An efficient search method for job-shop scheduling problems

We present an efficient search method for job-shop scheduling problems. Our technique is based on an innovative way of relaxing and subsequently reimposing the capacity constraints on some critical operations. We integrate this technique into a fast tabu search algorithm. Our computational results on benchmark problems show that this approach is very effective. Upper bounds for 11 well-known test problems are thus improved. Through the work presented We hope to move a step closer to the ultimate vision of an automated system for generating optimal or near-optimal production schedules. The peripheral conditions for such a system are ripe with the increasingly widespread adoption of enterprise information systems and plant floor tracking systems based on bar code or wireless technologies. One of the remaining obstacles, however, is the fact that scheduling problems arising from many production environments, including job-shops, are extremely difficult to solve. Motivated by recent success of local search methods in solving the job-shop scheduling problem, we propose a new diversification technique based on relaxing and subsequently reimposing the capacity constraints on some critical operations. We integrate this technique into a fast tabu search algorithm and are able to demonstrate its effectiveness through extensive computational experiments. In future research, we will consider other diversification techniques that are not restricted to critical operations.     

An efficient algorithm for solving constrained nonlinear programming problems

This paper discusses the basis for an efficient technique which transforms a general constrained nonlinear programming problem to a single unconstrained problem. The theoretical considerations are first presented. This is followed by a development of the algorithm. Lastly, an illustrated example is given to demonstrate the methodology.     

An interior feasible direction method with constraint projections for linear programming

A new feasible direction method for linear programming problems is presented. The method is not boundary following. The method proceeds from a feasible interior point in a direction that improves the objective function until a point on a constraint surface is met. At this point searches are initiated in the hyperplane of constant function value by using projections of the bounding constraints until n bounding constraints are identified that yield a vertex as candidate solution. If the vertex is not feasible or feasible with a worse function value, the next iteration is started from the centre of the simplex defined by the identified points on the bounding constraint surfaces. Otherwise the feasible vertex is tested for optimality. If not optimal a perturbed point with improved function value on an edge emanating from the vertex is calculated from which the next iteration is started. The method has successfully been applied to many test problems.     

Hybrid chaos optimization and affine scaling search algorithm for solving linear programming problems

In this study, we addressed Single Objective Linear Programming (SOLP). This article proposed a new combination of Chaos Optimization Algorithm (COA) with Affine Scaling Search (AFS) to be used as a Hybrid COA and AFS algorithm (Chaos AFS) for solving SOLP. The potential of COA as an emerging optimization algorithm to improve efficiency and effectiveness of AFS is investigated. Chaos AFS method is so-called numerical search algorithm that searches through the domain of decision variables of SOLP to obtain final feasible solution. An initial solution point, obtained from COA, will be used as starting solution point in AFS algorithm to improve the performance of AFS algorithm. The result shows that Hybrid COA and AFS for solving SOLP problems significantly improves the results of objective value compared to pure AFS and reduces the number of iteration steps compared to simplex and pure AFS.     

An efficient search method for multi-objective flexible job shop scheduling problems

Flexible job shop scheduling is very important in both fields of production management and combinatorial optimization. Owing to the high computational complexity, it is quite difficult to achieve an optimal solution to this problem with traditional optimization approaches. Motivated by some empirical knowledge, we propose an efficient search method for the multi-objective flexible job shop scheduling problems in this paper. Through the work presented in this work, we hope to move a step closer to the ultimate vision of an automated system for generating optimal or near-optimal production schedules. The final experimental results have shown that the proposed algorithm is a feasible and effective approach for the multi-objective flexible job shop scheduling problems.     

Optimizing search engines results using linear programming

When a query is passed to multiple search engines, each search engine returns a ranked list of documents. Researchers have demonstrated that combining results, in the form of a “metasearch engine”, produces a significant improvement in coverage and search effectiveness. This paper proposes a linear programming mathematical model for optimizing the ranked list result of a given group of Web search engines for an issued query. An application with a numerical illustration shows the advantages of the proposed method.     

An efficient binary chaotic symbiotic organisms search algorithm approaches for feature selection problems

The Journal of Supercomputing - Feature selection is one of the main steps in preprocessing data in machine learning, and its goal is to reduce features by removing additional and noisy features....     

An efficient algorithm for solving optimal control problems with linear terminal constraints

The optimization of nonlinear systems subject to linear terminal state variable constraints is considered. A technique for solving this class of problems is proposed that involves a piecewise polynomial parameterization of the system variables. The optimal control problem is thereby reduced to a linearly constrained parameter optimization problem which can be solved efficiently using the quadratically convergent Gold-farb-Lapidus algorithm. Illustrative numerical examples are presented.     

An efficient sequential linear quadratic algorithm for solving nonlinear optimal control problems

We develop a numerically efficient algorithm for computing controls for nonlinear systems that minimize a quadratic performance measure. We formulate the optimal control problem in discrete-time, but many continuous-time problems can be also solved after discretization. Our approach is similar to sequential quadratic programming for finite-dimensional optimization problems in that we solve the nonlinear optimal control problem using sequence of linear quadratic subproblems. Each subproblem is solved efficiently using the Riccati difference equation. We show that each iteration produces a descent direction for the performance measure, and that the sequence of controls converges to a solution that satisfies the well-known necessary conditions for the optimal control.     

