Two-machine flow-shop scheduling with rejection

We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1+?)R and a makespan value of at most (1+?)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them.     

Clustering and selecting suppliers based on simulated annealing algorithms

This study proposes two optimization mathematical models for the clustering and selection of suppliers. Model 1 performs an analysis of supplier clusters, according to customer demand attributes, including production cost, product quality and production time. Model 2 uses the supplier cluster obtained in Model 1 to determine the appropriate supplier combinations. The study additionally proposes a two-phase method to solve the two mathematical models. Phase 1 integrates k-means and a simulated annealing algorithm with the Taguchi method (TKSA) to solve for Model 1. Phase 2 uses an analytic hierarchy process (AHP) for Model 2 to weight every factor and then uses a simulated annealing algorithm with the Taguchi method (ATSA) to solve for Model 2. Finally, a case study is performed, using parts supplier segmentation and an evaluation process, which compares different heuristic methods. The results show that TKSA+ATSA provides a quality solution for this problem.     

A comparative runtime analysis of heuristic algorithms for satisfiability problems

The satisfiability problem is a basic core NP-complete problem. In recent years, a lot of heuristic algorithms have been developed to solve this problem, and many experiments have evaluated and compared the performance of different heuristic algorithms. However, rigorous theoretical analysis and comparison are rare. This paper analyzes and compares the expected runtime of three basic heuristic algorithms: RandomWalk, (1+1) EA, and hybrid algorithm. The runtime analysis of these heuristic algorithms on two 2-SAT instances shows that the expected runtime of these heuristic algorithms can be exponential time or polynomial time. Furthermore, these heuristic algorithms have their own advantages and disadvantages in solving different SAT instances. It also demonstrates that the expected runtime upper bound of RandomWalk on arbitrary k-SAT (k?3) is O(n(k−1)), and presents a k-SAT instance that has Θ(n(k−1)) expected runtime bound.     

Model-free Q-learning designs for linear discrete-time zero-sum games with application to H-infinity control

In this paper, the optimal strategies for discrete-time linear system quadratic zero-sum games related to the H-infinity optimal control problem are solved in forward time without knowing the system dynamical matrices. The idea is to solve for an action dependent value function Q(x,u,w) of the zero-sum game instead of solving for the state dependent value function V(x) which satisfies a corresponding game algebraic Riccati equation (GARE). Since the state and actions spaces are continuous, two action networks and one critic network are used that are adaptively tuned in forward time using adaptive critic methods. The result is a Q-learning approximate dynamic programming (ADP) model-free approach that solves the zero-sum game forward in time. It is shown that the critic converges to the game value function and the action networks converge to the Nash equilibrium of the game. Proofs of convergence of the algorithm are shown. It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the GARE of the linear quadratic discrete-time zero-sum game. The effectiveness of this method is shown by performing an H-infinity control autopilot design for an F-16 aircraft.     

Channel assignment via fast zeta transform

We show an O^?(n(?+1))-time algorithm for the channel assignment problem, where ? is the maximum edge weight. This improves on the previous O^?(n(?+2))-time algorithm by Král (2005) [1], as well as algorithms for important special cases, like L(2,1)-labeling. For the latter problem, our algorithm works in O^?(n³) time. The progress is achieved by applying the fast zeta transform in combination with the inclusion-exclusion principle.     

On the hardness of finding near-optimal multicuts in directed acyclic graphs

Given an edge-weighted (di)graph and a list of source-sink pairs of vertices of this graph, the minimum multicut problem consists in selecting a minimum-weight set of edges (or arcs), whose removal leaves no path from each source to the corresponding sink. This is a well-known NP-hard problem, and improving several previous results, we show that it remains APX-hard in unweighted directed acyclic graphs (DAG), even with only two source-sink pairs. This is also true if we remove vertices instead of arcs.     

Robust PID controller tuning based on the constrained particle swarm optimization

This paper proposes a novel tuning strategy for robust proportional-integral-derivative (PID) controllers based on the augmented Lagrangian particle swarm optimization (ALPSO). First, the problem of PID controller tuning satisfying multiple H_∞ performance criteria is considered, which is known to suffer from computational intractability and conservatism when any existing method is adopted. In order to give some remedy to such a design problem without using any complicated manipulations, the ALPSO based robust gain tuning scheme for PID controllers is introduced. It does not need any conservative assumption unlike the conventional methods, and often enables us to find the desired PID gains just by solving the constrained optimization problem in a straightforward way. However, it is difficult to guarantee its effectiveness in a theoretical way, because PSO is essentially a stochastic approach. Therefore, it is evaluated by several simulation examples, which demonstrate that the proposed approach works well to obtain PID controller parameters satisfying the multiple H_∞ performance criteria.     

