TOPOS – A new constructive algorithm for nesting problems

Abstract. In this paper we present a new constructive algorithm for nesting problems. The layout is built by successively adding a new piece to a partial solution, i.e. to the set of pieces previously nested. Several criteria to choose the next piece to place and its orientation are proposed and tested. Different objective functions are also proposed to evaluate and compare partial solutions. A total of 126 variants of the algorithm, generated by the complete set of combinations of criteria and objective functions, are computationally tested.     

Robust pole‐assignment for dynamic systems with uncertain parameters

Abstract

In this paper, by using discrete‐type Lyapunov stability criterion, new sufficient conditions for robust pole‐assignment of uncertain systems in a specified disk are presented. The norm bound on linear time‐invariant perturbations is obtained. The relationship between the allowable bound and the eigenvalues of the nominal system matrix is discussed. A design method for robust pole‐assignment is proposed. Examples are given to demonstrate the use of the proposed techniques.     

A hybrid Jaya algorithm for reliability–redundancy allocation problems

This article proposes an efficient improved hybrid Jaya algorithm based on time-varying acceleration coefficients (TVACs) and the learning phase introduced in teaching–learning-based optimization (TLBO), named the LJaya-TVAC algorithm, for solving various types of nonlinear mixed-integer reliability–redundancy allocation problems (RRAPs) and standard real-parameter test functions. RRAPs include series, series–parallel, complex (bridge) and overspeed protection systems. The search power of the proposed LJaya-TVAC algorithm for finding the optimal solutions is first tested on the standard real-parameter unimodal and multi-modal functions with dimensions of 30–100, and then tested on various types of nonlinear mixed-integer RRAPs. The results are compared with the original Jaya algorithm and the best results reported in the recent literature. The optimal results obtained with the proposed LJaya-TVAC algorithm provide evidence for its better and acceptable optimization performance compared to the original Jaya algorithm and other reported optimal results.     

An efficient genetic algorithm for TSK‐type neural fuzzy identifier design

Abstract

In this paper, an efficient genetic algorithm (EGA) of the Takagi‐Sugeno‐Kang (TSK) ‐type neural fuzzy identifier (TNFI) is proposed for solving various identification problems. For the proposed EGA method, the better chromosomes will be initially generated while the better mutation points will be determined to perform efficient mutation. The advantages of the proposed learning algorithm are that, first, it converges quickly and the obtained fuzzy rules are precise. Secondly, the proposed EGA method only requires a small population sizes.     

A computational algorithm for catalysts experiencing concentration‐dependent deactivation

Abstract

A computational algorithm is proposed for catalyst pellets or reactors experiencing concentration‐dependent deactivation. In the integration of the deactivation equation in each time interval, the concentration of poison, reactant or/and product is considered to be a constant. The value of concentration is recalculated from the mass balance equation before integrating the deactivation equation. By such an approach, the number of equations is reduced; thus a two‐dimensional problem can be converted to a single‐dimensional one.     

A topological sorting algorithm for three‐layer channel routing

Abstract

Three‐layer channel routing is an important problem in VLSI layout. In this paper, we present a topological sorting algorithm to determine the topological order on nets depending on the operations of the vertical constraint graph (VCG) and the horizontal constraint graph (HCG). According to the order, the base router can finish the connections of all nets. In the algorithm, the HVH mode is assumed, and some examples including Deutsch's difficult example are used as test problems.     

A robust adaptive algorithm for linear first‐order continuous‐time plants

Abstract

In this paper, an algorithm is presented for the adaptive stabilization of single‐input single‐output first‐order linear time‐varying continuous‐time plants. No knowledge is required to implement this algorithm. Particularly, the sign of the feedback gain is not constant. If the goal is not asymptotic stabilization towards zero, it is shown that the adaptive algorithm can ensure that the controlled output is forced toward a prespecified arbitrarily small interval around zero. Moreover, this adaptive algorithm allows for small bounded disturbances in the state and in the measured output.     

Application of genetic algorithm to the observer‐based controller design for neutral systems

Abstract

In this paper, the dynamic observer‐based controller design for a class of neutral systems with known and uncertain time delays is considered. Delay‐dependent and delay‐independent stabilizability criteria are proposed to guarantee the stability for the feedback control systems. Linear matrix inequality (LMI) and genetic algorithm (GA) are used to design the observer‐based control. Design procedure for the observer‐based control is provided. A numerical example is given to illustrate our results.     

