14272034
Optimal Anytime Constrained Simulated Annealing for Constrained Global Optimization
In this paper we propose an optimal anytime version of constrained simulated annealing (CSA) for solving constrained nonlinear programming problems (NLPs). One of the goals of the algorithm is to generate feasible solutions of certain prescribed quality using an average time of the same order of magnitude as that spent by the original CSA with an optimal cooling schedule in generating a solution of similar quality. Here, an optimal cooling schedule is one that leads to the shortest average total number of probes when the original CSA with the optimal schedule is run multiple times until it finds a solution. Our second goal is to design an anytime version of CSA that generates gradually improving feasible solutions as more time is spent, eventually finding a constrained global minimum (CGM). In our study, we have observed a monotonically non-decreasing function relating the success probability of obtaining a solution and the average completion time of CSA, and an exponential function relating the objective target that CSA is looking for and the average completion time. Based on these observations, we have designed CSAAT-ID the anytime CSA with iterative deepening that schedules multiple runs of CSA using a set of increasing cooling schedules and a set of improving objective targets. We then prove the optimality of our schedules and demonstrate experimentally the results on four continuous constrained NLPs. CSAAT-ID can be generalized to solving discrete, continuous, and mixed-integer NLPs, since CSA is applicable to solve problems in these three classes. Our approach can also be generalized to other stochastic search algorithms, such as genetic algorithms, and be used to determine the optimal time for each run of such algorithms.
12984676
Hybrid Evolutionary And Annealing Algorithms For Nonlinear Discrete Constrained Optimization
This paper presents a procedural framework that unifies various mechanisms to look for discrete-neighborhood saddle points in solving discrete constrained optimization problems (DCOPs). Our approach is based on the necessary and sufficient condition on local optimality in discrete space, which shows the one-to-one correspondence between the discrete-space constrained local minima of a problem and the saddle points of the corresponding Lagrangian function. To look for such saddle points, we study various mechanisms for performing ascents of the Lagrangian function in the original-variable subspace and descents in the Lagrange-multiplier subspace. Our results show that CSAEA, a combined constrained simulated annealing and evolutionary algorithm, performs well when using mutations and crossovers to generate trial points and accepting them based on the Metropolis probability. We apply iterative deepening to determine the optimal number of generations in CSAEA and show that its performance is robust with respect to changes in population size. To test the performance of the procedures developed, we apply them to solve some continuous and mixed-integer nonlinear programming (NLP) benchmarks and show that they obtain better results than those of existing algorithms.
16524073
Partitioning of temporal planning problems in mixed space using the theory of extended saddle points
We study the partitioning of temporal planning problems formulated as mixed-integer nonlinear programming problems, develop methods to reduce the search space of partitioned subproblems, and propose algorithms for resolving unsatisfied global constraints. The algorithms are based on the necessary and sufficient extended saddle-point condition for constrained local minimization developed in this paper. When compared with the MIPS planner in solving some PDDL2.1 planning problems, our distributed implementation of MIPS shows significant improvements in time and quality.
2308649
Subgoal ordering and granularity control for incremental planning
In this paper, we study strategies in incremental planning for ordering and grouping subproblems partitioned by the subgoals of a planning problem when each sub-problem is solved by a basic planner. To generate a rich set of partial orders for ordering subproblems, we propose a new ordering algorithm based on a relaxed plan built from the initial state to the goal state. The new algorithm considers both the initial and the goal states and can effectively order subgoals in such a way that greatly reduces the number of invalidations during incremental planning. We have also considered trade-offs between the granularity of the subgoal sets and the complexity of solving the overall planning problem. We show an optimal region of grain size that minimizes the total complexity of incremental planning. We propose an efficient strategy to dynamically adjust the grain size in partitioning in order to operate in this optimal region. We further evaluate a redundant-execution scheme that uses two different subgoal orders in order to improve the quality of the plans generated without greatly sacrificing run-time efficiency. Experimental results on using three basic planners (metric-FF, YAHSP, and LPG-TD-speed) show that our strategies are general for improving the time and quality of each of these planners across various benchmarks
1446328
Solving Large-Scale Nonlinear Programming Problems by Constraint Partitioning
In this paper, we present a constraint-partitioning approach for finding local optimal solutions of large-scale mixed-integer nonlinear programming problems (MINLPs). Based on our observation that MINLPs in many engineering applications have highly structured constraints, we propose to partition these MINLPs by their constraints into subproblems, solve each subproblem by an existing solver, and resolve those violated global constraints across the subproblems using our theory of extended saddle points. Constraint partitioning allows many MINLPs that cannot be solved by existing solvers to be solvable because it leads to easier subproblems that are significant relaxations of the original problem. The success of our approach relies on our ability to resolve violated global constraints efficiently, without requiring exhaustive enumerations of variable values in these constraints. We have developed an algorithm for automatically partitioning a large MINLP in order to minimize the number of global constraints, an iterative method for determining the optimal number of partitions in order to minimize the search time, and an efficient strategy for resolving violated global constraints. Our experimental results demonstrate significant improvements over the best existing solvers in terms of solution time and quality in solving a collection of mixed-integer and continuous nonlinear constrained optimization benchmarks. 