Improved deterministic algorithms for weighted matching and packing problems

Based on the method of (n,k)-universal sets, we present a deterministic parameterized algorithm for the weighted rd-matching problem with time complexity O^∗(4^{(r−1)k+o(k)}), improving the previous best upper bound O^∗(4^rk+o(k)). In particular, the algorithm applied to the unweighted 3d-matching problem results in a deterministic algorithm with time O^∗(16^k+o(k)), improving the previous best result O^∗(21.26^k). For the weighted r-set packing problem, we present a deterministic parameterized algorithm with time complexity O^∗(2^{(2r−1)k+o(k)}), improving the previous best result O^∗(2^2rk+o(k)). The algorithm, when applied to the unweighted 3-set packing problem, has running time O^∗(32^k+o(k)), improving the previous best result O^∗(43.62^k+o(k)). Moreover, for the weighted r-set packing and weighted rd-matching problems, we give a kernel of size O(k^r), which is the first kernelization algorithm for the problems on weighted versions.     

On the complexity of sandpile critical avalanches

In this work, we study The Abelian Sandpile Model from the point of view of computational complexity. We begin by studying the length distribution of sandpile avalanches triggered by the addition of two critical configurations: we prove that those avalanches are long on average, their length is bounded below by a constant fraction of the length of the longest critical avalanche which is, in most of the cases, superlinear. At the end of the paper we take the point of view of computational complexity, we analyze the algorithmic hardness of the problem consisting in computing the addition of two critical configurations, we prove that this problem is P complete, and we prove that most algorithmic problems related to The Abelian Sandpile Model are NC reducible to it.     

Negative selection algorithms on strings with efficient training and linear-time classification

A string-based negative selection algorithm is an immune-inspired classifier that infers a partitioning of a string space Σ^? into “normal” and “anomalous” partitions from a training set S containing only samples from the “normal” partition. The algorithm generates a set of patterns, called “detectors”, to cover regions of the string space containing none of the training samples. Strings that match at least one of these detectors are then classified as “anomalous”. A major problem with existing implementations of this approach is that the detector generating step needs exponential time in the worst case. Here we show that for the two most widely used kinds of detectors, the r-chunk and r-contiguous detectors based on partial matching to substrings of length r, negative selection can be implemented more efficiently by avoiding generating detectors altogether: for each detector type, training set S⊆Σ^? and parameter r≤? one can construct an automaton whose acceptance behaviour is equivalent to the algorithm’s classification outcome. The resulting runtime is O(|S|?r|Σ|) for constructing the automaton in the training phase and O(?) for classifying a string.     

Approximate dynamic programming-based approaches for input-output data-driven control of nonlinear processes

We propose two approximate dynamic programming (ADP)-based strategies for control of nonlinear processes using input-output data. In the first strategy, which we term ‘J-learning,’ one builds an empirical nonlinear model using closed-loop test data and performs dynamic programming with it to derive an improved control policy. In the second strategy, called ‘Q-learning,’ one tries to learn an improved control policy in a model-less manner. Compared to the conventional model predictive control approach, the new approach offers some practical advantages in using nonlinear empirical models for process control. Besides the potential reduction in the on-line computational burden, it offers a convenient way to control the degree of model extrapolation in the calculation of optimal control moves. One major difficulty associated with using an empirical model within the multi-step predictive control setting is that the model can be excessively extrapolated into regions of the state space where identification data were scarce or nonexistent, leading to performances far worse than predicted by the model. Within the proposed ADP-based strategies, this problem is handled by imposing a penalty term designed on the basis of local data distribution. A CSTR example is provided to illustrate the proposed approaches.     

On relational possibilistic clustering

This paper initially describes the relational counterpart of possibilistic c-means (PCM) algorithm, called relational PCM (or RPCM). RPCM is then improved to better handle arbitrary dissimilarity data. First, a re-scaling of the PCM membership function is proposed in order to obtain zero membership values when the distance to prototype equals the maximum value allowed in bounded dissimilarity measures. Second, a heuristic method of reference distance initialisation is provided which diminishes the known PCM tendency of producing coincident clusters. Finally, RPCM improved with our initialisation strategy is tested on both synthetic and real data sets with satisfactory results.     

Three-dimensional beta shapes

The Voronoi diagram of a point set has been extensively used in various disciplines ever since it was first proposed. Its application realms have been even further extended to estimate the shape of point clouds when Edelsbrunner and Mücke introduced the concept of α-shape based on the Delaunay triangulation of a point set.In this paper, we present the theory of β-shape for a set of three-dimensional spheres as the generalization of the well-known α-shape for a set of points. The proposed β-shape fully accounts for the size differences among spheres and therefore it is more appropriate for the efficient and correct solution for applications in biological systems such as proteins.Once the Voronoi diagram of spheres is given, the corresponding β-shape can be efficiently constructed and various geometric computations on the sphere complex can be efficiently and correctly performed. It turns out that many important problems in biological systems such as proteins can be easily solved via the Voronoi diagram of atoms in proteins and β-shapes transformed from the Voronoi diagram.     

