离散回溯搜索算法求解多柔性作业车间调度

针对柔性作业车间生产中机器和工序柔性与多能工的存在建立模型,并提出一种整数编码方案和设一种基于Pareto解集的离散回溯搜索算法进行求解。首先,采用精英化历史种群的方法提升历史种群引导当前种群进化的能力;其次,在交叉变异步骤用遗传交叉算子替代回溯搜索算法原有结构;再次,为保留更多较优解到当前种群,结合快速非支配排序方法更新当前种群;最后,求解数值实例,与多种智能算法进行对比,验证算法的可行性和有效性。     

Expected hitting times for Backtracking Adaptive Search

This article analyses a counting process associated with a stochastic process arising in global optimisation. Backtracking adaptive search (BAS) is a theoretical stochastic global optimisation algorithm modelling the temporary acceptance of solutions of lower quality. BAS generalises the pure adaptive search and hesitant adaptive search algorithms, whose full search duration distributions are known. This article gives the exact expected search duration for backtracking adaptive search.     

A reduced Hessian algorithm with line search filter method for nonlinear programming

This paper proposes a line search filter reduced Hessian method for nonlinear equality constrained optimization. The feature of the presented algorithm is that the reduced Hessian method is used to produce a search direction, a backtracking line search procedure to generate step size, some filtered rules to determine step acceptance, second order correction technique to reduce infeasibility and overcome the Maratos effects. It is shown that this algorithm does not suffer from the Maratos effects by using second order correction step, and under mild assumptions fast convergence to second order sufficient local solutions is achieved. The numerical experiment is reported to show the effectiveness of the proposed algorithm.     

Random backtracking in backtrack search algorithms for satisfiability

This paper proposes the utilization of randomized backtracking within complete backtrack search algorithms for propositional satisfiability (SAT). In recent years, randomization has become pervasive in SAT algorithms. Incomplete algorithms for SAT, for example the ones based on local search, often resort to randomization. Complete algorithms also resort to randomization. These include state-of-the-art backtrack search SAT algorithms that often randomize variable selection heuristics. Moreover, it is plain that the introduction of randomization in other components of backtrack search SAT algorithms can potentially yield new competitive search strategies. As a result, we propose a stochastic backtrack search algorithm for SAT, that randomizes both the variable selection and the backtrack steps of the algorithm. In addition, we relate randomized backtracking with a more general form of backtracking, referred to as unrestricted backtracking. Finally, experimental results for different organizations of randomized backtracking are described and compared, providing empirical evidence that the new search algorithm for SAT is a very competitive approach for solving hard real-world instances.     

An Affine Scaling Interior Trust-Region Algorithm Combining Backtracking Line Search with Filter Technique for Nonlinear Constrained Optimization

In this article, an affine scaling interior trust-region algorithm which employs backtracking line search with filter technique is presented for solving nonlinear equality constrained programming with nonnegative constraints on variables. At current iteration, the general full affine scaling trust-region subproblem is decomposed into a pair of trust-region subproblems in vertical and horizontal subspaces, respectively. The trial step is given by the solutions of the pair of trust-region subproblems. Then, the step size is decided by backtracking line search together with filter technique. This is different from traditional trust-region methods and has the advantage of decreasing the number of times that a trust-region subproblem must be resolved in order to determine a new iteration point. Meanwhile, using filter technique instead of merit function to determine a new iteration point can avoid the difficult decisions regarding the choice of penalty parameters. Under some reasonable assumptions, the new method possesses the property of global convergence to the first-order critical point. Preliminary numerical results show the effectiveness of the proposed algorithm.     

An application of the branch,bound, and remember algorithm to a new simple assembly line balancing dataset

The simple assembly line balancing problem (SALBP) is a well-studied NP-complete problem for which a new problem database of generated instances was published in 2013. This paper describes the application of a branch, bound, and remember (BB&R) algorithm using the cyclic best-first search strategy to this new database to produce provably exact solutions for 86% of the unsolved problems in this database. A new backtracking rule to save memory is employed to allow the BB&R algorithm to solve many of the largest problems in the database.     

非线性等式约束优化问题的仿射信赖域方法

提出非线性等式和有界约束优化问题的结合非单调技术的仿射信赖域方法. 结合信赖域方法和内点回代线搜索技术, 每一步迭代转到由一般信赖域子问题产生的回代步中且满足严格内点可行条件. 在合理的假设条件下, 证明了算法的整体收敛性和局部超线性收敛速率. 最后, 数值结果表明了所提供的算法具有有效性.     

An affine scaling trust-region algorithm with interior backtracking technique for solving bound-constrained nonlinear systems

In this paper, we propose a new affine scaling trust-region algorithm in association with nonmonotonic interior backtracking line search technique for solving nonlinear equality systems subject to bounds on variables. The trust-region subproblem is defined by minimizing a squared Euclidean norm of linear model adding the augmented quadratic affine scaling term subject only to an ellipsoidal constraint. By using both trust-region strategy and interior backtracking line search technique, each iterate switches to backtracking step generated by the general trust-region subproblem and satisfies strict interior point feasibility by line search backtracking technique. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.     

