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In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).

In this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.

The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.

The authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

The computational drawbacks of existing numerical methods have forced researchers to rely on heuristic algorithms. Heuristic methods are powerful in obtaining the solution of optimization problems. Although they are approximate methods (i.e. their solution are good, but not provably optimal), they do not require the derivatives of the objective function and constraints. Also, they use probabilistic transition rules instead of deterministic rules. The purpose of this paper is to present an improved ant colony optimization (IACO) for constrained engineering design problems.

IACO has the capacity to handle continuous and discrete problems by using sub‐optimization mechanism (SOM). SOM is based on the principles of finite element method working as a search‐space updating technique. Also, SOM can reduce the size of pheromone matrices, decision vectors and the number of evaluations. Though IACO decreases pheromone updating operations as well as optimization time, the probability of finding an optimum solution is not reduced.

Utilizing SOM in the ACO algorithm causes a decrease in the size of the pheromone vectors, size of the decision vector, size of the search space, the number of function evaluations, and finally the required optimization time. SOM performs as a search‐space‐updating rule, and it can exchange discrete‐continuous search domain to each other.

The suitability of using ACO for constrained engineering design problems is presented, and applied to optimal design of different engineering problems.

Reliability-based design optimizations (RBDOs) of engineering structures involve complex non-linear/non-differentiable performance functions, including both continuous and discrete variables. The gradient-based RBDO algorithms are less than satisfactory for these cases. The simulation-based approaches could also be computationally inefficient, especially when the double-loop strategy is used. This paper aims to present a pseudo-double loop flexible RBDO, which is efficient for solving problems, including both discrete/continuous variables.

The method is based on the hybrid improved binary bat algorithm (BBA) and weighed simulation method (WSM). According to this method, each BBA’s movement generates proper candidate solutions, and subsequently, WSM evaluates the reliability levels for design candidates to conduct swarm in a low-cost safe-region.

The accuracy of the proposed enhanced BBA and also the hybrid WSM-BBA are examined for ten benchmark deterministic optimizations and also four RBDO problems of truss structures, respectively. The solved examples reveal computational efficiency and superiority of the method to conventional RBDO approaches for solving complex problems including discrete variables.

Unlike other RBDO approaches, the proposed method is such organized that only one simulation run suffices during the optimization process. The flexibility future of the proposed RBDO framework enables a designer to present multi-level design solutions for different arrangements of the problem by using the results of the only one simulation for WSM, which is very helpful to decrease computational burden of the RBDO. In addition, a new suitable transfer function that enhanced convergence rate and search ability of the original BBA is introduced.

This paper demonstrates the use of genetic algorithms (GAs) for size optimization of trusses. The concept of rebirthing is shown to be considerably effective for problems involving continuous design variables. Some benchmark examples are studied involving 4‐bar, 10‐bar, 64‐bar, 200‐bar and 940‐bar two‐dimensional trusses. Both continuous and discrete variables are considered.

The purpose of this paper is to present an algorithm for global optimization of high‐dimensional real‐parameter cost functions.

This optimization algorithm, called differential ant‐stigmergy algorithm (DASA), based on a stigmergy observed in colonies of real ants. Stigmergy is a method of communication in decentralized systems in which the individual parts of the system communicate with one another by modifying their local environment.

The DASA outperformed the included differential evolution type algorithm in convergence on all test functions and also obtained better solutions on some test functions.

The DASA may find applications in challenging real‐life optimization problems such as maximizing the empirical area under the receiver operating characteristic curve of glycomics mass spectrometry data and minimizing the logistic leave‐one‐out calculation measure for the gene‐selection criterion.

The DASA is one of the first ant‐colony optimization‐based algorithms proposed for global optimization of the high‐dimensional real‐parameter problems.

This paper aims to focus on the trade-off between losses and converter cost.

The continual development of power electronic converters, for a wide range of applications such as renewable energy systems (interfacing photovoltaic panels via power converters), is characterized by the requirements for higher efficiency and lower production costs. To achieve such challenging objectives, a computer-aided design optimization based on genetic algorithms is developed in Matlab environment. The elitist non-dominated sorting genetic algorithm is used to perform search and optimization, whereas averaged models are used to estimate power losses in different semiconductors devices. The design problem requires minimizing the losses and cost of the boost converter under electrical constraints. The optimization variables are, as for them, the switching frequency, the boost inductor, the DC capacitor and the types of semiconductor devices (IGBT and MOSFET). It should be pointed out that boost topology is considered in this paper but the proposed methodology is easily applicable to other topologies.

The results show that such design methodology for DC-DC converters presents several advantages. In particular, it proposes to the designer a set of solutions – as an alternative of a single one – so that the authors can choose a posteriori the adequate solution for the application under consideration. This then allows the possibility of finding the best design among all the available choices. Furthermore, the design values for the selected solution were obtainable components.

