Heuristic Minimization Research Articles

Packet Loss Reduction During Rerouting

When a network failure is detected by an IP router, its routing table is updated for all affected routing entries. The packet loss resulting from this event depends on the network traffic associated with the updated routing table entries. In this paper, we model this process, define packet loss minimization heuristics relying on network traffic prediction models, and show by simulation that the resulting packet loss can be reduced compared to the default routing table update process.

Heuristics for makespan minimization on parallel batch processing machines with unequal job ready times

This research aims at minimizing the makespan of a set of identical batch processing machines arranged in parallel. Each job is defined by its processing time, ready time, and size. Each machine can process several jobs simultaneously as long as the machine capacity is not exceeded. The batch processing and ready times depend upon the batch composition. The batch processing time is equal to the longest processing job in the batch, and the batch ready time is equal to the largest ready time among those jobs in the batch. The problem under study is NP-hard. Consequently, a constructive heuristic is proposed and its performance with respect to solution quality and computational cost is compared against other solution approaches found in the literature. The computational experiments on a set of randomly generated instances show that the performance of the proposed heuristic is competitive with respect to solution quality and requires little computational cost.

A heuristic iterated-subspace minimization method with pattern search for unconstrained optimization

Recently, an increasing attention was paid on different procedures for an unconstrained optimization problem when the information of the first derivatives is unavailable or unreliable. In this paper, we consider a heuristic iterated-subspace minimization method with pattern search for solving such unconstrained optimization problems. The proposed method is designed to reduce the total number of function evaluations for the implementation of high-dimensional problems. Meanwhile, it keeps the advantages of general pattern search algorithm, i.e., the information of the derivatives is not needed. At each major iteration of such a method, a low-dimensional manifold, the iterated subspace, is constructed. And an approximate minimizer of the objective function in this manifold is then determined by a pattern search method. Numerical results on some classic test examples are given to show the efficiency of the proposed method in comparison with a conventional pattern search method and a derivative-free method.

Path Summaries and Path Partitioning in Modern XML Databases

XML path summaries are compact structures representing all the simple parent-child paths of an XML document. Such paths have also been used in many works as a basis for partitioning the document’s content in a persistent store, under the form of path indices or path tables. We revisit the notions of path summaries and path-driven storage model in the context of current-day XML databases. This context is characterized by complex queries, typically expressed in an XQuery subset, and by the presence of efficient encoding techniques such as structural node identifiers. We review a path summary’s many uses for query optimization, and given them a common basis, namely relevant paths. We discuss summary-based tree pattern minimization and present some efficient summary-based minimization heuristics. We consider relevant path computation and provide a time- and memory-efficient computation algorithm. We combine the principle of path partitioning with the presence of structural identifiers in a simple path-partitioned storage model, which allows for selective data access and efficient query plans. This model improves the efficiency of twig query processing up to two orders of magnitude over the similar tag-partitioned indexing model. We have implemented the path-partitioned storage model and path summaries in the XQueC compressed database prototype [8]. We present an experimental evaluation of a path summary’s practical feasibility and of tree pattern matching in a path-partitioned store.

Efficient binary reconstruction for non-destructive evaluation using gammagraphy

The localization and the sizing of 3D flaws within a homogeneous metallic medium is a major task for non-destructive evaluation (NDE). This paper addresses the problem of the reconstruction of such flaws using an efficient binary algorithm. Basically, the method rests on the fact that a simple binary constraint suffices for an accurate and robust reconstruction in the context of NDE. A heuristic minimization, computationally attractive, is designed in order to provide fast reconstructions. The proposed algorithm is compared with standard binary (the iterated conditional mode algorithm) and non-binary (penalized approach with convex potential Gibbs random fields) reconstruction techniques.

