Solving Engineering Optimization Problems Research Articles

A hybrid crow search algorithm based on rough searching scheme for solving engineering optimization problems

In this paper, a hybrid intelligent algorithm, named rough crow search algorithm (RCSA), by combining crow search algorithm (CSA) with rough searching scheme (RSS) is presented for solving engineering optimization problems. RCSA integrates the merits of the CSA and RSS to intensify the search in the promising region where the global solution resides. In terms of robustness and efficiency of the available optimization algorithms, some algorithms may not be in a position to specify the global optimal solution precisely but can rather specify them in a ‘rough sense’. Thus, the main reason for incorporating the RSS is handling the impreciseness and roughness of the available information about the global optimal, particularly for the problems with high dimensionality. By upper and lower approximations of the RST, the promising region becomes under siege. Therefore this can accelerate the optimum seeking operation and achieve the global optimum with a low computational cost. The proposed RCSA algorithm is validated on 30 benchmark problems of IEEE CEC 2005, IEEE CEC 2010 and 4 engineering design problems. The obtained results by RCSA are compared with different algorithms from the literature. The comparisons demonstrate that the RCSA outperform the other algorithms for almost all benchmark problems in terms of solution quality based on the results of statistical measures and Wilcoxon signed ranks test.

A new chaotic multi-verse optimization algorithm for solving engineering optimization problems

ABSTRACTMulti-verse optimization algorithm (MVO) is one of the recent meta-heuristic optimization algorithms. The main inspiration of this algorithm came from multi-verse theory in physics. However, MVO like most optimization algorithms suffers from low convergence rate and entrapment in local optima. In this paper, a new chaotic multi-verse optimization algorithm (CMVO) is proposed to overcome these problems. The proposed CMVO is applied on 13 benchmark functions and 7 well-known design problems in the engineering and mechanical field; namely, three-bar trust, speed reduce design, pressure vessel problem, spring design, welded beam, rolling element-bearing and multiple disc clutch brake. In the current study, a modified feasible-based mechanism is employed to handle constraints. In this mechanism, four rules were used to handle the specific constraint problem through maintaining a balance between feasible and infeasible solutions. Moreover, 10 well-known chaotic maps are used to improve the performance of MVO. The experimental results showed that CMVO outperforms other meta-heuristic optimization algorithms on most of the optimization problems. Also, the results reveal that sine chaotic map is the most appropriate map to significantly boost MVO’s performance.

Enhanced linear reformulation for engineering optimization models with discrete and bounded continuous variables

Abstract In this paper, we significantly extend the applicability of state-of-the-art ELDP (equations for linearizing discrete product terms) method by providing a new linearization to handle more complicated non-linear terms involving both of discrete and bounded continuous variables. A general class of “representable programming problems” is formally proposed for a much wider range of engineering applications. Moreover, by exploiting the logarithmic feature embedded in the discrete structure, we present an enhanced linear reformulation model which requires half an order fewer equations than the original ELDP. Computational experiments on various engineering design problems support the superior computational efficiency of the proposed linearization reformulation in solving engineering optimization problems with discrete and bounded continuous variables.

Krill herd algorithm based on cuckoo search for solving engineering optimization problems

This paper presents a hybrid krill herd (CSKH) approach to solve structural optimization problems. CSKH improved the Krill herd algorithm (KH) by combining KU/KA operator originated from cuckoo search algorithm (CS) with KH. In CSKH, a greedy selection scheme is used and often overtakes the original KH and CS. In addition, in order to further enhance the assessment of CSKH, a fraction of the worst krill is thrown away and substituted with newly randomly generated ones by KA operator at the end of each generation. The CSKH is applied to five real engineering problems to verify its performance. The experimental results have proven that CSKH algorithm is well capable of solving constrained engineering design problems more efficiently and effectively than the basic CS and KH algorithm.

A self-adaptive multi-population based Jaya algorithm for engineering optimization

Abstract Multi-population algorithms have been widely used for solving the real-world problems. However, it is not easy to get the number of sub-populations to be used for a given problem. This work proposes a self-adaptive multi-population based Jaya (SAMP-Jaya) algorithm for solving the constrained and unconstrained numerical and engineering optimization problems. The Jaya algorithm is a recently proposed advanced optimization algorithm and is not having any algorithmic-specific parameters to be tuned except the common control parameters of population size and the number of iterations. The search mechanism of the Jaya algorithm is upgraded in this paper by using the multi-population search scheme. It uses an adaptive scheme for dividing the population into sub-populations which control the exploration and exploitation rates of the search process based on the problem landscape. The robustness of the proposed SAMP-Jaya algorithm is tested on 15 CEC 2015 unconstrained benchmark problems in addition to 15 unconstrained and 10 constrained standard benchmark problems taken from the literature. The Friedman rank test is conducted in order to compare the performance of the algorithms. It has obtained first rank among six algorithms for 15 CEC 2015 unconstrained problems with the average scores of 1.4 and 1.9 for 10-dimension and 30-dimension problems respectively. Also, the proposed algorithm has obtained first rank for 15 unimodal and multimodal unconstrained benchmark problems with the average scores of 1.7667 and 2.2667 with 50000 and 200000 function evaluations respectively. The performance of the proposed algorithm is further compared with the other latest algorithms such as across neighborhood search (ANS) optimization algorithm, multi-population ensemble of mutation differential evolution (MEMDE), social learning particle swarm optimization algorithm (SL-PSO), competitive swarm optimizer (CSO) and it is found that the performance of the proposed algorithm is better in more than 65% cases. Furthermore, the proposed algorithm is used for solving a case study of the entropy generation minimization of a plate-fin heat exchanger (PFHE). It is found that the number of entropy generation units is reduced by 12.73%, 3.5% and 9.6% using the proposed algorithm as compared to the designs given by genetic algorithm (GA), particle swarm optimization (PSO) and cuckoo search algorithm (CSA) respectively. Thus the computational experiments have proved the effectiveness of the proposed algorithm for solving engineering optimization problems.

