Comments on “An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems” [Comput. Ind. Eng. 48 (2005) 409–425]

An effective hybrid optimization approach proposed by Xia and Wu [Xia, W. J., Wu, Z. M. (2005). An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems. Computers & Industrial Engineering, 48, 409–425] was recently published in Computers & Industrial Engineering journal to solve the multi-objective flexible job-shop scheduling problems. In this work, comments and suggestions are given to the recently published approach of Xia and Wu (2005). The comments like centralized the problem formulation and experimental comparison. The modification of the problem formulation is suggested in this work.     

Offline variants of the “lion and man” problem: —Some problems and techniques for measuring crowdedness and for safe path planning—

Consider the following safe path planning problem: Given a set of trajectories (paths) of k point robots with maximum unit speed in a bounded region over a (long) time interval [0,T], find another trajectory (if it exists) subject to the same maximum unit speed limit, that avoids (that is, stays at a safe distance of) each of the other k trajectories over the entire time interval. We call this variant the continuous model of the safe path planning problem. The discrete model of this problem is: Given a set of trajectories (paths) of k point robots in a graph over a (long) time interval 0,1,2,…,T, find a trajectory (path) for another robot, that avoids each of the other k at any time instant in the given time interval.We introduce the notions of the avoidance number of a region, and that of a graph, respectively, as the maximum number of trajectories which can be avoided in the region (respectively, graph). We give the first estimates on the avoidance number of the n×n grid G_n, and also devise an efficient algorithm for the corresponding safe path planning problem in arbitrary graphs. We then show that our estimates on the avoidance number of G_n can be extended for the avoidance number of a bounded (fat) region. In the final part of our paper, we consider other related offline questions, such as the maximum number of men problem and the spy problem.     

H∞ identification of “soft” uncertainty models

The paper investigates the problem of identifying uncertainty models of causal, SISO, LTI, discrete-time, BIBO stable, unknown systems, using frequency domain measurements corrupted by Gaussian noise of known covariance. Additive uncertainty models are looked for, consisting of a nominal model and an additive dynamic perturbation accounting for the modeling error. The nominal model is chosen within a class of affinely parametrized models with transfer function of given (possibly low) order. An estimate of the parameters minimizing the H_∞ modeling error is obtained by minimizing an upper bound of the worst-case (with respect to the modeling error) second moment of the estimation error. Then, a bound in the frequency domain guaranteeing to include, with probability α, the frequency response error between the estimated nominal model and the unknown system is derived.     

“ExTherm 2 ”: An interactive support package of experimental and computational thermodynamics

“ExTherm 2” shows clear advances over ExTHERM as presented in [J. Tomiska, CALPHAD 26 (2002) 143–154]: All three parts have been improved in powerfulness, comfort, and interactive work. Especially the module cM3_ is now designed for interactive evaluation by means of an overall best fit technique applicable on experimental data from calorimetric and vapor pressure measurements as well as from measurements on the electromotive force (emf) on all types of metal alloy. The new data bank module cM1_(ETD/ ExP/ PhD) is an easy-to-handle tool for interactive work in many applications in physical chemistry. The data bank ETD has been enlarged by a series of new molar mixing properties of all types of metal alloy systems, and two sub-modules are added: The first tool, ExP, makes extrapolating binary data to a high number of ternary systems of all types of metal alloy possible. And the second tool, PhD, is designed for simple interactive computations on binary phase diagrams, especially for education items.     

