Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems: A comparative study

Purpose: – 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, it is very time-consuming in use of finite element methods. The purpose of this paper is to study the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization, and compares it with the performance of Genetic Algorithms (GA). Design/methodology/approach: – In this paper, the enhanced multipoint approximation method (MAM) is utilized to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the Sequential Quadratic Programming (SQP) 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. Findings: – 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. Originality/value: – 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 φ defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects

A search algorithm for constrained engineering optimization and tuning the gains of controllers

In this work, the application of an optimization algorithm is investigated to optimize static and dynamic engineering problems. The methodology of the approach is to generate random solutions and find a zone for the initial answer and keep reducing the zones. The generated solution in each loop is independent of the previous answer that creates a powerful method. Simplicity as its main advantage and the interlaced use of intensification and diversification mechanisms--to refine the solution and avoid local minima/maxima--enable the users to apply that for a variety of problems. The proposed approach has been validated by several previously solved examples in structural optimization and scored good results. The method is also employed for dynamic problems in vibration and control. A modification has also been done on the method for high-dimensional test functions (functions with very large search domains) to converge fast to the global minimum or maximum; simulated for several well-known benchmarks successfully. For validation, a number of 9 static and 4 dynamic constrained optimization benchmark applications and 32 benchmark test functions are solved and provided, 45 in total. All the codes of this work are available as supplementary material in the online version of the paper on the journal website

A New Enhanced Hybrid Grey Wolf Optimizer (GWO) Combined with Elephant Herding Optimization (EHO) Algorithm for Engineering Optimization

Although the exploitation of GWO advances sharply, it has limitations for continuous implementing exploration. On the other hand, the EHO algorithm easily has shown its capability to prevent local optima. For hybridization and by considering the advantages of GWO and the abilities of EHO, it would be impressive to combine these two algorithms. In this respect, the exploitation and exploration performances and the convergence speed of the GWO algorithm are improved by combining it with the EHO algorithm. Therefore, this paper proposes a new hybrid Grey Wolf Optimizer (GWO) combined with Elephant Herding Optimization (EHO) algorithm. Twenty-three benchmark mathematical optimization challenges and six constrained engineering challenges are used to validate the performance of the suggested GWOEHO compared to both the original GWO and EHO algorithms and some other well-known optimization algorithms. Wilcoxon's rank-sum test outcomes revealed that GWOEHO outperforms others in most function minimization. The results also proved that the convergence speed of GWOEHO is faster than the original algorithms

Determination of Design of Optimal Actuator Location Based on Control Energy

The thesis deals with the selection of the sets of inputs and outputs using the energy properties of the controllability and observability of a system and aims to define input and output structures which require minimization of the energy for control and state reconstruction. Such a study explores the energy dimension of the properties of controllability and observability, develops computations for the controllability and observability Gramians for stable and unstable systems and examines measures of the degree of controllability and observability properties using SVD (Singular Value Decomposition) of Gramians to compute the maximal and minimal energy requirements. These characterize the relative degree of controllability and observability under conditions where the available energy is constrained. The notion of energy surfaces in the state space is introduced and this enables the characterization of restricted notions of controllability and observability when the available energy is bounded. The maximal and minimal energy requirements for different input vectors is demonstrated and this provides the basis for the development of strategies and methodologies for selection of systems of inputs and outputs to minimize the energy required for control, respectively state reconstruction. These results enable the development of input, output structure selection methodology using a novel optimization method. This thesis contributes in the further development of the area of systems, or global instrumentation, developed so far based on the assignment of structural characteristics by incorporating the role of energy requirements. The research provides energy based tools for the selection of input and outputs schemes with a main criterion the minimization of the energy required for control and observation and thus provide an alternative approach based on quantitative system properties in characterizing control and state observation as functions of given sets of inputs and output sets. The methodologies developed may be used as design tools where apart from energy requirements other design criteria may be also incorporated for the selection of inputs and outputs. The methodology that is used is based on linear systems theory and tools from numerical linear algebra. The solution to the problems considered here is an integral part of the effort to develop an integrated approach to control and global process instrumentation