A reliable algorithm for solving tenth-order boundary value problems

In this paper we present an efficient numerical algorithm for solving linear and nonlinear boundary value problems with two-point boundary conditions of tenth-order. The differential transform method is applied to construct the numerical solutions. The proposed algorithm avoids the complexity provided by other numerical approaches. Several illustrative examples are given to demonstrate the effectiveness of the present algorithm.      

An algorithm for local continuous optimization of traffic signals

In this paper, an algorithm for sensitivity analysis for equilibrium traffic network flows with link interferences is proposed. Based on this sensitivity analysis algorithm, a general algorithm is provided for solving the optimal design and management problems for traffic networks. In particular, this algorithm is applied to the optimal traffic signal setting problem. A numerical example is given to demonstrate the effectiveness of our algorithm.     

Bat algorithm for optimization of reinforced concrete columns

In structural mechanics, when the design contains two different materials with opposite mechanical behaviours and costs, the optimum design cannot exactly found. In that case, numerical optimization algorithms are a good source. Reinforced concrete design shows that behaviour since concrete is a cheap material comparing to steel while the tensile strength of concrete is very low to use. The cross sections are effective on the stresses and balance of tensile and compressive forces. This situation shows the importance of the dimension optimization of reinforced concrete members. Also, the number and size of the reinforcements need an optimization. The place of the reinforcements is effective on the place of tensile forces in the calculation of axial force and flexural moment capacity. In this paper, reinforced concrete columns are optimized for the cost minimization by employing a bio-inspired metaheuristic algorithm called bat algorithm. The idealization of the echolocation behaviour of bats is the inspiration of the bat algorithm. Differently from the algorithms, the bat algorithm uses global and local optimization with a changeable probability. The optimization process considers the security measures and slenderness of the according to the design regulation called ACI 318. The slenderness is taken into consideration by using a magnified design flexural moment, which is factored by a value defined according to the buckling load and axial load of columns. The proposed approach is applied for different numerical cases and the results are compared with the approach using harmony search algorithm. The present approach is effective for the optimization problem. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Novel Bat Algorithm based on Cross Boundary Learning and Uniform Explosion Strategy

Population-based algorithms have been used in many real-world problems. Bat algorithm(BA) is one of the states of the art of these approaches. Because of the super bat,on the one hand, BA can converge quickly; on the other hand, it is easy to fall into local optimum. Therefore, for typical BA algorithms, the ability of exploration and exploitation is not strong enough and it is hard to find a precise result. In this paper, we propose a novel bat algorithm based on cross boundary learning(CBL) and uniform explosion strategy(UES),namely BABLUE in short, to avoid the above contradiction and achieve both fast convergence and high quality. Different from previous opposition-based learning, the proposed CBL can expand the search area of population and then maintain the ability of global exploration in the process of fast convergence. In order to enhance the ability of local exploitation of the proposed algorithm, we propose UES, which can achieve almost the same search precise as that of firework explosion algorithm but consume less computation resource. BABLUE is tested with numerous experiments on unimodal, multimodal, one-dimensional, high-dimensional and discrete problems, and then compared with other typical intelligent optimization algorithms.The results show that the proposed algorithm outperforms other algorithms.     

An improved local branching approach for train formation planning

The train formation plan (TFP) determines routing and frequency of trains, and assigns the demands to trains. In this paper, an improved local branching algorithm is proposed for the TFP model in Iranian railway. This solution strategy is exact in nature, although it is designed to improve the heuristic behavior of the mixed integer programming (MIP) solver at hand. In the local branching algorithm, additional constraints are built in the model for the binary variables, but in the improved local branching algorithm, the additional constraints are built in the model for integer variables. A state-of-the-art method is applied for parameter tuning using design of experiments approach. To evaluate the proposed solution method, we have simulated and solved twenty test problems. The results show the efficiency and effectiveness of the proposed approach. The proposed algorithm is implemented for Iranian Railway network as a case study.     