Incomplete Dynamic Backtracking for Linear Pseudo-Boolean Problems

Many combinatorial problems can be modeled as 0/1 integer linear programs. Problems expressed in this form are usually solved by Operations Research algorithms, but good results have also been obtained using generalised SAT algorithms based on backtracking or local search, after transformation to pseudo-Boolean form. A third class of SAT algorithm uses non-systematic backtracking to combine constraint propagation with local search-like scalability, at the cost of completeness. This paper describes such an algorithm for pseudo-Boolean models. Experimental results on a variety of problems are encouraging, in some cases yielding improved solutions or performance compared to previous algorithms.     

Combining the Scalability of Local Search with the Pruning Techniques of Systematic Search

Systematic backtracking is used in many constraint solvers and combinatorial optimisation algorithms. It is complete and can be combined with powerful search pruning techniques such as branch-and-bound, constraint propagation and dynamic variable ordering. However, it often scales poorly to large problems. Local search is incomplete, and has the additional drawback that it cannot exploit pruning techniques, making it uncompetitive on some problems. Nevertheless its scalability makes it superior for many large applications. This paper describes a hybrid approach called Incomplete Dynamic Backtracking, a very flexible form of backtracking that sacrifices completeness to achieve the scalability of local search. It is combined with forward checking and dynamic variable ordering, and evaluated on three combinatorial problems: on the n-queens problem it out-performs the best local search algorithms; it finds large optimal Golomb rulers much more quickly than a constraint-based backtracker, and better rulers than a genetic algorithm; and on benchmark graphs it finds larger cliques than almost all other tested algorithms. We argue that this form of backtracking is actually local search in a space of consistent partial assignments, offering a generic way of combining standard pruning techniques with local search.     

Conflict-directed A and its role in model-based embedded systems

Artificial Intelligence has traditionally used constraint satisfaction and logic to frame a wide range of problems, including planning, diagnosis, cognitive robotics and embedded systems control. However, many decision making problems are now being re-framed as optimization problems, involving a search over a discrete space for the best solution that satisfies a set of constraints. The best methods for finding optimal solutions, such as A^*, explore the space of solutions one state at a time. This paper introduces conflict-directed A^*, a method for solving optimal constraint satisfaction problems. Conflict-directed A^* searches the state space in best first order, but accelerates the search process by eliminating subspaces around each state that are inconsistent. This elimination process builds upon the concepts of conflict and kernel diagnosis used in model-based diagnosis [J. de Kleer, B.C. Williams, Diagnosing multiple faults, Artif. Intell. 32(1) (1987) 97-130; J. de Kleer, A. Mackworth, R. Reiter, Characterizing diagnoses and systems, Artif. Intell. 56 (1992) 197-222] and in dependency-directed search [R. Stallman, G.J. Sussman, Forward reasoning and dependency-directed backtracking in a system for computer-aided circuit analysis, Artif. Intell. 9 (1977) 135-196; J. Gaschnig, Performance measurement and analysis of certain search algorithms, Technical Report CMU-CS-79-124, Carnegie-Mellon University, Pittsburgh, PA, 1979; J. de Kleer, B.C. Williams, Back to backtracking: controlling the ATMS, in: Proceedings of AAAI-86, 1986, pp. 910-917; M. Ginsberg, Dynamic backtracking, J. Artif. Intell. Res. 1 (1993) 25-46]. Conflict-directed A^* is a fundamental tool for building model-based embedded systems, and has been used to solve a range of problems, including fault isolation [J. de Kleer, B.C. Williams, Diagnosing multiple faults, Artif. Intell. 32(1) (1987) 97-130], diagnosis [J. de Kleer, B.C. Williams, Diagnosis with behavioral modes, in: Proceedings of IJCAI-89, 1989, pp. 1324-1330], mode estimation and repair [B.C. Williams, P. Nayak, A model-based approach to reactive self-configuring systems, in: Proceedings of AAAI-96, 1996, pp. 971-978], model-compilation [B.C. Williams, P. Nayak, A reactive planner for a model-based executive, in: Proceedings of IJCAI-97, 1997] and model-based programming [M. Ingham, R. Ragno, B.C. Williams, A reactive model-based programming language for robotic space explorers, in: Proceedings of ISAIRAS-01, 2001].     

Approximation of the distribution of convergence times for stochastic global optimisation

How long should we run a stochastic global optimisation algorithm such as simulated annealing? How should we tune such an algorithm? This paper proposes an approach to the study of these questions through successive approximation of a generic stochastic global optimisation algorithm with a sequence of stochastic processes, culminating in a backtracking adaptive search process. Our emerging understanding of backtracking adaptive search can thus be used to study the original algorithm. The first approximation, the averaged range process, has the same expected number of iterations to convergence as the original process.     

Routing by ranking: A link analysis method for the constrained dial-a-ride problem

The dial-a-ride problem involves the dispatching of a fleet of vehicles in order to transport a set of customers from specific pick-up nodes to specific drop-off nodes. Using a modified version of hyperlink-induced topic search (HITS), we characterize hubs as nodes with many out-links to other hubs and calculate a hub score for each pick-up and drop-off node. Ranking the nodes by hub score gives guidance to a backtracking algorithm for efficiently finding feasible solutions to the dial-a-ride problem.     