Multi-tracker Optimization Algorithm: A General Algorithm for Solving Engineering Optimization Problems

In this paper, a new computational population-based optimization algorithm, which is designed based on the advantages and disadvantages of other evolutionary optimization algorithms introduced so far, is proposed. This new algorithm, which is named as “multi-tracker optimization algorithm,” due to a multi-level structure of trackers within it, has some unique features, such as increasing the accuracy of the optimal point and continuous local search after convergence in order to escape from local minima simultaneously. Another important advantage of this algorithm is optimizing time-varying dynamical problems and tracking the optimal point. These characteristics make the algorithm very efficient for optimization problems, especially in the field of engineering. For a thorough investigation and comparison of this algorithm with other efficient optimization algorithms, different optimization problems such as static, dynamic, unconstrained and constrained, each of which has different challenges, are considered. The results of applying this algorithm on the abovementioned basic problems show the superiority of this algorithm over other efficient evolutionary algorithms.

A Hybrid PSO and DE Algorithm for Solving Engineering Optimization Problems

A Hybrid PSO and DE Algorithm for Solving Engineering Optimization Problems

AN INTRODUCTION OF KRILL HERD ALGORITHM FOR ENGINEERING OPTIMIZATION

A new metaheuristic optimization algorithm, called Krill Herd (KH), has been recently proposed by Gandomi and Alavi (2012). In this study, KH is introduced for solving engineering optimization problems. For more verification, KH is applied to six design problems reported in the literature. Further, the performance of the KH algorithm is com­pared with that of various algorithms representative of the state-of-the-art in the area. The comparisons show that the results obtained by KH are better than the best solutions obtained by the existing methods.

Cricket behaviour-based evolutionary computation technique in solving engineering optimization problems

Meta-heuristicalgorithms are widely used in various areas such as engineering, statistics, industrial, image processing, artificial intelligence etc. In this study, the Cricket algorithm which is a novel nature-inspired meta-heuristic algorithm approach which can be used for the solution of some global engineering optimization problems was introduced. This novel approach is a meta-heuristic method that arose from the inspiration of the behaviour of crickets in the nature. It has a structure for the use in the solution of various problems. In the development stage of the algorithm, the good aspects of the Bat, Particle Swarm Optimization and Firefly were experimented for being applied to this algorithm. In addition to this, because of the fact that these insects intercommunicate through sound, the physical principles of sound propagation in the nature were practiced in the algorithm. Thanks to this, the compliance of the algorithm to real life tried to be provided. This new developed approach was applied on the familiar global engineering problems and the obtained results were compared with the results of the algorithm applied to these problems.

A Novel Approach for Solving Engineering Optimization Problems Involving Equality Constraints

A Novel Approach for Solving Engineering Optimization Problems Involving Equality Constraints

A surrogate-based particle swarm optimization algorithm for solving optimization problems with expensive black box functions

In engineering applications, computer experiments such as finite element analysis and computational fluid dynamics are often used to model and analyse structural behaviours. In this article, a surrogate-based particle swarm optimization algorithm is proposed for solving optimization problems with expensive black box functions. An approximate optimization problem in which the black box functions are replaced by the hybrid surrogate models is efficiently solved to search and adjust the global optimum position during the iterative process. Since the presented method combines the merits of traditional optimization algorithms and particle swarm optimization, only a small number of particles is needed to achieve the optimal position after several iterations. Therefore, the method shows great advantages in solving engineering optimization problems with expensive black box functions. Several examples are presented to demonstrate the feasibility and effectiveness of the proposed method.

An Adaptive Particle Swarm Optimization Applied to Optimum Controller Design for AVR Power Systems

paper describes an improved version of particle swarm optimization (PSO) method, called adaptive particle swarm optimization (APSO), for solving engineering optimization problems especially in power system fields. This algorithm uses a novel PSO algorithm to increase convergence rate and avoid being trapped in local optimum. The APSO algorithm efficiency is verified using some benchmark functions. Numerical simulation results demonstrate that the APSO is fast and has much less computational cost. Then, the proposed APSO method is used for determining the parameters of the optimal proportional-integral- derivative (PID) controller for an AVR power system. The proposed approach has superior features including easy implementation, stable and fast convergence characteristics and good computational efficiency. Also, the proposed method is indeed more efficient and robust in improving the step response of the AVR system.

