The sine-cosine algorithm (SCA) is a new population-based meta-heuristic algorithm. In addition to exploiting sine and cosine functions to perform local and global searches (hence the name sine-cosine), the SCA introduces several random and adaptive parameters to facilitate the search process. Although it shows promising results, the search process of the SCA is vulnerable to local minima maxima due to the adoption of a fixed switch probability and the bounded magnitude of the sine and cosine functions (from -1 to 1). In this paper, we propose a new hybrid Q-learning sine-cosine- based strategy, called the Q-learning sine-cosine algorithm (QLSCA). Within the QLSCA, we eliminate the switching probability. Instead, we rely on the Q-learning algorithm (based on the penalty and reward mechanism) to dynamically identify the best operation during runtime. Additionally, we integrate two new operations (Le´vy flight motion and crossover) into the QLSCA to facilitate jumping out of local minima maxima and enhance the solution diversity. To assess its performance, we adopt the QLSCA for the combinatorial test suite minimization problem. Experimental results reveal that the QLSCA is statistically superior with regard to test suite size reduction compared to recent state-of-the-art strategies, including the original SCA, the particle swarm test generator (PSTG), adaptive particle swarm optimization (APSO) and the cuckoo search strategy (CS) at the 95 confidence level. However, concerning the comparison with discrete particle swarm optimization (DPSO), there is no significant difference in performance at the 95 confidence level. On a positive note, the QLSCA statistically outperforms the DPSO in certain configurations at the 90 confidence level.
@cite_25 @cite_1 developed a simulated annealing-based strategy for supporting the construction of a uniform and variable-strength @math test suite. A large random search space is generated in the implementation. When the algorithm iterates, the strategy chooses better test cases to construct the final test suite using the binary search process and a transformation equation. The search space is transformed from one state to another according to a probability equation. The results of the study are mainly concerned with the interaction strengths of two and three @cite_1 .
@cite_1 @cite_25
2154106236 2025003613 131057022 2104695995 1757513105 2065448588 2121957462 1510651616 2297520515 2124207853 2124106603 2004797988 2183434659 2787223504 1512015702 2000931246 2963702144 2024281442 2031397756 2161877964
We explore the ability of a simple simulated annealing procedure to assemble native-like structures from fragments of unrelated protein structures with similar local sequences using Bayesian scoring functions. Environment and residue pair specific contributions to the scoring functions appear as the first two terms in a series expansion for the residue probability distributions in the protein database; the decoupling of the distance and environment dependencies of the distributions resolves the major problems with current database-derived scoring functions noted by Thomas and Dill. The simulated annealing procedure rapidly and frequently generates native-like structures for small helical proteins and better than random structures for small b sheet containing proteins. Most of the simulated structures have native-like solvent accessibility and secondary structure patterns, and thus ensembles of these structures provide a particularly challenging set of decoys for evaluating scoring functions. We investigate the effects of multiple sequence information and different types of conformational constraints on the overall performance of the method, and the ability of a variety of recently developed scoring functions to recognize the native-like conformations in the ensembles of simulated structures. # 1997 Academic Press Limited In the maintenance phase, the regression test selection problem refers to selecting test cases from the initial suite of test cases used in the development phase. In this paper, we empirically compare five representative regression test selection algorithms, which include: Simulated Annealing, Reduction, Slicing, Dataflow, and Firewall algorithms. The comparison is based on eight quantitative and qualitative criteria. These criteria are: number of selected test cases, execution time, precision, inclusiveness, preprocessing requirements, type of maintenance, level of testing, and type of approach. The empirical results show that the five algorithms can be used for different requirements of regression testing. For example the Simulated Annealing algorithm can be used for emergency non-safety-critical maintenance situations with a large number of small modifications. Abstract : Testing is an expensive but essential part of any software project. Having the right methods to detect faults is a primary factor for success in the software industry. Component based systems are problematic because they are prone to unexpected interaction faults, yet these may be left undetected by traditional testing techniques. In all but the smallest of systems, it is not possible to test every component interaction. One can use a reduced test suite that guarantees to include a defined subset of interactions instead. A well studied combinatorial object, the covering array, can be used to achieve this goal. Constructing covering arrays for a specific software system is not always simple and the resulting object may not closely mirror the real test environment. Not only are new methods for building covering arrays needed, but new tools to support these are required as well. Our aim is to develop methods for building smaller test suites that provide stronger interaction coverage, while retaining the flexibility required in a practical test suite. We combine ideas from combinatorial design theory, computational search, statistical design of experiments