Slope constrained material design

We investigate a class of constrained inverse homogenization problems. The complexity of the topological solution is restricted using slope constraint regularization. We show existence of the solution for the inverse optimization problem in function space and outline a converging approximation scheme. We demonstrate how a proper numerical implementation can lead to a stable material design approach. We finally describe results for a comprehensive set of numerical test cases.     

Motion constraint

In this paper, we propose a hybrid postural control approach taking advantage of data-driven and goal-oriented methods while overcoming their limitations. In particular, we take advantage of the latent space characterizing a given motion database. We introduce a motion constraint operating in the latent space to benefit from its much smaller dimension compared to the joint space. This allows its transparent integration into a Prioritized Inverse Kinematics framework. If its priority is high the constraint may restrict the solution to lie within the motion database space. We are more interested in the alternate case of an intermediate priority level that channels the postural control through a spatiotemporal pattern representative of the motion database while achieving a broader range of goals. We illustrate this concept with a sparse database of large range full-body reach motions.     

An iterated “hyperplane exploration” approach for the quadratic knapsack problem

The quadratic knapsack problem (QKP) is a well-known combinatorial optimization problem with numerous applications. Given its NP-hard nature, finding optimal solutions or even high quality suboptimal solutions to QKP in the general case is a highly challenging task. In this paper, we propose an iterated “hyperplane exploration” approach (IHEA) to solve QKP approximately. Instead of considering the whole solution space, the proposed approach adopts the idea of searching over a set of hyperplanes defined by a cardinality constraint to delimit the search to promising areas of the solution space. To explore these hyperplanes efficiently, IHEA employs a variable fixing strategy to reduce each hyperplane-constrained sub-problem and then applies a dedicated tabu search procedure to locate high quality solutions within the reduced solution space. Extensive experimental studies over three sets of 220 QKP instances indicate that IHEA competes very favorably with the state-of-the-art algorithms both in terms of solution quality and computing efficiency. We provide additional information to gain insight into the key components of the proposed approach.     

Application of fuzzy goal programming approach to multi-objective linear fractional inventory model

In this paper, we propose a model and solution approach for a multi-item inventory problem without shortages. The proposed model is formulated as a fractional multi-objective optimisation problem along with three constraints: budget constraint, space constraint and budgetary constraint on ordering cost of each item. The proposed inventory model becomes a multiple criteria decision-making (MCDM) problem in fuzzy environment. This model is solved by multi-objective fuzzy goal programming (MOFGP) approach. A numerical example is given to illustrate the proposed model.     

Bi-dimensional knapsack problems with one soft constraint

In this paper, we consider bi-dimensional knapsack problems with a soft constraint, i.e., a constraint for which the right-hand side is not precisely fixed or uncertain. We reformulate these problems as bi-objective knapsack problems, where the soft constraint is relaxed and interpreted as an additional objective function. In this way, a sensitivity analysis for the bi-dimensional knapsack problem can be performed: The trade-off between constraint satisfaction, on the one hand, and the original objective value, on the other hand, can be analyzed. It is shown that a dynamic programming based solution approach for the bi-objective knapsack problem can be adapted in such a way that a representation of the nondominated set is obtained at moderate extra cost. In this context, we are particularly interested in representations of that part of the nondominated set that is in a certain sense close to the constrained optimum in the objective space. We discuss strategies for bound computations and for handling negative cost coefficients, which occur through the transformation. Numerical results comparing the bi-dimensional and bi-objective approaches are presented.     

快速判定几何约束奇异性的切面扰动法

针对冗余奇异和分支奇异的判定问题,提出一种新的切面扰动的判定方法.该方法将奇异的雅可比矩阵分为独立构型空间和奇异空间,变量沿独立构型空间的切面扰动,计算更新的雅克比矩阵的秩,依据秩亏的变化可以快速、稳定地判定约束奇异性.该算法克服了残量扰动法的数值迭代、计算量大和不稳定的缺点,并且在参数化特征造型系统InteSolid中得到验证.     

Consistency techniques for continuous constraints

We consider constraint satisfaction problems with variables in continuous, numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.Our approach is based on approximating regions of feasible solutions by 2 ^k -trees, a representation commonly used in computer vision and image processing. We give simple and stable algorithms for computing labelings with arbitrary degrees of consistency. The algorithms can process constraints and solution spaces of arbitrary complexity, but with a fixed maximal resolution.Previous work has shown that when constraints are convex and binary, path-consistency is sufficient to ensure global consistency. We show that for continuous domains, this result can be generalized to ternary and in fact arbitrary n-ary constraints using the concept of (3,2)-relational consistency. This leads to polynomial-time algorithms for computing globally consistent labelings for a large class of constraint satisfaction problems with continuous variables.     