A gradient projection method for the sparse signal reconstruction in compressive sensing

Many problems arising from machine learning, compressive sensing, linear inverse problem, and statistical inference involve finding sparse solutions to under-determined or ill-conditioned equations. In this paper, a gradient projection method is proposed to recover sparse signal in compressive sensing by solving the nonlinear convex constrained equations. The global convergence is established with the backtracking line search. Preliminary numerical experiments coping with the sparse signal reconstruction in compressive sensing are performed, which show that the proposed method is very effective and stable.     

CFD-based optimization of fuel injection strategies in a diesel engine using an adaptive gradient method

A computationally efficient computational fluid dynamics (CFD)-based optimization method with the capability of finding optimal engine operating conditions with respect to emissions and fuel consumption has been developed. The approach taken uses a steepest descent method for an adaptive cost function, where the line search is performed with a backtracking algorithm. The backtracking algorithm utilizes quadratic and cubic polynomials to accelerate the convergence, and the initial backtracking step employs an adaptive step size mechanism which depends on the steepness of the search direction. The adaptive cost function is based on the penalty method such that the penalty term is stiffened after every line search. The engine simulations are performed with a KIVA-3-based CFD code which is equipped with well-established spray, combustion and emission models. The application of this optimization tool is demonstrated for a non-road, medium-speed DI diesel engine which, for these simulations, utilizes a multi-orifice, asynchronous injection system. It has been demonstrated that this new injection method has a large potential for reducing emissions while maintaining a low fuel consumption. In addition, this optimization approach is computationally very efficient when good enough initial values are available.     

An affine scaling interior trust-region method combining with line search filter technique for optimization subject to bounds on variables

This paper proposes and analyzes an affine scaling trust-region method with line search filter technique for solving nonlinear optimization problems subject to bounds on variables. At the current iteration, the trial step is generated by the general trust-region subproblem which is defined by minimizing a quadratic function subject only to an affine scaling ellipsoidal constraint. Both trust-region strategy and line search filter technique will switch to trail backtracking step which is strictly feasible. Meanwhile, the proposed method does not depend on any external restoration procedure used in line search filter technique. A new backtracking relevance condition is given which is weaker than the switching condition to obtain the global convergence of the algorithm. The global convergence and fast local convergence rate of this algorithm are established under reasonable assumptions. Preliminary numerical results are reported indicating the practical viability and show the effectiveness of the proposed algorithm.     

A Two-Term PRP-Based Descent Method

In this paper, by the use of the project of the PRP (Polak–Ribiére–Polyak) conjugate gradient direction, we develop a PRP-based descent method for solving unconstrained optimization problem. The method provides a sufficient descent direction for the objective function. Moreover, if exact line search is used, the method reduces to the standard PRP method. Under suitable conditions, we show that the method with some backtracking line search or the generalized Wolfe-type line search is globally convergent. We also report some numerical results and compare the performance of the method with some existing conjugate gradient methods. The results show that the proposed method is efficient.     

Improvement heuristic for the flow-shop scheduling problem: An adaptive-learning approach

We propose an improvement-heuristic approach for the general flow-shop problem (n/m/C_max) based on the idea of adaptive learning. The approach employs a one-pass heuristic to give a good starting solution in the search space and uses a weight parameter to perturb the data of the original problem to obtain improved solutions. The weights are then adjusted employing a learning strategy which involves reinforcement and backtracking. The learning is similar to that in neural networks. The random perturbation allows a non-deterministic local search. We apply the improvement-heuristic approach in conjunction with three well-known heuristics in the literature, namely, Palmer’s Slope Index, CDS and NEH. We test our approach on several benchmark problem sets including Taillard’s, Carlier’s, Heller’s and Reeves’. We compare our results to the best-known upper-bound solutions and find that for many problems we match the best-known upper bound. For one problem we discover a new upper bound.     

Affine scaling inexact generalized Newton algorithm with interior backtracking technique for solving bound-constrained semismooth equations

We develop and analyze an affine scaling inexact generalized Newton algorithm in association with nonmonotone interior backtracking line technique for solving systems of semismooth equations subject to bounds on variables. By combining inexact affine scaling generalized Newton with interior backtracking line search technique, each iterate switches to inexact generalized Newton backtracking step to strict interior point feasibility. The global convergence results are developed in a very general setting of computing trial steps by the affine scaling generalized Newton-like method that is augmented by an interior backtracking line search technique projection onto the feasible set. Under some reasonable conditions we establish that close to a regular solution the inexact generalized Newton method is shown to converge locally p-order q-superlinearly. We characterize the order of local convergence based on convergence behavior of the quality of the approximate subdifferentials and indicate how to choose an inexact forcing sequence which preserves the rapid convergence of the proposed algorithm. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases.     

Regularized Newton Methods for Convex Minimization Problems with Singular Solutions

This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC², then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using a backtracking line search, we globalize an inexact regularized Newton method. We show that the unit stepsize is accepted eventually. Limited numerical experiments are presented, which show the practical advantage of the method.