and software engineering. We begin with a description of a framework for greedy algorithms that has formed the basis for several published methods and a widely used commercial tool. We compare this with a meta-heuristic search algorithm, simulated annealing. The results suggest that simulated annealing is more effective at finding smaller test suites, and in some cases improves on combinatorial methods as well. We then develop a mathematical model for variable strength interaction testing. This allows us to balance the cost and the time of testing by targeting individual subsets of components. We present construction techniques using meta-heuristic search and provide the first known bounds for objects of this type. We end by presenting some new cut-and-paste techniques that merge recursive combinatorial constructions Quantum annealing is a combinatorial optimization technique inspired by quantum mechanics. Here we show that a spin model for the k-coloring of large dense random graphs can be field tuned so that its acceptance ratio diverges during Monte Carlo quantum annealing, until a ground state is reached. We also find that simulations exhibiting such a diverging acceptance ratio are generally more effective than those tuned to the more conventional pattern of a declining and or stagnating acceptance ratio. This observation facilitates the discovery of solutions to several well-known benchmark k-coloring instances, some of which have been open for almost two decades. This paper is motivated by two applications, namely i) generalizations of cuckoo hashing, a computationally simple approach to assigning keys to objects, and ii) load balancing in content distribution networks, where one is interested in determining the impact of content replication on performance. These two problems admit a common abstraction: in both scenarios, performance is characterized by the maximum weight of a generalization of a matching in a bipartite graph, featuring node and edge capacities. Our main result is a law of large numbers characterizing the asymptotic maximum weight matching in the limit of large bipartite random graphs, when the graphs admit a local weak limit that is a tree. This result specializes to the two application scenarios, yielding new results in both contexts. In contrast with previous results, the key novelty is the ability to handle edge capacities with arbitrary integer values. An analysis of belief propagation algorithms (BP) with multivariate belief vectors underlies the proof. In particular, we show convergence of the corresponding BP by exploiting monotonicity of the belief vectors with respect to the so-called upshifted likelihood ratio stochastic order. This auxiliary result can be of independent interest, providing a new set of structural conditions which ensure convergence of BP. We study the asymptotic behavior as timet → + ∞ of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt → + ∞, a nonstationary Markov chain may exhibit “phase transitions.” Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC log(t t0) ast→+∞, with a computable constantC andt0 the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t−1+e) for some 0⩽e<1, with e=0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal “annealing schedule.” This optimal choice reflects the competition between two physical effects: (a) The “adiabatic” effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the “super-cooling” effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly. This paper presents a new algorithm based on integrating genetic algorithms, tabu search and simulated annealing methods to solve the unit commitment problem. The core of the proposed algorithm is based on genetic algorithms. Tabu search is used to generate new population members in the reproduction phase of the genetic algorithm. A simulated annealing method is used to accelerate the convergence of the genetic algorithm by applying the simulated annealing test for all the population members. A new implementation of the genetic algorithm is introduced. The genetic algorithm solution is coded as a mix between binary and decimal representation. The fitness function is constructed from the total operating cost of the generating units without penalty terms. In the tabu search part of the proposed algorithm, a simple short-term memory procedure is used to counter the danger of entrapment at a local optimum, and the premature convergence of the genetic algorithm. A simple cooling schedule has been implemented to apply the simulated annealing test in the algorithm. Numerical results showed the superiority of the solutions obtained compared to genetic algorithms, tabu search and simulated annealing methods, and to two exact algorithms. A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica symmetric results and also allows for the inclusion of replica symmetry breaking effects. For the 3-SAT problem, we find two transitions as the ratio α of logical clauses per Boolean variables increases. At the first one ( a_s 3.96 ), a non-trivial organization of the solution space in geometrically separated clusters emerges. The multiplicity of these clusters as well as the typical distances between different solutions are calculated. At the second threshold ( a_c 4.48 ), satisfying assignments disappear and a finite fraction ( B_o 0.13 ) of variables are overconstrained and take the same values in all optimal (though unsatisfying) assignments. These values have to be compared to ( a_c 4.27 ), ( B_o 0.4 ) obtained from numerical experiments on small instances. Within the present variational approach, the SAT-UNSAT transition naturally appears as a mixture of a first and a second order transition. For the mixed 2+p-SAT with p<2 5, the behavior is as expected much simpler: a unique smooth transition from SAT to UNSAT takes place at ( a_c = 1 (1 - p) ). We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random function Y(x) : x is an