Comparing computer-supported dynamic modeling and ‘paper & pencil’ concept mapping technique in students’ collaborative activity

This study aims at highlighting the collaborative activity of two high school students (age 14) in the cases of modeling the complex biological process of plant growth with two different tools: the ‘paper & pencil’ concept mapping technique and the computer-supported educational environment ‘ModelsCreator’. Students’ shared activity in both cases is carried out in the presence of a facilitator providing technical as well as cognitive support when necessary. The objective of the study is to highlight the ways in which the collaborating students are engaged in the plant growth modeling activity in the two cases and also identify the activity’s similar and different aspects in each one. Our analysis is carried out on two complementary axes, the first of which concerns the process of collaboratively creating a plant growth model with each different tool, while the second has to do with the students’ conceptualizations of the biological aspect of the modeling task in each case. A two-level analytic tool for the modeling process has been derived within the theoretical framework of ‘activity theory’ on the basis of the OCAF scheme for basic modeling operations and the scheme of Stratford et al. [Stratford, S. J., Krajcik, J., & Soloway, E. (1998). Secondary students’ dynamic modeling processes: analyzing, reasoning about, synthesizing, and testing models of stream ecosystems. Journal of Science Education and Technology, 7(3), 215–234.] for higher-order modeling actions. According to our results, four major modeling actions (analysis, synthesis, testing-interpreting, technical and cognitive support) performed through a plethora of modeling operations define the steps of the modeling process in both cases, while specific qualitative differences can be actually identified. Finally, the students’ conceptualizations of the biological aspect of the modeling task in the two-case activity is analyzed in regard with their capability of shifting reasoning between macro- and micro-levels, while educational implications are also discussed.     

Computational modeling issues and methods for the “regulatory problem” in engineering – Solutions to the structural dynamics and static frame problems

Many of the problems addressed through engineering analysis include a set of regulatory (or other) probabilistic requirements that must be demonstrated with some degree of confidence through the analysis. Problems cast in this environment can pose new challenges for computational analyses in both model validation and model-based prediction. The “regulatory problems” given for the “Sandia challenge problems exercise”, while relatively simple, provide an opportunity to demonstrate methods that address these challenges. This paper describes and illustrates methods that can be useful in analysis of the regulatory problem. Specifically, we discuss:

(1) an approach for quantifying variability and uncertainty separately to assess the regulatory requirements and provide a statement of confidence; and

(2) a general validation metric to focus the validation process on a specific range of the predictive distribution (the predictions near the regulatory threshold).

These methods are illustrated using the challenge problems. Solutions are provided for both the static frame and structural dynamics problems.

The identification of nonlinear models for process control using tailored “plant-friendly” input sequences

This paper considers certain practical aspects of the identification of nonlinear empirical models for chemical process dynamics. The primary focus is the identification of second-order Volterra models using input sequences that offer the following three advantages: (1) they are “plant friendly;” (2) they simplify the required computations; (3) they can emphasize certain model parameters over others. To provide a quantitative basis for discussing the first of these advantages, this paper defines a friendliness index f that relates to the number of changes that occur in the sequence. For convenience, this paper also considers an additional nonlinear model structure: the Volterra–Laguerre model. To illustrate the practical utility of the input sequences considered here, second-order Volterra and Volterra–Laguerre models are developed that approximate the dynamics of a first-principles model of methyl methacrylate polymerization.     

Stabilizability of multivariable systems and the Ljusternik— nirel'mann category of real Grassmannians

In this paper a numeric criterion, k(m, p) n, is given for stabilizability by constant gain output feedback of the generic linear multivariable system with m inputs, n states, and p outputs. This criterion is defined in terms of a topological invariant of the space of gains, both finite and infinite, arising from an interpretation of the problem of stabilizability as a problem concerning open covers of this space. This invariant, originally considered by Ljusternik and nirel'mann in the calculus of variations, can be estimated from below by using a theorem of Eilenberg together with the methods of the Schubert calculus, thus leading to some very explicit corollaries concerning generic stabilizability. As far as I am aware, these corollaries cannot be derived from existing results concerning pole-assignability. After passing to a problem on coverings of the (compactified) gain space, the main technical problem which remains in a high gain stability analysis — stated here as a High Gain Lemma — which appears to be of independent interest. That is, the topological argument implies that the closed-loop system is ‘stable’ for some gain, possibly infinite. If the root-locus map were defined and continuous at all infinite gains, then the conclusion that the system is stabilizable by finite gain could be deduced from a simple continuity argument. However, it is known that if mp > n then the root-locus map has points of discontinuity at infinity, and, since mp n is now known to be necessary for generic stabilizability, in most cases of interest one requires a far more subtle argument than one would give, for example, in the scalar case.     

