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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.

This paper aims to present the optimum two-plane discrete balancing procedure for rigid rotor. The discrete two-plane balancing in which rotor is balanced to minimize the residual effects or the reactions on the bearing supports using discrete parameters such as masses and their angular positions on two balancing planes.

Therefore as a multi-objective optimization problem is formulated by considering reaction forces on the bearing supports as a multi objective functions and discrete parameters on each balancing plane as design variables. These multi-objective functions are converted into a single-objective function using appropriate weighting factors. Further, this optimization problem is solved using discrete optimization algorithm, based on Jaya algorithm.

The performance of the discrete Jaya algorithm is compared to genetic algorithm (GA) algorithm. It is found that Jaya algorithm is computationally more efficient than GA algorithm. A number of masses per plane are used to balance the rotor. A comparison of reaction forces using number of masses per plane is investigated.

The effectiveness of the proposed methodology is tested by the balancing problem of rotor available in the literature. The influence of a number of balance masses on bearing forces and objective function are discussed. ADAMS software is used for validation of a developed balancing approach.

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.

In this article, a practical design methodology is proposed for discrete sizing optimization of high-rise concrete buildings with a focus on large-scale and real-life structures.

This framework relies on a computationally efficient approximation of the constraint and objective functions using a radial basis function model with a linear tail, also called the combined response surface methodology (RSM) in this article. Considering both the code-stipulated constraints and other construction requirements, three sub-optimization problems were constructed based on the relaxation model of the original problem, and then the structural weight could be automatically minimized under multiple constraints and loading scenarios. After modulization, the obtained results could meet the discretization requirements. By integrating the commercially available ETABS, a dedicated optimization software program with an independent interface was developed and details for practical software development were also presented in this paper.

The proposed framework was used to optimize different high-rise concrete buildings, and case studies showed that material usage could be saved by up to 12.8% compared to the conventional design, and the over-limit constraints could be adjusted, which proved the feasibility and effectiveness.

This methodology can therefore be applied by engineers to explore the optimal distribution of dimensions for high-rise buildings and to reduce material usage for a more sustainable design.

Continuous process improvement is a hard problem, especially in high variety/low volume environments due to the complex interrelationships between processes. The purpose of this paper is to address the process improvement issues by simultaneously investigating the job sequencing and buffer size optimization problems.

This paper proposes a continuous process improvement implementation framework using a modified genetic algorithm (GA) and discrete event simulation to achieve multi-objective optimization. The proposed combinatorial optimization module combines the problem of job sequencing and buffer size optimization under a generic process improvement framework, where lead time and total inventory holding cost are used as two combinatorial optimization objectives. The proposed approach uses the discrete event simulation to mimic the manufacturing environment, the constraints imposed by the real environment and the different levels of variability associated with the resources.

Compared to existing evolutionary algorithm-based methods, the proposed framework considers the interrelationship between succeeding and preceding processes and the variability induced by both job sequence and buffer size problems on each other. A computational analysis shows significant improvement by applying the proposed framework.

Significant body of work exists in the area of continuous process improvement, discrete event simulation and GAs, a little work has been found where GAs and discrete event simulation are used together to implement continuous process improvement as an iterative approach. Also, a modified GA simultaneously addresses the job sequencing and buffer size optimization problems by considering the interrelationships and the effect of variability due to both on each other.

The problem of structural optimization of trusses subject to stress and frequency constraints is considered from a practical viewpoint. Assuming that the choice of members has to be from a discrete set of available sections, the solution is attempted using a mathematical programming approach and an approximate two‐step procedure involving a continuous variable optimization followed by a discrete programming algorithm. The latter approach is highly promising for problems involving stress and frequency constraints. Detailed results are presented using several benchmark problems.

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.

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.

Life cycle analysis (LCA) is more and more used in the context of electromagnetic product design. But it is often used to check a design solution regarding environmental impacts after technical and economical choices. This paper aims to investigate life cycle impact optimization (LCIO) and compare it with the classical life cycle cost optimization (LCCO).

First, a model of a dry-type transformer using different materials for windings and the magnetic core is presented. LCCO, which is a mixed continuous-discrete, multi-objective technico-economic optimization, is done using both deterministic and genetic algorithms. LCCO results and optimization performances are analyzed, and an LCA is presented for a set of optimal solutions. The final part is dedicated to LCIO, where the paper shows that these optimal solutions are close to those obtained with LCCO.

This paper investigated LCIO using an environmental impacts model that has been introduced in the optimization framework Component Architecture for the Design of Engineering Systems. The paper shows how a mixed continuous-discrete, multi-objective technico-economic optimization can be done using an efficient deterministic optimization algorithm such as Sequential Quadratic Programming. Thanks to the technico-economic-environmental model and the efficient optimization algorithm, both LCCO and LCIO were performed separately and together. It has been shown that optimal solutions are similar, leading to the conclusion that only one modeling is required (economic or environmental) but on the life cycle.

The classical sequential methodology of design is improved here by the use of a model of calculation of the environmental impacts allowing the optimization. This original optimization allowed the authors to show that an analysis of the life cycle from an economic point of view or from an environmental point of view led to quasi-equivalent technical solutions. The key is to take into account the life cycle of the product.

Much work has been done on the optimization of the discrete variable structure design. In order to handle the optimization problem effectively, the related theories, methods, and other beneficial results were summarized. On the basis of analyzing the predecessors' research, the development direction was introduced. Then, some practical methods, including their improvements, for discrete structural optimization were analyzed. Finally, the Ant Colony Optimization algorithms were shown as promising methods. This work has significance in theory and practice for the development of structural optimization.