Discretization orders and efficient computation of cartesian coordinates for distance geometry

Distance geometry is a class of problems where the position of points in space is to be identified by using information about some relative distances between these points. Although continuous approaches are usually employed, problems belonging to this class can be discretized when some particular assumptions are satisfied. These assumptions strongly depend on the order in which the points to be positioned are considered. We discuss new discretization assumptions that are weaker than previously proposed ones, and present a greedy algorithm for an automatic identification of discretization orders. The use of these weaker assumptions motivates the development of a new method for computing point coordinates. Computational experiments show the effectiveness and efficiency of the proposed approaches when applied to protein instances.     

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.     

A mixture experiments multi-objective hyper-heuristic

This paper proposes a hyper-heuristic that combines genetic algorithm with mixture experiments to solve multi-objective optimisation problems. At every iteration, the proposed algorithm combines the selection criterion (rank indicator) of a number of well-established evolutionary algorithms including NSGA-II, SPEA2 and two versions of IBEA. Each indicator is called according to an associated probability calculated and updated during the search by means of mixture experiments. Mixture experiments are a particular type of experimental design suitable for the calibration of parameters that represent probabilities. Their main output is an explanatory model of algorithm performance as a function of its parameters. By finding the maximum (probability distribution) of the surface represented by this model, we also find a good algorithm parameterisation. The design of mixture experiments approach allowed the authors to identify and exploit synergies between the different rank indicators at the different stages of the search. This is demonstrated by our experimental results in which the proposed algorithm compared favourably against other well-established algorithms.     

Partitioned Random Search for Global Optimization with Sampling Cost and Discounting Factor

The method of partitioned random search has been proposed in recent years to obtain an as good as possible solution for the global optimization problem (1). A practical algorithm has been developed and applied to real-life problems. However, the design of this algorithm was based mainly on intuition. The theoretical foundation of the method is an important issue in the development of efficient algorithms for such problems. In this paper, we generalize previous theoretical results and propose a sequential sampling policy for the partitioned random search for global optimization with sampling cost and discounting factor. A proof of the optimality of the proposed sequential sampling policy is given by using the theory of optimal stopping.     

Balanced train timetabling on a single-line railway with optimized velocity

This paper aims to find an optimal balanced schedule with the least delay-ratio (i.e., the ratio of the total delay time and the total free-run time) by considering the impacts of the train velocity. A rigorous optimization model is proposed under the consideration of feasible speed constraint for finding the optimal velocity for each train on the railway line. To obtain an approximately optimal scheduling strategy, a combination of the improved TAS (ITAS) method and the genetic algorithm (GA), called GA-ITAS method, is in particular proposed to effectively solve the proposed model. The results of numerical experiments demonstrate the efficiency and effectiveness of the proposed approaches.     

A new multi-objective discrete robust optimization algorithm for engineering design

This paper proposes a novel multi-objective discrete robust optimization (MODRO) algorithm for design of engineering structures involving uncertainties. In the present MODRO procedure, grey relational analysis (GRA), coupled with principal component analysis (PCA), was used as a multicriteria decision making model for converting multiple conflicting objectives into one unified cost function. The optimization process was iterated using the successive Taguchi approach to avoid the limitation that the conventional Taguchi method fails to deal with a large number of design variables and design levels. The proposed method was first verified by a mathematical benchmark example and a ten-bar truss design problem; and then it was applied to a more sophisticated design case of full scale vehicle structure for crashworthiness criteria. The results showed that the algorithm is able to achieve an optimal design in a fairly efficient manner attributable to its integration with the multicriteria decision making model. Note that the optimal design can be directly used in practical applications without further design selection. In addition, it was found that the optimum is close to the corresponding Pareto frontier generated from the other approaches, such as the non-dominated sorting genetic algorithm II (NSGA-II), but can be more robust as a result of introduction of the Taguchi method. Due to its independence on metamodeling techniques, the proposed algorithm could be fairly promising for engineering design problems of high dimensionality.     