解灰色非线性规划问题的随机搜索算法

对带约束条件的灰色非线性规划问题进行了探讨,首先将原灰色约束非线性规划问题进行均值白化处理,转化成一个确定型的带约束条件的非线性规划问题,对该确定型的非线性约束规划问题提出一个基于分布估计算法的随机搜索方法,对所提出的求解方法的关键技术作了详细的说明并给出了具体的算法步骤。 初步的数值算例表明所提出的方法是可行有效的     

An efficient variable neighborhood search heuristic for very large scale vehicle routing problems

In this paper, we present an efficient variable neighborhood search heuristic for the capacitated vehicle routing problem. The objective is to design least cost routes for a fleet of identically capacitated vehicles to service geographically scattered customers with known demands. The variable neighborhood search procedure is used to guide a set of standard improvement heuristics. In addition, a strategy reminiscent of the guided local search metaheuristic is used to help escape local minima. The developed solution method is specifically aimed at solving very large scale real-life vehicle routing problems. To speed up the method and cut down memory usage, new implementation concepts are used. Computational experiments on 32 existing large scale benchmarks, as well as on 20 new very large scale problem instances, demonstrate that the proposed method is fast, competitive and able to find high-quality solutions for problem instances with up to 20,000 customers within reasonable CPU times.     

高效求解整数线性规划问题的分支算法

为了提高求解一般整数线性规划问题的效率,提出了一种基于目标函数超平面移动的分支算法。对于给定的目标函数整数值,首先利用线性规划松弛问题的最优单纯形表确定变量的上、下界,然后将变量的上、下界条件加入约束条件中对相应的目标函数超平面进行切割,最后应用分支定界算法中的分支方法来搜寻目标函数超平面上的可行解。通过对一些经典的数值例子的求解计算并与经典的分支定界算法进行比较,结果表明,该算法减少了分支数和单纯形迭代数,具有较大的实用价值。     

An alternating direction method for second-order conic programming

An alternating direction dual augmented Lagrangian method for second-order cone programming (SOCP) problems is proposed. In the algorithm, at each iteration it first minimizes the dual augmented Lagrangian function with respect to the dual variables, and then with respect to the dual slack variables while keeping the other two variables fixed, and then finally it updates the Lagrange multipliers. Convergence result is given. Numerical results demonstrate that our method is fast and efficient, especially for the large-scale second-order cone programming.     

Optimality conditions for linear programming problems with fuzzy coefficients

The optimality conditions for linear programming problems with fuzzy coefficients are derived in this paper. Two solution concepts are proposed by considering the orderings on the set of all fuzzy numbers. The solution concepts proposed in this paper will follow from the similar solution concept, called the nondominated solution, in the multiobjective programming problem. Under these settings, the optimality conditions will be naturally elicited.     

An algorithm for the prediction of search trajectory in nonlinear programming problems and optimum design

A simple modification of some methods of mathematical (nonlinear) programming is suggested (Newton's method and the steepest descent method are taken as examples). The modification is made in order to reduce the number of steps for some sequential search methods. The reduction is achieved by extrapolation of the results obtained by the previous search steps. The computation of prognosis points is proposed instead of the large amount of calculation necessary to do thek-th step of the approach process. The extrapolation formulae are obtained by using elements of the random numbers theory. Results of computational tests and solutions of optimum design problems for a frame and a shell demonstrate the efficiency of the proposed method.     

Neural network for solving extended linear programming problems.

A neural network for solving extended linear programming problems is presented and is shown to be globally convergent to exact solutions. The proposed neural network only uses simple hardware in which no analog multiplier for variables is required, and has no parameter tuning problem. Finally, an application of the neural network to the L(1 )-norm minimization problem is given.     

An efficient representation for linear constraints

An efficient representation for the linear constraints generated by a recent CACSD (computer-aided control system design) method has been developed. The linear constraints arise from engineering constraints on the time- and frequency-domain responses of the closed-loop system. The representation reduces the storage requirements and improves the efficiency of the quadratic programming algorithm used by the design method. The algorithm performs two distinct operations on the individual constraints. The first determines if a constraint has been satisfied and the second is the computation of the distance in a specified search direction     

An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems

This paper proposes a modified harmony search (MHS) algorithm with an intersect mutation operator and cellular local search for continuous function optimization problems. Instead of focusing on the intelligent tuning of the parameters during the searching process, the MHS algorithm divides all harmonies in harmony memory into a better part and a worse part according to their fitness. The novel intersect mutation operation has been developed to generate new -harmony vectors. Furthermore, a cellular local search also has been developed in MHS, that helps to improve the optimization performance by exploring a huge search space in the early run phase to avoid premature, and exploiting a small region in the later run phase to refine the final solutions. To obtain better parameter settings for the proposed MHS algorithm, the impacts of the parameters are analyzed by an orthogonal test and a range analysis method. Finally, two sets of famous benchmark functions have been used to test and evaluate the performance of the proposed MHS algorithm. Functions in these benchmark sets have different characteristics so they can give a comprehensive evaluation on the performance of MHS. The experimental results show that the proposed algorithm not only performs better than those state-of-the-art HS variants but is also competitive with other famous meta-heuristic algorithms in terms of the solution accuracy and efficiency.