A genetic algorithm for the multi-stage and parallel-machine scheduling problem with job splitting – A case study for the solar cell industry

This paper studies a multi-stage and parallel-machine scheduling problem with job splitting which is similar to the traditional hybrid flow shop scheduling (HFS) in the solar cell industry. The HFS has one common hypothesis, one job on one machine, among the research. Under the hypothesis, one order cannot be executed by numerous machines simultaneously. Therefore, multiprocessor task scheduling has been advocated by scholars. The machine allocation of each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage is determined. However, machine allocation and production sequence decisions are highly interactive. As a result, this study, motivated from the solar cell industry, is going to explore these issues. The multi-stage and parallel-machine scheduling problem with job splitting simultaneously determines the optimal production sequence, multiprocessor task scheduling and machine configurations through dynamically splitting a job into several sublots to be processed on multiple machines. We formulate this problem as a mixed integer linear programming model considering practical characteristics and constraints. A hybrid-coded genetic algorithm is developed to find a near-optimal solution. A preliminary computational study indicates that the developed algorithm not only provides good quality solutions but outperforms the classic branch and bound method and the current heuristic in practice.     

A hybrid neural network–genetic algorithm approach for permutation flow shop scheduling

The objective of this paper is to find a sequence of jobs for the permutation flow shop to minimise the makespan. The shop consists of 10 machines. A feed-forward back-propagation artificial neural network (ANN) is used to solve the problem. The network is trained with the optimal sequences for five-, six- and seven-job problems. This trained network is then used to solve a problem with a greater number of jobs. The sequence obtained using the neural network is used to generate the initial population for the genetic algorithm (GA) using the random insertion perturbation scheme (RIPS). The makespan of the sequence obtained by this approach (ANN-GA-RIPS) is compared with that obtained using GA starting with a random population (ANN-GA). It was found that the ANN-GA-RIPS approach performs better than ANN-GA starting with a random population. The results obtained are compared with those obtained using the Nawaz, Enscore and Ham (NEH) heuristic and upper bounds of Taillard's benchmark problems. ANN-GA-RIPS performs better than the NEH heuristic and the results are found to be within 5% of the upper bounds.     

A new harmony search algorithm for solving mixed–discrete engineering optimization problems

In general design optimization problems, it is usually assumed that the design variables are continuous. However, many practical problems in engineering design require considering the design variables as integer or discrete values. The presence of discrete and integer variables along with continuous variables adds to the complexity of the optimization problem. Very few of the existing methods can yield a globally optimal solution when the objective functions are non-convex and non-differentiable. This article presents a mixed–discrete harmony search approach for solving these nonlinear optimization problems which contain integer, discrete and continuous variables. Some engineering design examples are also presented to demonstrate the effectiveness of the proposed method.     

A new spanning tree-based genetic algorithm for the design of multi-stage supply chain networks with nonlinear transportation costs

The design of configuration and the transportation planning are crucial issues to the effectiveness of multi-stage supply chain networks. The decision makers are interested in the determination the optimal locations of the hubs and the optimal transportation routes to minimize the total costs incurred in the whole system. One may formulate this problem as a 0-1 mixed integer non-linear program though commercial packages are not able to efficiently solve this problem due to its complexity. This study proposes a new spanning tree-based Genetic Algorithm (GA) using determinant encoding for solving this problem. Also, we employ an efficient heuristic that fixes illegal spanning trees existing in the chromosomes obtained from the evolutionary process of the proposed GA. Our numerical experiments demonstrate that the proposed GA outperforms the other previously published GA in the solution quality and convergence rate.     

A cuckoo search algorithm by Lévy flights for solving reliability redundancy allocation problems

A new metaheuristic optimization algorithm, called cuckoo search (CS), was recently developed by Yang and Deb (2009 Yang, X.S. and Deb, S., 2009. Cuckoo search via Lévy flights. In: Proceedings of world congress on nature &; biologically inspired computing (NaBIC 2009), 9–11 December 2009, Coimbatore, India. Piscataway, NJ: IEEE Press, 210–214.[Crossref] , [Google Scholar], 2010 Yang, X.S. and Deb, S., 2010. Engineering optimisation by cuckoo search. International Journal of Mathematical Modelling and Numerical Optimisation, 1, 330–343. doi: 10.1504/IJMMNO.2010.035430[Crossref] , [Google Scholar]). This article uses CS and Lévy flights to solve the reliability redundancy allocation problem. The redundancy allocation problem involves setting reliability objectives for components or subsystems in order to meet the resource consumption constraint, e.g. the total cost. The difficulties facing the redundancy allocation problem are to maintain feasibility with respect to three nonlinear constraints, namely, cost, weight and volume-related constraints. The redundancy allocation problems have been studied in the literature for decades, usually using mathematical programming or metaheuristic optimization algorithms. The performance of the algorithm is tested on five well-known reliability redundancy allocation problems and is compared with several well-known methods. Simulation results demonstrate that the optimal solutions obtained by CS are better than the best solutions obtained by other methods.     