Heuristics for Area Minimization in LUT-Based FPGA Technology Mapping

In this paper, an iterative technology-mapping tool called IMap is presented. It supports depth-oriented (area is a secondary objective), area-oriented (depth is a secondary objective), and duplication-free mapping modes. The edge-delay model (as opposed to the more commonly used unit-delay model) is used throughout. Two new heuristics are used to obtain area reductions over previously published methods. The first heuristic predicts the effects of various mapping decisions on the area of the final solution, and the second heuristic bounds the depth of the mapping solution at each node. In depth-oriented mode, when targeting five lookup tables (LUTs), IMap obtains depth optimal solutions that are 44.4%, 19.4%, and 5% smaller than those produced by FlowMap, CutMap, and DAOMap, respectively. Targeting the same LUT size in area-oriented mode, IMap obtains solutions that are 17.5% and 9.4% smaller than those produced by duplication-free mapping and ZMap, respectively. IMap is also shown to be highly efficient. Runtime improvements of between 2.3times and 82times are obtained over existing algorithms when targeting five LUTs. Area and runtime results comparing IMap to the other mappers when targeting four and six LUTs are also presented

Unmanned Aerial Vehicle Path Following for Target Observation in Wind

This work provides flight-path geometry, guidance laws, and synchronous camera angles to observe a ground target from an unmanned aerial vehicle. The observation of the target is affected by wind, aircraft performance, and camera limits. Analytic expressions are derived for paths that result in constant line-of-sight orientation of the target relative to the aircraft body frame. Using minimal heuristics, a guidance law based on “good helmsman” behavior is developed and implemented, and stability of its integration with aircraft dynamics is assessed. An observer estimates wind data, which are used to orient path geometry about the target. Results are demonstrated in high-fidelity simulation. Nomenclature a = helmsman sensitivity parameter c(·) = cos(·) d = distance Fb = body-fixed frame Fs = Serret‐Frenet frame g = gravity constant r = radius s = arclength position along desired path s(·) = sin(·) t(·) = tan(·)

CB3: An Adaptive Error Function for Backpropagation Training

Effective backpropagation training of multi-layer perceptrons depends on the incorporation of an appropriate error or objective function. Classification-Based (CB) error functions are heuristic approaches that attempt to guide the network directly to correct pattern classification rather than using common error minimization heuristics, such as Sum-Squared Error (SSE) and Cross-Entropy (CE), which do not explicitly minimize classification error. This work presents CB3, a novel CB approach that learns the error function to be used while training. This is accomplished by learning pattern confidence margins during training, which are used to dynamically set output target values for each training pattern. On 11 applications, CB3 significantly outperforms previous CB error functions, and also reduces average test error over conventional error metrics using 0---1 targets without weight decay by 1.8%, and by 1.3% over metrics with weight decay. The CB3 also exhibits lower model variance and tighter mean confidence interval.

Classification-based objective functions

Backpropagation, similar to most learning algorithms that can form complex decision surfaces, is prone to overfitting. This work presents classification-based objective functions, an approach to training artificial neural networks on classification problems. Classification-based learning attempts to guide the network directly to correct pattern classification rather than using common error minimization heuristics, such as sum-squared error (SSE) and cross-entropy (CE), that do not explicitly minimize classification error. CB1 is presented here as a novel objective function for learning classification problems. It seeks to directly minimize classification error by backpropagating error only on misclassified patterns from culprit output nodes. CB1 discourages weight saturation and overfitting and achieves higher accuracy on classification problems than optimizing SSE or CE. Experiments on a large OCR data set have shown CB1 to significantly increase generalization accuracy over SSE or CE optimization, from 97.86% and 98.10%, respectively, to 99.11%. Comparable results are achieved over several data sets from the UC Irvine Machine Learning Database Repository, with an average increase in accuracy from 90.7% and 91.3% using optimized SSE and CE networks, respectively, to 92.1% for CB1. Analysis indicates that CB1 performs a fundamentally different search of the feature space than optimizing SSE or CE and produces significantly different solutions.

HSM2: A new heuristic state minimization algorithm for finite state machine

This paper proposes a heuristic state minimization algorithm (HSM2) for finite state machines (FSM). HSM2 focuses on the generation and adjustment of the closed cover. First an initial closed cover is generated by heuristically selecting proper maximal compatibles to satisfy all the covering and closure conditions, and then it is adjusted to be a minimal or near minimal closed cover by heuristically removing repeated states. Experimental results show that the algorithm is faster and obtains better or the same solutions compared with conventional methods.