element of [0, 1] corresponds to its random oscillations in the y-axis, typically encapsulated by its (co) variation around a mean level. In contrast, its phase variation refers to fluctuations in the x-axis, often caused by random time changes. We formalise similar notions for a point process, and nonparametrically separate them based on realisations of i.i.d. copies Pi(i) of the phase-varying point process. A key element in our approach is to demonstrate that when the classical phase variation assumptions of Functional Data Analysis (FDA) are applied to the point process case, they become equivalent to conditions interpretable through the prism of the theory of optimal transportation of measure. We demonstrate that these induce a natural Wasserstein geometry tailored to the warping problem, including a formal notion of bias expressing over-registration. Within this framework, we construct nonparametric estimators that tend to avoid over-registration in finite samples. We show that they consistently estimate the warp maps, consistently estimate the structural mean, and consistently register the warped point processes, even in a sparse sampling regime. We also establish convergence rates, and derivev root n-consistency and a central limit theorem in the Cox process case under dense sampling, showing rate optimality of our structural mean estimator in that case. We present a systematic approach to the automatic generation of platform-independent benchmarks of realistic structure and tailored complexity for evaluating verification tools for reactive systems. The idea is to mimic a systematic constraint-driven software development process by automatically transforming randomly generated temporal-logic-based requirement specifications on the basis of a sequence of property-preserving, randomly generated structural design decisions into executable source code of a chosen target language or platform. Our automated transformation process steps through dedicated representations in terms of Buchi automata, Mealy machines, decision diagram models, and code models. It comprises LTL synthesis, model checking, property-oriented expansion, path condition extraction, theorem proving, SAT solving, and code motion. This setup allows us to address different communities via a growing set of programming languages, tailored sets of programming constructs, different notions of observation, and the full variety of LTL properties--ranging from mere reachability over general safety properties to arbitrary liveness properties. The paper illustrates the corresponding tool chain along accompanying examples, emphasizes the current state of development, and sketches the envisioned potential and impact of our approach. A comparison of two methods for surmounting the multiple-minima problem, Simulated Annealing (SA) and Monte Carlo with Minimization (MCM), is presented with applications to [Met]-enkephalin in the absence and in the presence of water. SA explores a continuous space of internal variables, while MCM explores a discrete space consisting of the local energy minima on that space. Starting from random conformations chosen from the whole conformational space in both cases, it is found that, while SA converges to low-energy structures significantly faster than MCM, the former does not converge to a unique minimum whereas the latter does. Furthermore, the behavior of the RMS deviations with respect to the apparent global minimum (for enkephalin in the absence of water) shows no correlation with the observed overall energy decrease in the case of SA, whereas such a correlation is quite evident with MCM; this implies that, even though the potential energy decreases in the annealing process, the Monte Carlo SA trajectory does not proceed towards the global minimum. Possible reasons for these differences between the two methods are discussed. It is concluded that, while SA presents attractive prospects for possibly improving or refining given structures, it must be considered inferior to MCM, at least in problems where little or no structural information is available for the molecule of interest. This paper describes the development of a novel metaheuristic that combines an electromagnetic-like mechanism (EM) and the great deluge algorithm (GD) for the University course timetabling problem. This well-known timetabling problem assigns lectures to specific numbers of timeslots and rooms maximizing the overall quality of the timetable while taking various constraints into account. EM is a population-based stochastic global optimization algorithm that is based on the theory of physics, simulating attraction and repulsion of sample points in moving toward optimality. GD is a local search procedure that allows worse solutions to be accepted based on some given upper boundary or level'. In this paper, the dynamic force calculated from the attraction-repulsion mechanism is used as a decreasing rate to update the level' within the search process. The proposed method has been applied to a range of benchmark university course timetabling test problems from the literature. Moreover, the viability of the method has been tested by comparing its results with other reported results from the literature, demonstrating that the method is able to produce improved solutions to those currently published. We believe this is due to the combination of both approaches and the ability of the resultant algorithm to converge all solutions at every search process. Simulated annealing is a stochastic optimization procedure which is widely applicable and has been found effective in several problems arising in computeraided circuit design. This paper derives the method in the context of traditional optimization heuristics and presents experimental .studies of its computational efficiency when applied to graph partitioning and traveling salesman problems. Dan Gelatt and I, with help from several of our colleagues, have explored