A hybrid quantum evolutionary algorithm for solving engineering optimization problems

Evolutionary Algorithms (EA) have been successfully employed for solving difficult constrained engineering optimization problems. However, EA implementations often suffer from premature convergence due to the lack of proper balance between exploratio

Two improved harmony search algorithms for solving engineering optimization problems

This paper describes two new harmony search (HS) meta-heuristic algorithms for engineering optimization problems with continuous design variables. The key difference between these algorithms and traditional (HS) method is in the way of adjusting bandwidth (bw). bw is very important factor for the high efficiency of the harmony search algorithms and can be potentially useful in adjusting convergence rate of algorithms to optimal solution. First algorithm, proposed harmony search (PHS), introduces a new definition of bandwidth (bw). Second algorithm, improving proposed harmony search (IPHS) employs to enhance accuracy and convergence rate of PHS algorithm. In IPHS, non-uniform mutation operation is introduced which is combination of Yang bandwidth and PHS bandwidth. Various engineering optimization problems, including mathematical function minimization problems and structural engineering optimization problems, are presented to demonstrate the effectiveness and robustness of these algorithms. In all cases, the solutions obtained using IPHS are in agreement or better than those obtained from other methods.

Data Mining based mutation function for engineering problems with mixed continuous-discrete design variables

Genetic algorithms are well established for solving engineering optimization problems having both continuous and discrete design variables. In this paper, a mutation function for discrete design variables based on Data Mining is introduced. The M5P Data Mining algorithm is used to build rules for the prediction of the optimization objectives with respect to the discrete design variables. The most promising combinations of discrete design variables are then selected in the mutation function of the genetic algorithm GAME to create children. This approach results in faster convergence and better results for both single and multi-objective problems when compared with a standard mutation scheme of discrete design variables. The optimization of a vehicle space frame showed that a mutation probability between 40% and 60% for the discrete design variables results in the fastest convergence. A multi-objective aerospace conceptual design example showed a substantial improvement in the number of pareto-optimal solutions found after 100 generations.

Distributed evolutionary algorithms with hierarchical evaluation

A distributed evolutionary algorithm is presented that is based on a hierarchy of (fitness or cost function) evaluation passes within each deme and is efficient in solving engineering optimization problems. Starting with non-problem-specific evaluations (using surrogate models or metamodels, trained on previously evaluated individuals) and ending up with high-fidelity problem-specific evaluations, intermediate passes rely on other available lower-fidelity problem-specific evaluations with lower CPU cost per evaluation. The sequential use of evaluation models or metamodels, of different computational cost and modelling accuracy, by screening the generation members to get rid of non-promising individuals, leads to reduced overall computational cost. The distributed scheme is based on loosely coupled demes that exchange regularly their best-so-far individuals. Emphasis is put on the optimal way of coupling distributed and hierarchical search methods. The proposed method is tested on mathematical and compressor cascade airfoil design problems.

A superlinearly convergent method of feasible directions

Method of feasible directions (MFD) is one of the most important methods for solving engineering optimization problems. There exist two types of MFD: one has at most a linear convergence rate and the other has a superlinear convergence rate. The former type includes Zoutendijk's MFD, Topkis–Veinott's MFD, Pironneau–Polak's MFD, Cawood–Kostreva's Norm-Relaxed MFD, and a modified MFD. The latter includes Panier–Tits' FSQP approaches. However, the price of the superlinearly convergent MFD for achieving superlinearity is rather high computational cost per single iteration. This paper presents an algorithm based on the modified MFD. The theoretical analysis shows that this algorithm is locally superlinearly convergent. This algorithm has attained the same convergence rate as FSQP while it only needs to solve two subproblems instead of three subproblems in FSQP. Hence, this algorithm should be computationally more efficient than FSQP.

A Hybrid Variable Metric Update for the Recursive Quadratic Programming Method

The Recursive Quadratic Programming (RQP) method has become known as one of the most effective and efficient algorithms for solving engineering optimization problems. The RQP method uses variable metric updates to build approximations of the Hessian of the Lagrangian. If the approximation of the Hessian of the Lagrangian converges to the true Hessian of the Lagrangian, then the RQP method converges quadratically. The choice of a variable metric update has a direct effect on the convergence of the Hessian approximation. Most of the research performed with the RQP method uses some modification of the Broyden-Fletcher-Shanno (BFS) variable metric update. This paper describes a hybrid variable metric update that yields good approximations to the Hessian of the Lagrangian. The hybrid update combines the best features of the Symmetric Rank One and BFS updates, but is less sensitive to inexact line searches than the BFS update, and is more stable than the SR1 update. Testing of the method shows that the efficiency of the RQP method is unaffected by the new update but more accurate Hessian approximations are produced. This should increase the accuracy of the solutions obtained with the RQP method, and more importantly, provide more reliable information for post optimality analyses, such as parameter sensitivity studies.