Minimizing cost-related objective in synchronous scheduling of parallel factories in the virtual production network

This paper will introduce the Monte Carlo-based heuristic with seven local searches (LSs) which are carefully designed for distributed production network scheduling. Distributed production network consists of the number of different individual factories that joins together to form a network, in which these factories can operate more economically than operating individually and each individual factory usually focuses on self-benefits. Some realistic features such as heterogeny of factories and the transportation among factories are incorporated in our problem definition. However, in such network, each individual factory usually focuses on self-benefits and it plans to optimize its own profit. In this problem, among F exit factories in the network, F′ factories are interested in the total earliness costs and the remaining factories (F″ = F − F′) are interested in the total tardiness cost. Cost minimization is achieved through the minimization of earliness in F′factories, tardiness in F″ factories and the total costs of operation time of all jobs. This algorithm initializes with best known non-cooperative local scheduling and then the LSs search simultaneously through the same solution space, starting from the same current solution. Upon receiving the solutions from the LSs, the new solution will be accepted based on the Monte Carlo acceptance criterion. This criterion always accepts an improved solution and, in order to escape local minima, accept the worse solutions with a certain probability, which this probability decreases with deteriorating solutions. After solving the mixed integer linear programming by the CPLEX solver in the small-size instances, the results obtained by heuristic are compared with two genetic algorithms in the large-size instances. The results of the scheduling before cooperation in production network were also considered in the experiments.     

Energy-efficient topology control algorithm for maximizing network lifetime in wireless sensor networks with mobile sink

Uneven energy consumption is an inherent problem in wireless sensor networks characterized by multi-hop routing and many-to-one traffic pattern. Such unbalanced energy dissipation can significantly reduce network lifetime. In this paper, we study the problem of prolonging network lifetime in large-scale wireless sensor networks where a mobile sink gathers data periodically along the predefined path and each sensor node uploads its data to the mobile sink over a multi-hop communication path. By using greedy policy and dynamic programming, we propose a heuristic topology control algorithm with time complexity O(n(m + n log n)), where n and m are the number of nodes and edges in the network, respectively, and further discuss how to refine our algorithm to satisfy practical requirements such as distributed computing and transmission timeliness. Theoretical analysis and experimental results show that our algorithm is superior to several earlier algorithms for extending network lifetime.     

Search space reduction in QoS routing

To provide real-time service or engineer constrained-based paths, networks require the underlying routing algorithm to be able to find low-cost paths that satisfy given quality-of-service constraints. However, the problem of constrained shortest (least-cost) path routing is known to be NP-hard, and some heuristics have been proposed to find a near-optimal solution. However, these heuristics either impose relationships among the link metrics to reduce the complexity of the problem which may limit the general applicability of the heuristic, or are too costly in terms of execution time to be applicable to large networks. In this paper, we focus on solving the delay-constrained minimum-cost path problem, and present a fast algorithm to find a near-optimal solution. This algorithm, called delay-cost-constrained routing (DCCR), is a variant of the k-shortest-path algorithm. DCCR uses a new adaptive path weight function together with an additional constraint imposed on the path cost, to restrict the search space. Thus, DCCR can return a near-optimal solution in a very short time. Furthermore, we use a variant of the Lagrangian relaxation method proposed by Handler and Zang [Networks 10 (1980) 293] to further reduce the search space by using a tighter bound on path cost. This makes our algorithm more accurate and even faster. We call this improved algorithm search space reduction + DCCR (SSR + DCCR). Through extensive simulations, we confirm that SSR + DCCR performs very well compared to the optimal but very expensive solution.     

A combinatorial particle swarm optimisation for solving permutation flowshop problems

The m-machine permutation flowshop problem PFSP with the objectives of minimizing the makespan and the total flowtime is a common scheduling problem, which is known to be NP-complete in the strong sense, when m ? 3. This work proposes a new algorithm for solving the permutation FSP, namely combinatorial Particle Swarm Optimization. Furthermore, we incorporate in this heuristic an improvement procedure based on the simulated annealing approach. The proposed algorithm was applied to well-known benchmark problems and compared with several competing metaheuristics.     