No-Longer-Foreign: Teaching an ML compiler to speak C “natively”

We present a new foreign-function interface for SML/NJ. It is based on the idea of data-level interoperability—the ability of ML programs to inspect as well as manipulate C data structures directly.The core component of this work is an encoding of the almost² complete C type system in ML types. The encoding makes extensive use of a “folklore” typing trick, taking advantage of ML's polymorphism, its type constructors, its abstraction mechanisms, and even functors. A small low-level component which deals with C struct and union declarations as well as program linkage is hidden from the programmer's eye by a simple program-generator tool that translates C declarations to corresponding ML glue code.     

Term Collections in λ and ρ-calculi

The ρ-calculus generalises term rewriting and the λ-calculus by defining abstractions on arbitrary patterns and by using a pattern-matching algorithm which is a parameter of the calculus. In particular, equational theories that do not have unique principal solutions may be used. In the latter case, all the principal solutions of a matching problem are stored in a “structure” that can also be seen as a collection of terms.Motivated by the fact that there are various approaches to the definition of structures in the ρ-calculus, we study in this paper a version of the λ-calculus with term collections.The contributions of this work include a new syntax and operational semantics for a λ-calculus with term collections, which is related to the λ-calculi with strict parallel functions studied by Boudol and Dezani et al. and a proof of the confluence of the β-reduction relation defined for the calculus (which is a suitable extension of the standard rule of β-reduction in the λ-calculus).     

Anisotropic <Emphasis Type="Italic">ε</Emphasis>-optimal model reduction for linear discrete time-invariant system

We consider an ε-optimal model reduction problem for a linear discrete time-invariant system, where the anisotropic norm of reduction error transfer function is used as a performance criterion. For solving the main problem, we state and solve an auxiliary problem of H ₂ ε-optimal reduction of a weighted linear discrete time system. A sufficient optimality condition defining a solution to the anisotropic ε-optimal model reduction problem has the form of a system of cross-coupled nonlinear matrix algebraic equations including a Riccati equation, four Lyapunov equations, and five special-type nonlinear equations. The proposed approach to solving the problem ensures stability of the reduced model without any additional technical assumptions. The reduced-order model approximates the steady-state behavior of the full-order system.     

Finite dominating sets for the multi-facility ordered median problem in networks and algorithmic applications

We identify a finite dominating set (FDS) for a special case of the multi-facility ordered median problem in networks, in which the λ-weights can take at least two different values. This FDS result not only includes the FDS research for the p-center problem, but also extends the case of a<b in the λ-weights provided by Kalcsics et al. (Kalcsics, J., Nickel, S., Puerto, J. (2003). Multi-facility ordered median problems: A further analysis. Networks, 41(1), 1–12). Furthermore, based on the FDS result, we devise an exact algorithm for the problem. In addition, we present a polynomial time algorithm for the problem with at most three different values in the λ-weights in tree networks. Finally, we pose an open problem on identifying the existence of a polynomial size FDS for the multi-facility convex ordered median problem in networks.     

An alternative solution to the H∞-optimal control problem

In this paper we present an alternative solution to the problem min _{X ε H^n×n∞} |A + BXC|_∞ where A, B, rmand C are rational matrices in H^n×n_∞. The solution circumvents the need to extract the matrix inner factors of B and C, providing a multivariable extension of Sarason's H^∞-interpolation theory [1] to the case of matrix-valued B(s) and C(s). The result has application to the diagonally-scaled optimization problem int |D(A + BXC)D⁻¹|_∞, where the infimum is over D, X εH^n×n_∞, D diagonal.     

Approximation by Bézier type of Meyer–König and Zeller operators

In this paper, we give direct, inverse and equivalence approximation theorems for the Bézier type of Meyer–König and Zeller operator with unified Ditzian–Totik modulus ω_φ^λ(f,t) (0≤λ≤1).     