A hybrid ACO-GRASP algorithm for clustering analysis

Cluster analysis is an important tool for data exploration and it has been applied in a wide variety of fields like engineering, economics, computer sciences, life and medical sciences, earth sciences and social sciences. The typical cluster analysis consists of four steps (i.e. feature selection or extraction, clustering algorithm design or selection, cluster validation and results interpretation) with feedback pathway. These steps are closely related to each other and affect the derived clusters. In this paper, a new metaheuristic algorithm is proposed for cluster analysis. This algorithm uses an Ant Colony Optimization to feature selection step and a Greedy Randomized Adaptive Search Procedure to clustering algorithm design step. The proposed algorithm has been applied with very good results to many data sets.     

Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.     

Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method

In the last decades, heuristic techniques have become established as suitable approaches for solving optimal control problems. Unlike deterministic methods, they do not suffer from locality of the results and do not require any starting guess to yield an optimal solution. The main disadvantages of heuristic algorithms are the lack of any convergence proof and the capability of yielding only a near optimal solution, if a particular representation for control variables is adopted. This paper describes the indirect swarming method, based on the joint use of the analytical necessary conditions for optimality, together with a simple heuristic technique, namely the particle swarm algorithm. This methodology circumvents the previously mentioned disadvantages of using heuristic approaches, while retaining their advantageous feature of not requiring any starting guess to generate an optimal solution. The particle swarm algorithm is chosen among the different available heuristic techniques, due to its apparent simplicity and the recent promising results reported in the scientific literature. Two different orbital maneuvering problems are considered and solved with great numerical accuracy, and this testifies to the effectiveness of the indirect swarming algorithm in solving low-thrust trajectory optimization problems.     

A quantum-behaved simulated annealing algorithm-based moth-flame optimization method

This study develops an improved moth-flame optimization algorithm, which is a recently proposed optimizer based on moth behavior in nature. It has achieved favorable results in medical science, educational evaluation, and other fields. However, the convergence rate of the original moth-flame optimization algorithm is too fast in the running process, and it is prone to fall into local optimum, which leads to the failure to produce the high-quality optimal result. Accordingly, this paper proposes a reinforced technique for the moth-flame optimization algorithm. Firstly, the simulated annealing strategy is introduced into the moth-flame optimization algorithm to boost the advantage of the algorithm in the local exploitation process. Then, the idea of the quantum rotation gate is integrated to enhance the global exploration ability of the algorithm and ameliorate the diversity of the moth. These two steps maintain the relationship between exploitation and exploration as well as strengthen the performance of the algorithm in both phases. After that, the method is compared with ten well-regarded and ten alternative algorithms on benchmark functions to verify the effectiveness of the approach. Also, the Wilcoxon signed rank and Friedman assessment were performed to verify the significance of the proposed method against other counterparts. The simulation results reveal that the two introduced strategies significantly improve the exploration and exploitation capacity of moth-flame optimization algorithm. Finally, the algorithm is utilized to feature selection and two engineering problems, including pressure vessel design and multiple disk clutch brake problems. In these practical applications, the novel algorithm also achieves particularly notable results, which also illustrates that the algorithm is qualified is an effective auxiliary appliance in solving complex optimization problems.     

A Staged Continuous Tabu Search Algorithm for the Global Optimization and its Applications to the Design of Fiber Bragg Gratings

A novel staged continuous Tabu search (SCTS) algorithm is proposed for solving global optimization problems of multi-minima functions with multi-variables. The proposed method comprises three stages that are based on the continuous Tabu search (CTS) algorithm with different neighbor-search strategies, with each devoting to one task. The method searches for the global optimum thoroughly and efficiently over the space of solutions compared to a single process of CTS. The effectiveness of the proposed SCTS algorithm is evaluated using a set of benchmark multimodal functions whose global and local minima are known. The numerical test results obtained indicate that the proposed method is more efficient than an improved genetic algorithm published previously. The method is also applied to the optimization of fiber grating design for optical communication systems. Compared with two other well-known algorithms, namely, genetic algorithm (GA) and simulated annealing (SA), the proposed method performs better in the optimization of the fiber grating design.     