Efficient optimization by modifying the objective function: applications to timing-driven VLSI layout

When minimizing a given objective function is challenging because of, for example, combinatorial complexity or points of nondifferentiability, one can apply more efficient and easier-to-implement algorithms to modified versions of the function. In the ideal case, one can employ known algorithms for the modified function that have a thorough theoretical and empirical record and for which public implementations are available. The main requirement here is that minimizers of the objective function do not change much through the modification, i.e., the modification must have a bounded effect on the quality of the solution. Review of classic and recent placement algorithms suggests a dichotomy between approaches that either: (a) heuristically minimize potentially irrelevant objective function (e.g., VLSI placement with quadratic wirelength) motivated by the simplicity and speed of a standard minimization algorithm; or (b) devise elaborate problem-specific minimization heuristics for more relevant objective functions (e.g., VLSI placement with linear wirelength). Smoothness and convexity of the objective functions typically enable efficient minimization. If either characteristic is not present in the objective function, one can modify and/or restrict the objective to special values of parameters to provide the missing properties. After the minimizers of the modified function are found, they can be further improved with respect to the original function by fast local search using only function evaluations. Thus, it is the modification step that deserves most attention. In this paper, we approximate convex nonsmooth continuous functions by convex differentiable functions which are parameterized by a scalar /spl beta/>0 and have convenient limit behavior as /spl beta//spl rarr/0. This allows the use of Newton-type algorithms for minimization and, for standard numerical methods, translates into a tradeoff between solution quality and speed. We prove that our methods apply to arbitrary multivariate convex piecewise-linear functions that are widely used in synthesis and analysis of electrical networks. The utility of our approximations is particularly demonstrated for wirelength and nonlinear delay estimations used by analytical placers for VLSI layout, where they lead to more solvable problems than those resulting from earlier comparable approaches [29]. For a particular delay estimate, we show that, while convexity is not straightforward to prove, it holds for a certain range of parameters, which, luckily, are representative of real-world technologies.

Verification of State/Event Systems by Quotienting

A rather new approach towards compositional verification of concurrent systems is the quotient technique, where components are gradually removed from the concurrent system while transforming the specification accordingly. When the intermediate specifications can be kept small using heuristics for minimization, the state explosion problem<br />is avoided and there are already promising experimental results for systems with an interleaving semantics, including real-time systems. This paper extends the quotienting approach to deal with a synchronous framework in the shape of state/event systems. <br />A state/event system is a concurrent system with a set of interdependent components operating synchronously according to stimuli (input events) provided by an environment while producing output events in return for the environment. A compositional modal logic M suitable for expressing general safety and liveness properties subsystems is introduced. A quotient construction for building components from a state/event system into the specification is presented and heuristics for minimizing formulae are proposed. The techniques are demonstrated on an example. The correctness of the techniques are justified by proofs in an appendix.

Simulated Annealing Search Algorithm for the Determination of Activation Energies and Arrhenius Prefactors from Limited Experimental Kinetic Data

We present a kinetics search algorithm that can be used to determine the activation energies and Arrhenius prefactors for the elementary reaction steps in an overall reaction scheme from a small set of concentration versus time data. The algorithm assumes the availability of a small set of experimental kinetic data for species concentrations for at least two different temperatures. The search algorithm is based upon the minimization of a so-called error function that is the squared difference between the experimentally measured species concentrations and species concentrations that are predicted from a guessed set of activation energies and Arrhenius prefactors that govern each of the elementary steps in the reaction mechanism. The activation energy search algorithm presented in this work is based on the Simulated Annealing heuristic minimization algorithm. We test the search algorithm on three types of chemical reactions: a consecutive reaction with a reversible step, a parallel reaction, and a represen...