A new solution branch for the Blasius equation—A shrinking sheet problem

In this work, a similarity equation of the momentum boundary layer is studied for a moving flat plate with mass transfer in a stationary fluid. The solution is applicable to the practical problem of a shrinking sheet with a constant sheet velocity. Theoretical estimation of the solution domain is obtained. It is shown that the solution only exists with mass suction at the wall surface. The equation with the associated boundary conditions is solved using numerical techniques. Greatly different from the continuously stretching surface problem and the Blasius problem with a free stream, quite complicated behavior is observed in the results. It is seen that there are three different solution zones divided by two critical mass transfer parameters, f₀₁≈1.7028 and f₀₂≈1.7324. When f₀<f₀₁, there is no solution for this problem, multiple solutions for f₀₁<f₀≤f₀₂, and one solution when (f₀=f₀₁)(f₀>f₀₂). There is a terminating point for the solution domain and the terminating point corresponds to a special algebraically decaying solution for the current problem. The current results provide a new solution branch of the Blasius equation, which is greatly different from the previous study and provide more insight into the understanding of the Blasius equation.     

Extensions to “Output prediction under scarce data operation: control applications”

Albertos et al. (Automatica, 35 (1999) 1671–1681), proposed a simple and computationally cheap output estimation algorithm for systems where some output data is missing. In the original paper, a stability analysis of the algorithm is provided for the special case that every Nth sample of the output is observed. We here show how the stability can be analysed for arbitrary periodical missing data patterns.     

An inequality governing nonlinear H∞ control

This note gives necessary and sufficient conditions for solving a reasonable version of the nonlinear H^∞ control problem. The most objectionable hypothesis is elegant and holds in the linear case, but every possibly may not be forced for nonlinear systems. What we discover in distinction to Isidori and Astolfi (1992) and Ball et al. (1993) is that the key formula is not a (nonlinear) Riccati partial differential inequality, but a much more complicated inequality mixing partial derivatives and an approximation theoretic construction called the best approximation operator. This Chebeshev-Riccati inequality when specialized to the linear case gives the famous solution to the H^∞ control problem found in Doyle et al. (1989). While complicated the Chebeshev-Riccati inequality is (modulo a considerable number of hypotheses behind it) a solution to the nonlinear H^∞ control problem. It should serve as a rational basis for discovering new formulas and compromises. We follow the conventions of Ball et al. (1993) and this note adds directly to that paper.     

Packet Routing in Networks with Long Wires

In this paper, we examine the packet routing problem for networks with wires of differing length. We consider this problem in a network independent context, in which routing time is expressed in terms of "congestion" and "dilation" measures for a set of packet paths. We give, for any constant ε > 0, a randomized on-line algorithm for routing any set of N packets in O((C lg^ε(Nd) + D lg(Nd))/lg lg(Nd)) time, where C is the maximum congestion and D is the length of the longest path, both taking wire delays into account, and d is the longest path in terms of number of wires. We also show that for edge-simple paths, there exists a schedule (which could be found off-line) of length O((cd_max + D) (lg(d_max)/lg lg (d_max))), where d_max is the maximum wire delay in the network. These results improve upon previous routing results which assume that unit time suffices to traverse a wire of any length. They also yield improved results for job-shop scheduling as long as we incorporate a technical restriction on the job-shop problem.     

Robust H∞ control for linear discrete-time systems with norm-bounded time-varying uncertainty

The problem of robust H_∞ analysis and synthesis for linear discrete-time systems with norm-bounded time-varying uncertainty is studied in this paper. It will be shown that this problem is equivalent to the problem of H_∞ analysis and synthesis of an auxiliary system. The necessary and sufficient conditions for the equivalency are proved. Thus the original problem can be solved by existing H_∞ control methods.     

Probabilistic π-Calculus and Event Structures

This paper proposes two semantics of a probabilistic variant of the π-calculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of non-deterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed π-calculus.