Low-autocorrelation binary sequences: On improved merit factors and runtime predictions to achieve them

The search for binary sequences with a high figure of merit, known as the low autocorrelation binary sequence (labs) problem, represents a formidable computational challenge. To mitigate the computational constraints of the problem, we consider solvers that accept odd values of sequence length L and return solutions for skew-symmetric binary sequences only – with the consequence that not all best solutions under this constraint will be optimal for each L. In order to improve both, the search for best merit factor and the asymptotic runtime performance, we instrumented three stochastic solvers, the first two are state-of-the-art solvers that rely on variants of memetic and tabu search (lssMAts and lssRRts), the third solver (lssOrel) organizes the search as a sequence of independent contiguous self-avoiding walk segments. By adapting a rigorous statistical methodology to performance testing of all three combinatorial solvers, experiments show that the solver with the best asymptotic average-case performance, lssOrel_8 = 0.000032 * 1.1504^L, has the best chance of finding solutions that improve, as L increases, figures of merit reported to date. The same methodology can be applied to engineering new labs solvers that may return merit factors even closer to the conjectured asymptotic value of 12.3248.     

A note on two-stage hybrid flowshop scheduling with missing operations

The scheduling problem in a multi-stage hybrid flowshop has been the subject of considerable research. All the studies on this subject assume that each job has to be processed on all the stages, i.e., there are no missing operations for a job at any stage. However, missing operations usually exist in many real-life production systems, such as a system in a stainless steel factory investigated in this note. The studied production system in the factory is composed of two stages in series. The first stage contains only one machine while the second stage consists of two identical machines (namely a 1 × 2 hybrid flowshop). In the system, some jobs have to be processed on both stages, but others need only to be processed on the second stage. Accordingly, the addressed scheduling problem is a 1 × 2 hybrid flowshop with missing operations at the first stage. In this note, we develop a heuristic for the problem to generate a non-permutation schedule (NPS) from a given permutation schedule, with the objective of minimizing the makespan. Computational results demonstrate that the heuristic can efficiently generate better NPS solutions.     

On the influence of the number of algorithms,problems, and independent runs in the comparison of evolutionary algorithms

When conducting a comparison between multiple algorithms on multiple optimisation problems it is expected that the number of algorithms, problems and even the number of independent runs will affect the final conclusions. Our question in this research was to what extent do these three factors affect the conclusions of standard Null Hypothesis Significance Testing (NHST) and the conclusions of our novel method for comparison and ranking the Chess Rating System for Evolutionary Algorithms (CRS4EAs). An extensive experiment was conducted and the results were gathered and saved of k = 16 algorithms on N = 40 optimisation problems over n = 100 runs. These results were then analysed in a way that shows how these three values affect the final results, how they affect ranking and which values provide unreliable results. The influence of the number of algorithms was examined for values k = {4, 8, 12, 16}, number of problems for values N = {5, 10, 20, 40}, and number of independent runs for values n = {10, 30, 50, 100}. We were also interested in the comparison between both methods – NHST's Friedman test with post-hoc Nemenyi test and CRS4EAs – to see if one of them has advantages over the other. Whilst the conclusions after analysing the values of k were pretty similar, this research showed that the wrong value of N can give unreliable results when analysing with the Friedman test. The Friedman test does not detect any or detects only a small number of significant differences for small values of N and the CRS4EAs does not have a problem with that. We have also shown that CRS4EAs is an appropriate method when only a small number of independent runs n are available.     

Gröbner Bases over Galois Rings with an Application to Decoding Alternant Codes

We develop a theory of Gröbner bases over Galois rings, following the usual formulation for Gröbner bases over finite fields. Our treatment includes a division algorithm, a characterization of Gröbner bases, and an extension of Buchberger’s algorithm. One application is towards the problem of decoding alternant codes over Galois rings. To this end we consider the module M =  {(a, b) :aS ≡ b  mod x^r} of all solutions to the so-called key equation for alternant codes, where S is a syndrome polynomial. In decoding, a particular solution (Σ, Ω)  ∈ M is sought satisfying certain conditions, and such a solution can be found in a Gröbner basis of M. Applying techniques introduced in the first part of this paper, we give an algorithm which returns the required solution.     