Assessment of boolean minimization in symbolic empirical learning

We report research on the assessment of Boolean minimization in symbolic empirical learning. We view training examples as logical expressions and implement Boolean Minimization (BM) heuristics to optimize input and to learn symbolic knowledge rules. We base our work on a B M learning system called B M L. B M L includes three components : a preprocessing, a B M, and a postprocessing component. The system incorporates Espresso-II, a popular system in very large scale integration design. The preprocessing and postprocessing components include utilities that support preparation of training exampleson the one hand and assessment of learned output on the other. We test B M L using 10 different domains and compare performance with C4 . 5 , AQ15 , NewId , and CN2 using classification accuracy and rule quality statistics. We conclude by reviewing results and by discussing areas for future research .

A genetic algorithm for RKRO minimization

We show that there is a close relation between Ordered Kronecker Functional Decision Diagrams (OKFDDs) and two-level AND/EXOR expressions. This relation, together with efficient OKFDD algorithms, can be utilized for exact and heuristic minimization of these AND/EXOR expressions, called Reduced Kronecker Expressions (RKROs). RKROs depend on the Variable Ordering (VO) and Decomposition Type List (DTL) of the corresponding OKFDD. We propose several (exact and heuristical) minimization algorithms for fixed VO and perform experimental results. A Genetic Algorithm (GA) is applied to minimize RKROs with respect to VO and DTL in parallel. We applied our GA to a large set of benchmark functions to show the efficiency of our approach.

Fast OFDD-based minimization of fixed polarity Reed-Muller expressions

We present methods to minimize fixed polarity Reed-Muller expressions (FPRMs), i.e., two-level fixed polarity AND/EXOR canonical representations of Boolean functions, using ordered functional decision diagrams (OFDDs). We investigate the close relation between both representations and use efficient algorithms on OFDDs for exact and heuristic minimization of FPRMs. In contrast to previously published methods, our algorithm can also handle circuits with several outputs. Experimental results on large benchmarks are given to show the efficiency of our approach.

Compositional Model Checking of Real Time Systems

A major problem in applying model checking to finite-state systems<br />is the potential combinatorial explosion of the state space arising from<br />parallel composition. Solutions of this problem have been attempted for<br />practical applications using a variety of techniques. Recent work by Andersen<br />[And95] proposes a very promising compositional model checking<br />technique, which has experimentally been shown to improve results obtained<br />using Binary Decision Diagrams.<br />In this paper we make Andersen's technique applicable to systems described<br />by networks of timed automata. We present a quotient construction,<br />which allows timed automata components to be gradually moved from<br />the network expression into the specification. The intermediate specifications<br />are kept small using minimization heuristics suggested by Andersen.<br />The potential of the combined technique is demonstrated using a prototype<br />implemented in CAML.

Heuristic minimization of multiple-valued relations

An approach to minimization that is based on a state-of-the-art paradigm for the two-level minimization of functions is presented. Some special properties of relations, in contrast to functions, which must be carefully considered in realizing a high-quality procedure for solving the minimization problem are clarified. An efficient heuristic method to find an optimal sum-of-products representation for a multiple-valued relation is proposed and implemented in the program GYOCRO. It uses multiple-valued decision diagrams (MDDs) to represent the characteristic functions for the relations. Experimental results are presented and compared with previous exact and heuristic Boolean relation minimizers to demonstrate the effectiveness of the proposed method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Heuristic minimization of Boolean relations using testing techniques

A Boolean relation is a one-to-many multioutput Boolean mapping and is a generalization of incompletely specified logic functions. Boolean relations arise in several contexts (for instance, in a finite state machine with sets of equivalent states). Minimization of Boolean relations is important from the point of view of synthesis, especially synthesis for testability. A fast heuristic procedure for finding an optimal sum-of-products representation for a function compatible with a Boolean relation is described. Starting with an initial function compatible with the relation, a process of iterative logic improvement based on test generation techniques is used to derive a minimal function.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Boolean function minimization in the class of disjunctive normal forms

The survey focuses on minimization of boolean functions in the class of disjunctive normal forms (d.n.f.s) and covers the publications from 1953 to 1986. The main emphasis is on the mathematical direction of research in boolean function minimization: bounds of parameters of boolean functions and algorithmic difficulties of minimal d.n.f. synthesis). The survey also presents a classification of minimization algorithms and gives some examples of minimization heuristics with their efficiency bounds.