A multi-population hybrid biased random key genetic algorithm for hop-constrained trees in nonlinear cost flow networks

Genetic algorithms and other evolutionary algorithms have been successfully applied to solve constrained minimum spanning tree problems in a variety of communication network design problems. In this paper, we enlarge the application of these types of algorithms by presenting a multi-population hybrid genetic algorithm to another communication design problem. This new problem is modeled through a hop-constrained minimum spanning tree also exhibiting the characteristic of flows. All nodes, except for the root node, have a nonnegative flow requirement. In addition to the fixed charge costs, nonlinear flow dependent costs are also considered. This problem is an extension of the well know NP-hard hop-constrained Minimum Spanning Tree problem and we have termed it hop-constrained minimum cost flow spanning tree problem. The efficiency and effectiveness of the proposed method can be seen from the computational results reported.     

A linear formulation for disk conformal parameterization of simply-connected open surfaces

Surface parameterization is widely used in computer graphics and geometry processing. It simplifies challenging tasks such as surface registrations, morphing, remeshing and texture mapping. In this paper, we present an efficient algorithm for computing the disk conformal parameterization of simply-connected open surfaces. A double covering technique is used to turn a simply-connected open surface into a genus-0 closed surface, and then a fast algorithm for parameterization of genus-0 closed surfaces can be applied. The symmetry of the double covered surface preserves the efficiency of the computation. A planar parameterization can then be obtained with the aid of a Möbius transformation and the stereographic projection. After that, a normalization step is applied to guarantee the circular boundary. Finally, we achieve a bijective disk conformal parameterization by a composition of quasi-conformal mappings. Experimental results demonstrate a significant improvement in the computational time by over 60%. At the same time, our proposed method retains comparable accuracy, bijectivity and robustness when compared with the state-of-the-art approaches. Applications to texture mapping are presented for illustrating the effectiveness of our proposed algorithm.     

A cross entropy based algorithm for reliability problems

The Cross Entropy method has recently been applied to combinatorial optimization problems with promising results. This paper proposes a Cross Entropy based algorithm for reliability optimization of complex systems, where one wants to maximize the reliability of a system through optimal allocation of redundant components while respecting a set of budget constraints. We illustrate the effectiveness of the proposed algorithm on two classes of problems, software system reliability optimization and complex network reliability optimization, by testing it on instances from the literature as well as on randomly generated large scale instances. Furthermore, we show how a Cross Entropy-based algorithm can be fine-tuned by using a training scheme based upon the Response Surface Methodology. Computational results show the effectiveness as well as the robustness of the algorithm on different classes of problems.     

An efficient multi-objective PSO algorithm assisted by Kriging metamodel for expensive black-box problems

The huge computational overhead is the main challenge in the application of community based optimization methods, such as multi-objective particle swarm optimization and multi-objective genetic algorithm, to deal with the multi-objective optimization involving costly simulations. This paper proposes a Kriging metamodel assisted multi-objective particle swarm optimization method to solve this kind of expensively black-box multi-objective optimization problems. On the basis of crowding distance based multi-objective particle swarm optimization algorithm, the new proposed method constructs Kriging metamodel for each expensive objective function adaptively, and then the non-dominated solutions of the metamodels are utilized to guide the update of particle population. To reduce the computational cost, the generalized expected improvements of each particle predicted by metamodels are presented to determine which particles need to perform actual function evaluations. The suggested method is tested on 12 benchmark functions and compared with the original crowding distance based multi-objective particle swarm optimization algorithm and non-dominated sorting genetic algorithm-II algorithm. The test results show that the application of Kriging metamodel improves the search ability and reduces the number of evaluations. Additionally, the new proposed method is applied to the optimal design of a cycloid gear pump and achieves desirable results.