Using continuous features in the maximum entropy model

We investigate the problem of using continuous features in the maximum entropy (MaxEnt) model. We explain why the MaxEnt model with the moment constraint (MaxEnt-MC) works well with binary features but not with the continuous features. We describe how to enhance constraints on the continuous features and show that the weights associated with the continuous features should be continuous functions instead of single values. We propose a spline-based solution to the MaxEnt model with non-linear continuous weighting functions and illustrate that the optimization problem can be converted into a standard log-linear model at a higher-dimensional space. The empirical results on two classification tasks that contain continuous features are reported. The results confirm our insight and show that our proposed solution consistently outperforms the MaxEnt-MC model and the bucketing approach with significant margins.     

Efficient synthesis of out-of-core algorithms using a nonlinear optimization solver

We address the problem of efficient out-of-core code generation for a special class of imperfectly nested loops encoding tensor contractions arising in quantum chemistry computations. These loops operate on arrays too large to fit in physical memory. The problem involves determining optimal tiling of loops and placement of disk I/O statements. This entails a search in an explosively large parameter space. We formulate the problem as a nonlinear optimization problem and use a discrete constraint solver to generate optimized out-of-core code. The solution generated using the discrete constraint solver consistently outperforms other approaches by up to a factor of four. Measurements on sequential and parallel versions of the generated code demonstrate the effectiveness of the approach.     

An associate constraint network approach to extract multi-lingual information for crime analysis

International crime and terrorism have drawn increasing attention in recent years. Retrieving relevant information from criminal records and suspect communications is important in combating international crime and terrorism. However, most of this information is written in languages other than English and is stored in various locations. Information sharing between countries therefore presents the challenge of cross-lingual semantic interoperability. In this work, we propose a new approach – the associate constraint network – to generate a cross-lingual concept space from a parallel corpus, and benchmark it with a previously developed technique, the Hopfield network. The associate constraint network is a constraint programming based algorithm, and the problem of generating the cross-lingual concept space is formulated as a constraint satisfaction problem. Nodes and arcs in an associate constraint network represent extracted terms from parallel corpora and their associations. Constraints are defined for the nodes in the associate constraint network, and node consistency and network satisfaction are also defined. Backmarking is developed to search for a feasible solution. Our experimental results show that the associate constraint network outperforms the Hopfield network in precision, recall and efficiency. The cross-lingual concept space that is generated with this method can assist crime analysts to determine the relevance of criminals, crimes, locations and activities in multiple languages, which is information that is not available in traditional thesauri and dictionaries.     

A constraint-based approach to spatiotemporal reasoning

We introduce a form of spatiotemporal reasoning that uses homogeneous representations of time and the three dimensions of space. The basis of our approach is Allen's temporal logic on the one hand and general constraint satisfaction algorithms on the other, where we present a new view of constraint reasoning to cope with the affordances of spatiotemporal reasoning as introduced here. As a realization for constraint reasoning, we suggest a massively parallel implementation in form of Boltzmann machines.     

Discrete optimisation based on the combined use of reinforcement and constraint satisfaction schemes

A new approach is presented for finding near-optimal solutions to discrete optimisation problems that is based on the cooperation of two modules: an optimisation module and a constraint satisfaction module. The optimisation module must be able to search the problem state space through an iterative process of sampling and evaluating the generated samples. To evaluate a generated point, first a constraint satisfaction module is employed to map that point to another one satisfying the problem constraints, and then the cost of the new point is used as the evaluation of the original one. The scheme that we have adopted for testing the effectiveness of the method uses a reinforcement learning algorithm in the optimisation module and a general deterministic constraint satisfaction algorithm in the constraint satisfaction module. Experiments using this scheme for the solution of two optimisation problems indicate that the proposed approach is very effective in providing feasible solutions of acceptable quality.     

Automatic sensor placement from vision task requirements

The problem of automatically generating the possible camera locations for observing an object is defined, and an approach to its solution is presented. The approach, which uses models of the object and the camera, is based on meeting the requirements that: the spatial resolution be above a minimum value, all surface points be in focus, all surfaces lie within the sensor field of view and no surface points be occluded. The approach converts each sensing requirement into a geometric constraint on the sensor location, from which the three-dimensional region of viewpoints that satisfies that constraint is computed. The intersection of these regions is the space where a sensor may be located. The extension of this approach to laser-scanner range sensors is also described. Examples illustrate the resolution, focus, and field-of-view constraints for two vision tasks     

Modeling and solving the steelmaking and casting scheduling problem

We propose a general model for the problem of planning and scheduling steelmaking and casting activities obtained by combining common features and constraints of the operations from a real plant and the literature. For tackling the problem, we develop a simulated annealing approach based on a solution space made of job permutations, which uses as submodule a chronological constructive procedure that assigns processing times and resources to jobs. Our technique, properly tuned in a statistically principled way, is able to find good solutions for a large range of different settings and horizons. In addition, it outperforms both a greedy procedure and a constraint‐based solver developed for comparison purposes on almost all instances. Finally, we have collected several real‐world instances that we make available on the web along with the solution validator and our best results.     