Scheduling flow lines with buffers by ant colony digraph

This work starts from modeling the scheduling of n jobs on m machines/stages as flowshop with buffers in manufacturing. A mixed-integer linear programing model is presented, showing that buffers of size n ? 2 allow permuting sequences of jobs between stages. This model is addressed in the literature as non-permutation flowshop scheduling (NPFS) and is described in this article by a disjunctive graph (digraph) with the purpose of designing specialized heuristic and metaheuristics algorithms for the NPFS problem. Ant colony optimization (ACO) with the biologically inspired mechanisms of learned desirability and pheromone rule is shown to produce natively eligible schedules, as opposed to most metaheuristics approaches, which improve permutation solutions found by other heuristics. The proposed ACO has been critically compared and assessed by computation experiments over existing native approaches. Most makespan upper bounds of the established benchmark problems from Taillard (1993) and Demirkol, Mehta, and Uzsoy (1998) with up to 500 jobs on 20 machines have been improved by the proposed ACO.     

Utilize 100% redundancy to offer higher-level multiple fault restoration in WDM networks without wavelength conversion

This study addresses the problem of achieving higher-level multi-fault restoration in wavelength division multiplexing (WDM) networks with no wavelength conversion capability. A heuristic scheme, designated as the Directional Cycle Decomposition Algorithm (DCDA), is developed to maximize the number of tolerable faults utilizing only 100% redundancy in WDM networks without wavelength conversion. The redundancy is calculated as the required spare capacity over the given working capacity. The process of identifying the maximum number of tolerable faults is modeled as a constrained ring cover set problem. DCDA decomposes this problem into three steps and has an overall computational complexity of O(∣E∣∣V∣(C + 1) + ∣E∣(C² + 1)), where ∣V∣, ∣E∣ and C represent the number of vertices, the number of edges in the graph and the number of cycles in the cycle cover, respectively. The evaluation results reveal that the average number of tolerable simultaneous faults increases considerably under DCDA and the maximum number of tolerable simultaneous faults approaches the optimal solution provided by the brute-force method. DCDA facilitates an improved best-effort multi-fault restorability for a variety of planar and non-planar network topologies. An analytical method is proposed to facilitate a rapid estimation of the multi-fault restorability in a network using DCDA without the need for experimental evaluations. In addition, an approximation method is developed to obtain an estimate of the multi-fault restorability directly from DCDA without the requirement for a detailed knowledge of the network topology and restoration routes. The results show that the average errors in the approximated restorability values obtained using this method range from 0.12% (New Jersey) to 1.58% (Cost 239).     

Optimization of simulated systems: OptQuest and alternatives

This article illustrates the general problem known as ‘simulation optimization’ through an (s, S) inventory management system. In this system, the goal function to be minimized is the expected value of specific inventory costs. Moreover, specific constraints must be satisfied for some random simulation responses, namely the service or fill rate, and for some deterministic simulation inputs, namely the constraint s < S. Results are reported for three optimization methods, including the popular OptQuest method. The optimality of the resulting solutions is tested through the so-called Karush–Kuhn–Tucker (KKT) conditions.     

Symmetric and symplectic exponentially fitted Runge–Kutta–Nyström methods for Hamiltonian problems

The construction of symmetric and symplectic exponentially fitted modified Runge–Kutta–Nyström (SSEFRKN) methods is considered. Based on the symmetry, symplecticity, and exponentially fitted conditions, new explicit modified RKN integrators with FSAL property are obtained. The new integrators integrate exactly differential systems whose solutions can be expressed as linear combinations of functions from the set { exp(± iωt)}, ω > 0, i² = −1, or equivalently from the set { cos(ωt), sin(ωt)}. The phase properties of the new integrators are examined and their periodicity regions are obtained. Numerical experiments are accompanied to show the high efficiency and competence of the new SSEFRKN methods compared with some highly efficient nonsymmetric symplecti EFRKN methods in the literature.     

Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits

We perform a stability and convergence analysis of sequential methods for coupled flow and geomechanics, in which the mechanics sub-problem is solved first. We consider slow deformations, so that inertia is negligible and the mechanical problem is governed by an elliptic equation. We use Biot’s self-consistent theory to obtain the classical parabolic-type flow problem. We use a generalized midpoint rule (parameter α between 0 and 1) time discretization, and consider two classical sequential methods: the drained and undrained splits.The von Neumann method provides sharp stability estimates for the linear poroelasticity problem. The drained split with backward Euler time discretization (α = 1) is conditionally stable, and its stability depends only on the coupling strength, and it is independent of time step size. The drained split with the midpoint rule (α = 0.5) is unconditionally unstable. The mixed time discretization, with α = 1.0 for mechanics and α = 0.5 for flow, has the same stability properties as the backward Euler scheme. The von Neumann method indicates that the undrained split is unconditionally stable when α ? 0.5.We extend the stability analysis to the nonlinear regime (poro-elastoplasticity) via the energy method. It is well known that the drained split does not inherit the contractivity property of the continuum problem, thereby precluding unconditional stability. For the undrained split we show that it is B-stable (therefore unconditionally stable at the algorithmic level) when α ? 0.5.We also analyze convergence of the drained and undrained splits, and derive the a priori error estimates from matrix algebra and spectral analysis. We show that the drained split with a fixed number of iterations is not convergent even when it is stable. The undrained split with a fixed number of iterations is convergent for a compressible system (i.e., finite Biot modulus). For a nearly-incompressible system (i.e., very large Biot modulus), the undrained split loses first-order accuracy, and becomes non-convergent in time.We also study the rate of convergence of both splits when they are used in a fully-iterated sequential scheme. When the medium permeability is high or the time step size is large, which corresponds to a high diffusion of pressure, the error amplification of the drained split is lower and therefore converges faster than the undrained split. The situation is reversed in the case of low permeability and small time step size.We provide numerical experiments supporting all the stability and convergence estimates of the drained and undrained splits, in the linear and nonlinear regimes. We also show that our spatial discretization (finite volumes for flow and finite elements for mechanics) removes the well-documented spurious instability in consolidation problems at early times.     

Irregular Primes and Cyclotomic Invariants to 12 Million

Computations of irregular primes and associated cyclotomic invariants were extended to all primes up to 12 million using multisectioning/convolution methods and a novel approach which originated in the study of Stickelberger codes Shokrollahi (1996). The latter idea reduces the problem to that of finding zeros of a polynomial overF_pof degree  <  (p −  1) / 2 among the quadratic nonresidues mod p. Use of fast polynomial gcd-algorithms gives anO (p log²p loglog p)-algorithm for this task. A more efficient algorithm, with comparable asymptotic running time, can be obtained by using Schönhage–Strassen integer multiplication techniques and fast multiple polynomial evaluation algorithms; this approach is particularly efficient when run on primes p for whichp −  1 has small prime factors. We also give some improvements on previous implementations for verifying the Kummer–Vandiver conjecture and for computing the cyclotomic invariants of a prime.     

Guided local search as a network planning algorithm that incorporates uncertain traffic demands

A search based heuristic for the optimisation of communication networks where traffic forecasts are uncertain and the problem is NP-complete is presented. While algorithms such as genetic algorithms (GA) and simulated annealing (SA) are often used for this class of problem, this work applies a combination of newer optimisation techniques specifically: fast local search (FLS) as an improved hill climbing method and guided local search (GLS) to allow escape from local minima. The GLS + FLS combination is compared with an optimised GA and SA approaches. It is found that in terms of implementation, the parameterisation of the GLS + FLS technique is significantly simpler than that for a GA and SA. Also, the self-regularisation feature of the GLS + FLS approach provides a distinctive advantage over the other techniques which require manual parameterisation. To compare numerical performance, the three techniques were tested over a number of network sets varying in size, number of switch circuit demands (network bandwidth demands) and levels of uncertainties on the switch circuit demands. The results show that the GLS + FLS outperforms the GA and SA techniques in terms of both solution quality and optimisation speed but even more importantly GLS + FLS has significantly reduced parameterisation time.     

Coarse-Grained Parallel Geometric Search

We present a parallel algorithm for solving thenext element search problemon a set of line segments, using a BSP-like model referred to as thecoarse grained multicomputer(CGM). The algorithm requiresO(1) communication rounds (h-relations withh=O(n/p)),O((n/p) log n) local computation, andO((n/p) log p) memory per processor, assumingn/p⩾p. Our result implies solutions to the point location, trapezoidal decomposition, and polygon triangulation problems. A simplified version for axis-parallel segments requires onlyO(n/p) memory per processor, and we discuss an implementation of this version. As in a previous paper by Develliers and Fabri (Int. J. Comput. Geom. Appl.6(1996), 487–506), our algorithm is based on a distributed implementation of segment trees which are of sizeO(n log n). This paper improves onop. cit.in several ways: (1) It studies the more general next element search problem which also solves, e.g., planar point location. (2) The algorithms require onlyO((n/p) log n) local computation instead ofO(log p*(n/p) log n). (3) The algorithms require onlyO((n/p) log p) local memory instead ofO((n/p) log n).     