Dissipative analysis and control of state-space symmetric systems

The paper addresses the problem of analysis and static output feedback control synthesis for strict quadratic dissipativity of linear time-invariant systems with state-space symmetry. As a particular case of dissipative systems, we consider the mixed H_∞ and positive real performance criterion and we develop an explicit expression for calculating the H_∞ norm of these systems. Subsequently, an explicit parametrization of the static output feedback control gains that solve the mixed H_∞ and positive real performance problem is obtained. Numerical examples demonstrate the use and computational advantages of the proposed explicit solutions.     

A discrete-time stable controller for an omni-directional mobile robot based on an approximated model

An adaptive controller based on multi-input fuzzy rules emulated networks (MIFRENs) is introduced for omni-directional mobile robot systems in the discrete-time domain without any kinematic or dynamic models. An approximated model for unknown systems is developed by using two MIFRENs with an online learning algorithm in addition to the stability analysis. The main theorem in this model is proposed to guarantee closed-loop performance and system robustness for all adjustable parameters inside MIFRENs. The system is validated by an experimental setup with a FESTO omni-directional mobile robot called Robotino^®. The proposed algorithm is shown to have superior performance compared to that of an algorithm that uses only an embedded controller. The advantage of the MIFREN initial setting is verified comparing its results with those of a controller that is based on neural networks.     

Triangulation of molecular surfaces

Given a molecule, which consists of a set of atoms, a molecular surface is defined for a spherical probe approximating a solvent molecule. Molecular surface is used for both the visualization of the molecule and the computation of various molecular properties such as the area and volume of a protein, which are important for studying problems such as protein docking and folding.In this paper, we present an O(n) time algorithm, in the worst case, for triangulating molecular surface based on the combinatorial information provided by the β-shape of the molecule with n atoms. The proposed algorithm takes advantage of the concise representation of topology among atoms stored in the β-shape.A molecular surface consists of two parts: a blending surface consisting of blending patches and a (solvent) contact surface consisting of (solvent) contact patches. For each blending patch, the algorithm uses compact masks for the construction of a triangular mesh in O(c^′) time in the worst case, where c^′ is the number of point evaluations on the blending patch. For each contact patch, the algorithm uses a template, for each atom type, for the triangulation of the boundary of the atom. Then, the triangular mesh is trimmed off by hyperplanes where each hyperplane corresponds to an arc of the boundary of the contact patch. The triangulation of a contact patch takes O(c^″) time in the worst case, where c^″ is the number of point evaluations on the boundary of an atom. Since there are at most O(n) patches, the worst case time complexity is O(n).The proposed algorithm also handles internal voids and guarantees the watertightness of the produced triangular mesh of a molecular surface. In addition, the level-of-detail is easily achieved as a by-product of the proposed scheme. The proposed algorithm is fully implemented and statistics from experiments are also collected.     

A necessary and sufficient condition for parameter insensitive disturbance-rejection problem with state feedback

In this paper a necessary and sufficient condition for a parameter insensitive disturbance-rejection problem with state feedback which was pointed out as an open problem by Bhattacharyya to be solvable is proved. A constructive algorithm of simultaneously (A,B)-invariant subspaces for a finite-number of linear systems and a relationship between simultaneously (A,B)-invariant subspaces and generalized (A,B)-invariant subspaces play an important role to prove the main result.     

Split Bregman method for large scale fused Lasso

Ordering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an ?₁ norm regularizer. However, due to nonseparability and nonsmoothness of the regularization term, solving the fused Lasso problem is computationally demanding. Existing solvers can only deal with problems of small or medium size, or a special case of the fused Lasso problem in which the predictor matrix is the identity matrix. In this paper, we propose an iterative algorithm based on the split Bregman method to solve a class of large-scale fused Lasso problems, including a generalized fused Lasso and a fused Lasso support vector classifier. We derive our algorithm using an augmented Lagrangian method and prove its convergence properties. The performance of our method is tested on both artificial data and real-world applications including proteomic data from mass spectrometry and genomic data from array comparative genomic hybridization (array CGH). We demonstrate that our method is many times faster than the existing solvers, and show that it is especially efficient for large p, small n problems, where p is the number of variables and n is the number of samples.     

Three results on frequency assignment in linear cellular networks

In the frequency assignment problem we are given a graph representing a wireless network and a sequence of requests, where each request is associated with a vertex. Each request has two more attributes: its arrival and departure times, and it is considered active from the time of arrival to the time of departure. We want to assign frequencies to all requests so that at each time step any two active requests associated with the same or adjacent vertices use different frequencies. The objective is to minimize the number of frequencies used.We focus exclusively on the special case of the problem when the underlying graph is a linear network (path). For this case, we consider both the offline and online versions of the problem, and we present three results. First, in the incremental online case, where the requests arrive over time, but never depart, we give an algorithm with an optimal (asymptotic) competitive ratio . Second, in the general online case, where the requests arrive and depart over time, we improve the current lower bound on the (asymptotic) competitive ratio to . Third, we prove that the offline version of this problem is NP-complete.