The authors focus on the general aspect of the discrete optimization approach proposed here. It can also be used by power electronics designers with the help of additional constraints in accordance with their specific applications. Furthermore, the use of such non-ideal average models with the multi-objective optimization is the original contribution of the paper and it has not been suggested so far.

The purpose of this paper is to investigate the impact of different mathematical formulations of the problem of optimal design of electrical machines on the results obtained using a local optimization solver. The aim is to investigate the efficiency and reliability of standard local solvers when handling different mathematical formulations. This could provide guidelines for designers in practical engineering applications.

The paper proposes six equivalent mathematical formulations of the optimal design problem of a slotless permanent‐magnet electric rotating machine. The authors investigate the impact of these different mathematical formulations on the results obtained using a local optimization solver which is well‐known in the engineering community: MatLab's fmincon function. The paper first computationally compares the six proposed formulations with a fixed value for the number of pole pairs p, that gives continuous optimization problems, then discusses some results when p is free on three mixed‐integer formulations.

The paper shows that, even though the considered formulations are mathematically equivalent, their numerical performances are different when an optimization solver, such as the one proposed by MatLab in fmincon, is used. Thus, the designer must take care about the formulation of the design problem in order to make more efficient the use of these kind of algorithms.

In the context of engineering applications, one usually resorts to well known and easy to use optimization solvers. The same optimization problem can be often formulated in different ways. Furthermore, the formal description of optimization problems has an impact on the applicability and efficiency of the corresponding solution methods. This is usually not taken into account when optimization solvers are exploited. The originality of this paper is in building on the theory of reformulations in mathematical optimization to investigate and highlight the impact of formulation differences.

The purpose of this paper is to present a new computational framework to address future preliminary design needs for aircraft subsystems. The ability to investigate multiple candidate technologies forming subsystem architectures is enabled with the provision of automated architecture generation, analysis and optimization. Main focus lies with a demonstration of the frameworks workings, as well as the optimizers performance with a typical form of application problem.

The core aspects involve a functional decomposition, coupled with a synergistic mission performance analysis on the aircraft, architecture and component levels. This may be followed by a complete enumeration of architectures, combined with a user defined technology filtering and concept ranking procedure. In addition, a hybrid heuristic optimizer, based on ant systems optimization and a genetic algorithm, is employed to produce optimal architectures in both component composition and design parameters. The optimizer is tested on a generic architecture design problem combined with modified Griewank and parabolic functions for the continuous space.

Insights from the generalized application problem show consistent rediscovery of the optimal architectures with the optimizer, as compared to a full problem enumeration. In addition multi-objective optimization reveals a Pareto front with differences in component composition as well as continuous parameters.

This paper demonstrates the frameworks application on a generalized test problem only. Further publication will consider real engineering design problems.

The paper addresses the need for future conceptual design methods of complex systems to consider a mixed concept space of both discrete and continuous nature via automated methods.

This paper aims to conduct the optimization of the multi-stage gas turbine with the effect of the cooling air injection based on the adjoint method.

Continuous adjoint method is combined with the S2 surface code.

The optimization of the stagger angles, stacking lines and the passage can improve the attack angles and restrain the development of the boundary, reducing the secondary flow loss caused by the cooling air injection.

The aerodynamic performance of the gas turbine can be improved via the optimization of blade and passage based on the adjoint method.

The results of the first study on the adjoint method applied to the S2 surface through flow calculation including the cooling air effect are presented.

This paper presents a computer‐aided design (CAD) tool for the design of isolated dc‐dc converters.

This tool, developed in Matlab environment, is based on multiobjective optimization (MO) using genetic algorithms. The Elitist Nondominated Sorting Genetic Algorithm is used to perform search and optimization whereas analytical models are used to model the power converters. The design problem requires minimizing the weight, losses and cost of the converter while ensuring the satisfaction of a number of constraints. The optimization variables are, as for them, the operating frequency, the current density, the maximum flux density, the transformer dimensions, the wire diameter, the core material, the conductor material, the converter topology (among Flyback, Forward, Push‐Pull, half‐bridge and full‐bridge topologies), the number of semiconductor devices associated in parallel, the number of cells associated in series or parallel as well as the kinds of input and output connections (serial or parallel) of these cells. Finally, the design of an auxiliary railway power supply is presented and discussed.

The results show that such tool to design dc‐dc power converters presents several advantages. In particular, it proposes to the designer a set of solutions – instead of a single one – so that he can choose a posteriori which solution best fits the application under consideration. Moreover, interesting solutions not considered a priori can be found with this tool.

To the best of the authors’ knowledge, such a CAD tool including a MO procedure taking several topologies into account has not been suggested so far.