determines how a population and its elitist sub-population evolve. A whole population consists of three major sub-populations: the first is the current generation's elitist sub-population, the second is obtained from the pure crossover of the elitist sub-population with another existing sub-population, and the third is the result of a crossover between the elitist and random sub-populations. Genetic operations such as reproduction and crossover are applied among sub-populations during the process of population recombination. The refinement of the elitist sub-population is then implemented in order to improve the converged solution that was obtained from the recombination. The refinement of elitist sub-populations facilitates the locations of a more enhanced design by altering the binary values in chromosomes. The proposed method is verified through a number of nonlinear and/or multi-modal functions and constrained optimization problems. [ABSTRACT FROM PUBLISHER]

A multi-objective freight train routing problem with fuzzy information is investigated in this article. To handle the fuzziness in the railway transportation system, the measure ℳλ (i.e. the convex combination of a possibility measure and a necessity measure) is first introduced. Then, a min–max chance-constrained programming model is constructed to obtain optimal train routing plans. In order to solve the model, a potential route algorithm, fuzzy simulation and tabu search algorithm are integrated as a hybrid algorithm. Finally, some numerical experiments are performed to show the applications of the model and the algorithm. [ABSTRACT FROM PUBLISHER]

This article presents a particle swarm optimization algorithm for solving general constrained optimization problems. The proposed approach introduces different methods to update the particle's information, as well as the use of a double population and a special shake mechanism designed to avoid premature convergence. It also incorporates a simple constraint-handling technique. Twenty-four constrained optimization problems commonly adopted in the evolutionary optimization literature, as well as some structural optimization problems are adopted to validate the proposed approach. The results obtained by the proposed approach are compared with respect to those generated by algorithms representative of the state of the art in the area. [ABSTRACT FROM AUTHOR]

Many engineering optimization problems involve models that might not exhibit the necessary smoothness to warrant efficient use of gradient algorithms. Many of these problems are also subject to constraints that might be simulation-based and as costly to compute as the objective function. Traditionally, such problems are solved using either penalty methods or lexicographic ordering that evaluates aggregate constraints prior to computing objective values. This study describes a cost-effective approach to performing such optimizations. After classifying all constraints depending on their computational cost, points not satisfying linear constraints are feasibilized, and a suitable penalty term constructed. A sequential lexicographic ordering is then applied in which inexpensive nonlinear constraints take precedence over expensive ones, which in turn take precedence over objective function values. The performance advantage of the proposed method over traditional ones is demonstrated with a set of analytical test problems, and with oilfield-production optimization examples that use 'black-box' simulators. [ABSTRACT FROM AUTHOR]

Incorporating local search heuristics is often very useful in designing an effective evolutionary algorithm. In this article a simplified quadratic approximation (SQA) is used as a local search operator for enhancing the performance of standard differential evolution (DE). The emphasis of this article is placed on demonstrating how this local search scheme can improve the performance of DE for the constrained optimization. The proposed approach was tested with a well-known constrained benchmark suite and four engineering design problems. Experimental results show that the proposed hybrid DE with SQA performs better than the standard DE. In addition, the results obtained are very competitive when comparing the proposed approach against other state-of-the-art techniques and some DE-based methods. The proposed approach is also compared with a modified version of the evolution strategy and a modified DE strategy for engineering design problems. [ABSTRACT FROM AUTHOR]

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables. [ABSTRACT FROM AUTHOR]

A hybrid particle swarm optimization algorithm is proposed for the cost-effective solution of single objective constrained engineering problems. The algorithm implements original strategies aimed to reduce computational effort of optimizations when dealing with real-world problems. Taking inspiration from evolutionary algorithms, a selection mechanism among particles is proposed allowing significant reductions in the solution cost. To enlarge the exploration space, a multi-start approach is frequently adopted, randomly reinitializing the swarm; the injection of optimized particles—obtained in previous runs—into the successive randomly generated starting swarms has been investigated as an expedient to accelerate convergence to the optimal solution. In order to avoid the algorithm to remain trapped into local minima, an innovative scheme has been proposed to update the inertia factor multiplying the previous velocity of the swarm. The proposed algorithm has been validated using standard engineering and purely mathematical problems commonly recognized as valid benchmark functions in specialized literature. [ABSTRACT FROM AUTHOR]

Constrained optimization problems (COPs) are very important in that they frequently appear in the real world. A COP, in which both the function and constraints may be nonlinear, consists of the optimization of a function subject to constraints. Constraint handling is one of the major concerns when solving COPs with particle swarm optimization (PSO) combined with the Nelder-Mead simplex search method (NM-PSO). This article proposes embedded constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, as a special operator in NM-PSO for dealing with constraints. Experiments using 13 benchmark problems are explained and the NM-PSO results are compared with the best known solutions reported in the literature. Comparison with three different meta-heuristics demonstrates that NM-PSO with the embedded constraint operator is extremely effective and efficient at locating optimal solutions. [ABSTRACT FROM AUTHOR]