GPU-based parallel vertex substitution algorithm for the p-median problem

We introduce a GPU-based parallel vertex substitution (pVS) algorithm for the p-median problem using the CUDA architecture by NVIDIA. pVS is developed based on the best profit search algorithm, an implementation of vertex substitution (VS), that is shown to produce reliable solutions for p-median problems. In our approach, each candidate solution in the entire search space is allocated to a separate thread, rather than dividing the search space into parallel subsets. This strategy maximizes the usage of GPU parallel architecture and results in a significant speedup and robust solution quality. Computationally, pVS reduces the worst case complexity from sequential VS’s O(p · n²) to O(p · (n ? p)) on each thread by parallelizing computational tasks on GPU implementation. We tested the performance of pVS on two sets of numerous test cases (including 40 network instances from OR-lib) and compared the results against a CPU-based sequential VS implementation. Our results show that pVS achieved a speed gain ranging from 10 to 57 times over the traditional VS in all test network instances.     

Approximate Solutions of Polynomial Equations

In this paper, we introduce “approximate solutions" to solve the following problem: given a polynomial F(x, y) over Q, where x represents an n -tuple of variables, can we find all the polynomials G(x) such that F(x, G(x)) is identically equal to a constant c in Q ? We have the following: let F(x, y) be a polynomial over Q and the degree of y in F(x, y) be n. Either there is a unique polynomial g(x)  ∈ Q [ x ], with its constant term equal to 0, such that F(x, y)  = ∑_j = 0ⁿc_j(y − g(x))^jfor some rational numbers c_j, hence, F(x, g(x)  + a)  ∈ Q for all a ∈ Q, or there are at most t distinct polynomials g₁(x),⋯ , g_t(x), t ≤ n, such that F(x, g_i(x))  ∈ Q for 1  ≤ i ≤ t. Suppose that F(x, y) is a polynomial of two variables. The polynomial g(x) for the first case, or g₁(x),⋯ , g_t(x) for the second case, are approximate solutions of F(x, y), respectively. There is also a polynomial time algorithm to find all of these approximate solutions. We then use Kronecker’s substitution to solve the case of F(x, y).     

Evaluating the use of ECG signal in low frequencies as a biometry

Traditional strategies, such as fingerprinting and face recognition, are becoming more and more fraud susceptible. As a consequence, new and more fraud proof biometrics modalities have been considered, one of them being the heartbeat pattern acquired by an electrocardiogram (ECG). While methods for subject identification based on ECG signal work with signals sampled in high frequencies (>100 Hz), the main goal of this work is to evaluate the use of ECG signal in low frequencies for such aim. In this work, the ECG signal is sampled in low frequencies (30 Hz and 60 Hz) and represented by four feature extraction methods available in the literature, which are then feed to a Support Vector Machines (SVM) classifier to perform the identification. In addition, a classification approach based on majority voting using multiple samples per subject is employed and compared to the traditional classification based on the presentation of single samples per subject each time. Considering a database composed of 193 subjects, results show identification accuracies higher than 95% and near to optimality (i.e., 100%) when the ECG signal is sampled in 30 Hz and 60 Hz, respectively, being the last one very close to the ones obtained when the signal is sampled in 360 Hz (the maximum frequency existing in our database). We also evaluate the impact of: (1) the number of training and testing samples for learning and identification, respectively; (2) the scalability of the biometry (i.e., increment on the number of subjects); and (3) the use of multiple samples for person identification.     

Solving Genus Zero Diophantine Equations with at Most Two Infinite Valuations

Let f(X, Y) be an absolutely irreducible polynomial with integer coefficients such that the curve defined by the equation f(X, Y)  =  0 is of genus 0 having at most two infinite valuations. This paper describes a practical general method for the explicit determination of all integer solutions of the diophantine equation f(X, Y)  =  0. Several elaborated examples are given. Furthermore, a necessary and sufficient condition for a curve of genus 0 to have infinitely many integer points is obtained.