 
Research supported by National Science Foundation Grant IIS 03-12084.
16055310
Step-by-Step Regression: A More Efficient Alternative for Polynomial Multiple Linear Regression in Stream Cube
Facing tremendous and potentially infinite stream data, it is impossible to record them entirely. Thus synopses are required to be generated timely to capture the underlying model for stream management systems. Traditionally, curve fitting through Multiple Linear Regression (MLR) is a powerful and efficient modeling tool. In order to further accelerate its processing efficiency, we propose Step-by-step Regression (SR) as a more efficient alternative. As revealed in experiments, it speeds up for more than 40 times. In addition, inspired by previous work, we integrated SR into cube environment through similar compression technique to perform online analytical processing and mining over data stream. Finally, experiments show that SR not only significantly alleviates the computation pressure on the front ends of data stream management systems, but also results in a much smaller stream cube for on line analysis and real-time surveillance.
33634754
Reconstruction and Fusion of Multi-modality Spinal Images
53249448
Efficiently generating test vectors with state pruning
14759214
Real-coded ECGA for economic dispatch
In this paper, we propose a new approach that consists of the extended compact genetic algorithm (ECGA) and split-on-demand (SoD), an adaptive discretization technique, to economic dispatch (ED) problems with nonsmooth cost functions. ECGA is designed for handling problems with decision variables of the discrete type, while the decision variables of ED problems are oftentimes real numbers. Thus, in order to employ ECGA to tackle ED problems, SoD is utilized for discretizing the continuous decision variables and works as the interface between ECGA and the ED problem. Furthermore, ED problems in practice are usually hard for traditional mathematical programming methodologies because of the equality and inequality constraints. Hence, in addition to integrating ECGA and SoD, in this study, we devise a repair operator specifically for making the infeasible solutions to satisfy the equality constraint. To examine the performance and effectiveness, we apply the proposed framework to two different-sized ED problems with nonsmooth cost function considering the valve-point effects. The experimental results are compared to those obtained by various evolutionary algorithms and demonstrate that handling ED problems with the proposed framework is a promising research direction.
712
Rational Radial Distortion Models with Analytical Undistortion Formulae
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial distortion is to find a radial distortion model that allows easy undistortion as well as satisfactory accuracy. This paper presents a new class of rational radial distortion models with easy analytical undistortion formulae. Experimental results are presented to show that with this class of rational radial distortion models, satisfactory and comparable accuracy is achieved.
18226391
Rough-Set Multiple-Criteria ABC Analysis
Multiple-criteria ABC (MCABC) analysis is conducted using a dominance-based rough set approach. ABC analysis, a well-known technique for inventory planning and control, divides stock-keeping units (SKUs) into three classes according to annual dollar usage. But MCABC analysis offers more managerial flexibility by including other criteria, such as lead time and criticality, in the classification of SKUs. The objective of this paper is to propose an MCABC method that uses the dominance-based rough set approach to generate linguistic rules that represent a decision-maker's preferences based on the classification of a test data set. These linguistic rules are then used to classify all SKUs. A case study demonstrates that the procedure is feasible.