A parallel run‐time iterative load balancing algorithm for solution‐adaptive finite element meshes on hypercubes

Abstract

To efficiently execute a finite element program on a hypercube, we need to map nodes of the corresponding finite element graph to processors of a hypercube such that each processor has approximately the same amount of computational load and the communication among processors is minimized. If the number of nodes of a finite element graph will not be increased during the execution of a program, the mapping only needs to be performed once. However, if a finite element graph is solution‐adaptive, that is, the number of nodes will be increased discretely due to the refinement of some finite elements during the execution of a program, a run‐time load balancing algorithm has to be performed many times in order to balance the computational load of processors while keeping the communication cost as low as possible. In this paper, we propose a parallel iterative load balancing algorithm (ILB) to deal with the load imbalancing problem of a solution‐adaptive finite element program. The proposed algorithm has three properties. First, the algorithm is simple and easy to be implemented. Second, the execution of the algorithm is fast. Third, it guarantees that the computational load will be balanced after the execution of the algorithm. We have implemented the proposed algorithm along with two parallel mapping algorithms, parallel orthogonal recursive bisection (ORB) [19] and parallel recursive mincut bipartitioning (MC) [8], on a 16‐node NCUBE‐2. Three criteria, the execution time of load balancing algorithms, the computation time of an application program under different load balancing algorithms, and the total execution time of an application program (under several refinement phases) are used for performance evaluation. Experimental results show that (1) the execution time of ILB is very short compared to those of MC and ORB; (2) the mappings produced by ILB are better than those of ORB and MC; and (3) the speedups produced by ILB are better than those of ORB and MC.     

Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems

In this article, a hybrid global–local optimization algorithm is proposed to solve continuous engineering optimization problems. In the proposed algorithm, the harmony search (HS) algorithm is used as a global-search method and hybridized with a spreadsheet ‘Solver’ to improve the results of the HS algorithm. With this purpose, the hybrid HS–Solver algorithm has been proposed. In order to test the performance of the proposed hybrid HS–Solver algorithm, several unconstrained, constrained, and structural-engineering optimization problems have been solved and their results are compared with other deterministic and stochastic solution methods. Also, an empirical study has been carried out to test the performance of the proposed hybrid HS–Solver algorithm for different sets of HS solution parameters. Identified results showed that the hybrid HS–Solver algorithm requires fewer iterations and gives more effective results than other deterministic and stochastic solution algorithms.     

A k, k-ε optimality selection based multi objective genetic algorithm with applications to vehicle engineering

In the paper, a multi objective genetic algorithm based on the concept of k-optimality and k-ε-optimality (KEMOGA) is introduced and applied. Pareto optimality alone is not always adequate for selecting a final solution because the Pareto optimal set can be very large. The k-optimality approach and the more general k-ε-optimality method, can be used to rank the Pareto-optimal solutions. The two methods have been included into a genetic algorithm selection procedure. The k-optimality method searches for points which remain Pareto-optimal when all of the subsets of n-k objectives (n is the number of objective functions) are optimised. The k-ε approach considers not only if an objective is worse than the others but also the entity of this variation through the introduction of a vector of indifference thresholds. The KEMOGA has been applied for the solution of two engineering problems. The selection of the stiffness and damping of a passively suspended vehicle in order to get the best compromise between discomfort, road holding and working space and a complex problem related to the optimisation of the tyre/suspension system of a sport car. The final design solution, found by means of the KEMOGA seems consistent with the solution selected by skilled suspensions specialists. The proposed approach has been tested and validated on a complex optimization problem. The solved problem deals with the optimization of the tyre/suspension system of a sport car. The proposed approach (KEMOGA) has shown to be very effective in terms of computational efficiency and accuracy.     

A branch and bound algorithm for scheduling problem of a robot‐centered manufacturing cell

Abstract

An alternative formulation of the scheduling problem in a robot‐centered manufacturing cell has been described here, which was originally formulated by Lin et al. [7] as a mixed integer programming problem. An efficient procedure based on the branch and bound technique has been proposed. In order to reduce the complexity of the branching procedure, several sequencing rules [4] have been imbedded into the proposed procedure and an integrated algorithm has then been presented. The computational results have indicated the proposed algorithm to be efficient. Finally, conclusions and some suggestions are given.     

Sequentially linearizable initial‐boundary value problems for a neo‐hookean cylinder

Abstract

The sequential linearizabilities of some initial‐boundary value problems for the plane‐strain equations of motion of the neo‐Hookean solid are studied. The initial‐boundary value problems are formulated for a cylinder in plane‐strain condition and subjected to shear and radial deformations or tractions on its inner and outer surfaces. The results obtained extend the previous concept about the sequential linearizability of the governing equations for the neo‐Hookean solid to the sequential linearizability of initial‐boundary value problems for the governing equations.     

Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems

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, ?-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.