稳定化的有限频段H∞控制及有限频段跟踪问题

基于GKYP引理的动态输出反馈设计,未保证设计后闭环系统的稳定性。针对以小增益作为指标的有限频段动态输出反馈问题,在不增加新变量的前提下,增加稳定性约束,使得设计后的闭环系统渐近稳定且满足有限频段性能指标。针对增加约束后难以找到可行解的情况,基于零空间条件的不惟一性,补充了另一种零空间条件,从而扩大了问题的可行域。将改进后的方法应用于有限频段跟踪问题的研究,通过仿真例子验证,有限频段动态输出反馈虽然存在保守性,但在合理选择基矩阵R的情况下,仍然可以使得其保守性小于传统的全频段最优H∞控制的保守性。     

StrSolve: solving string constraints lazily

Reasoning about strings is becoming a key step at the heart of many program analysis and testing frameworks. Stand-alone string constraint solving tools, called decision procedures, have been the focus of recent research in this area. The aim of this work is to provide algorithms and implementations that can be used by a variety of program analyses through a well-defined interface. This separation enables independent improvement of string constraint solving algorithms and reduces client effort. We present StrSolve, a decision procedure that reasons about equations over string variables. Our approach scales well with respect to the size of the input constraints, especially compared to other contemporary techniques. Our approach performs an explicit search for a satisfying assignment, but constructs the search space lazily based on an automata representation. We empirically evaluate our approach by comparing it with four existing string decision procedures on a number of tasks. We find that our prototype is, on average, several orders of magnitude faster than the fastest existing approaches, and present evidence that our lazy search space enumeration accounts for most of that benefit.     

Robot arm reaching through neural inversions and reinforcement learning

We present a neural method that computes the inverse kinematics of any kind of robot manipulators, both redundant and non-redundant. Inverse kinematics solutions are obtained through the inversion of a neural network that has been previously trained to approximate the manipulator forward kinematics. The inversion provides difference vectors in the joint space from difference vectors in the workspace. Our differential inverse kinematics (DIV) approach can be viewed as a neural network implementation of the Jacobian transpose method for arm kinematic control that does not require previous knowledge of the arm forward kinematics. Redundancy can be exploited to obtain a special inverse kinematic solution that meets a particular constraint (e.g. joint limit avoidance) by inverting an additional neural network The usefulness of our DIV approach is further illustrated with sensor-based multilink manipulators that learn collision-free reaching motions in unknown environments. For this task, the neural controller has two modules: a reinforcement-based action generator (AG) and a DIV module that computes goal vectors in the joint space. The actions given by the AG are interpreted with regard to those goal vectors.     

Bounded approximate decentralised coordination via the max-sum algorithm

In this paper we propose a novel approach to decentralised coordination, that is able to efficiently compute solutions with a guaranteed approximation ratio. Our approach is based on a factor graph representation of the constraint network. It builds a tree structure by eliminating dependencies between the functions and variables within the factor graph that have the least impact on solution quality. It then uses the max-sum algorithm to optimally solve the resulting tree structured constraint network, and provides a bounded approximation specific to the particular problem instance. In addition, we present two generic pruning techniques to reduce the amount of computation that agents must perform when using the max-sum algorithm. When this is combined with the above mentioned approximation algorithm, the agents are able to solve decentralised coordination problems that have very large action spaces with a low computation and communication overhead. We empirically evaluate our approach in a mobile sensor domain, where mobile agents are used to monitor and predict the state of spatial phenomena (e.g., temperature or gas concentration). Such sensors need to coordinate their movements with their direct neighbours to maximise the collective information gain, while predicting measurements at unobserved locations. When applied in this domain, our approach is able to provide solutions which are guaranteed to be within 2% of the optimal solution. Moreover, the two pruning techniques are extremely effective in decreasing the computational effort of each agent by reducing the size of the search space by up to 92%.     

Optimal control problems with a continuous inequality constraint on the state and the control

We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved.     

Solution of a non-convex optimization arising in PI/PID control design

As shown by Åström et al. (Automatica 34(5) (1998) 585), the problem of designing a stabilizing PI controller based on minimizing integral of error associated with step load disturbance while subjecting to constraints on maximum sensitivity and/or complementary sensitivity amounts to that of finding the maximum allowable integral gain. The latter problem is a non-convex optimization problem whose true solution cannot be obtained with a guarantee by a gradient-based search algorithm. In this paper, we present a novel and effective approach to solve such a non-convex optimization problem. Our approach is based on regarding an equality constraint set on controller gain parameters as a two-dimensional value set in the complex plane and using the notion of principal points to characterize its boundary. With this treatment, we are able to derive analytical expressions for describing the boundary of an equality constraint set in the controller gain plane. These expressions allow one to trace the boundaries of equality constraint sets using an existing path-following algorithm. Hence, by constructing the boundary of the feasible domain in the controller gain space, the maximum allowable integral gain can be obtained. In addition to having the ability to obtain global optimal solution, our approach can handle sensitivity and complementary sensitivity constraints simultaneously without using an iterative procedure.