a general framework for optimization which uses computer simulation methods from condensed matter physics and an equivalence (which can be made rigorous) between the many undetermined parameters of the system being optimized and the particles in an imaginary physical system. The energy of the physical system is given by the objective function of the optimization problem. States of low energy in the imaginary physical system are thus the near-global optimum configurations sought in the optimization problem. The trick we have used to find these is to model statistically the evolution of the physical system at a series of temperatures which allow it to "anneal" into a state of high order and very low energy. Arguments for the validity of this approach, and some ideas which help in understanding how to use it effectively, are given in a paper which We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. We address an open question, regarding whether a lattice code with lattice decoding (as opposed to maximum-likelihood (ML) decoding) can achieve the additive white Gaussian noise (AWGN) channel capacity. We first demonstrate how minimum mean-square error (MMSE) scaling along with dithering (lattice randomization) techniques can transform the power-constrained AWGN channel into a modulo-lattice additive noise channel, whose effective noise is reduced by a factor of spl radic (1+SNR SNR). For the resulting channel, a uniform input maximizes mutual information, which in the limit of large lattice dimension becomes 1 2 log (1+SNR), i.e., the full capacity of the original power constrained AWGN channel. We then show that capacity may also be achieved using nested lattice codes, the coarse lattice serving for shaping via the modulo-lattice transformation, the fine lattice for channel coding. We show that such pairs exist for any desired nesting ratio, i.e., for any signal-to-noise ratio (SNR). Furthermore, for the modulo-lattice additive noise channel lattice decoding is optimal. Finally, we show that the error exponent of the proposed scheme is lower bounded by the Poltyrev exponent. Let f be a random Boolean formula that is an instance of 3-SAT. We consider the problem of computing the least real number k such that if the ratio of the number of clauses over the number of variables of f strictly exceeds k , then f is almost certainly unsatisfiable. By a well-known and more or less straightforward argument, it can be shown that kF5.191. This upper bound was improved by to 4.758 by first providing new improved bounds for the occupancy problem. There is strong experimental evidence that the value of k is around 4.2. In this work, we define, in terms of the random formula f, a decreasing sequence of random variables such that, if the expected value of any one of them converges to zero, then f is almost certainly unsatisfiable. By letting the expected value of the first term of the sequence converge to zero, we obtain, by simple and elementary computations, an upper bound for k equal to 4.667. From the expected value of the second term of the sequence, we get the value 4.601q . In general, by letting the U This work was performed while the first author was visiting the School of Computer Science, Carleton Ž University, and was partially supported by NSERC Natural Sciences and Engineering Research Council . of Canada , and by a grant from the University of Patras for sabbatical leaves. The second and third Ž authors were supported in part by grants from NSERC Natural Sciences and Engineering Research . Council of Canada . During the last stages of this research, the first and last authors were also partially Ž . supported by EU ESPRIT Long-Term Research Project ALCOM-IT Project No. 20244 . †An extended abstract of this paper was published in the Proceedings of the Fourth Annual European Ž Symposium on Algorithms, ESA’96, September 25]27, 1996, Barcelona, Spain Springer-Verlag, LNCS, . pp. 27]38 . That extended abstract was coauthored by the first three authors of the present paper. Correspondence to: L. M. Kirousis Q 1998 John Wiley & Sons, Inc. CCC 1042-9832r98r030253-17 253 It is common practice to decay the learning rate. Here we show one can usually obtain the same learning curve on both training and test sets by instead increasing the batch size during training. This procedure is successful for stochastic gradient descent (SGD), SGD with momentum, Nesterov momentum, and Adam. It reaches equivalent test accuracies after the same number of training epochs, but with fewer parameter updates, leading to greater parallelism and shorter training times. We can further reduce the number of parameter updates by increasing the learning rate @math and scaling the batch size @math . Finally, one can increase the momentum coefficient @math and scale @math , although this tends to slightly reduce the test accuracy. Crucially, our techniques allow us to repurpose existing training schedules for large batch training with no hyper-parameter tuning. We train Inception-ResNet-V2 on ImageNet to @math validation accuracy in under 2500 parameter updates, efficiently utilizing training batches of 65536 images. We resolve in the affirmative a question of Boppana and Bui: whether simulated annealing can, with high probability and in polynomial time, find the optimal bisection of a random graph in npr when p − R = Θ(nΔ − 2) for Δ 2. (The random graph model npr specifies a “planted” bisection of density r, separating two n 2-vertex subsets of slightly higher density p.) We show that simulated “annealing” at an appropriate fixed temperature (i.e., the Metropolis algorithm) finds the unique smallest bisection in O(n2 + ) steps with very high probability, provided . (By using a slightly modified neighborhood structure, the number of steps can be reduced to O(n1+).) We leave open the question of whether annealing is effective for Δ in the range , whose lower limit represents the threshold at which the planted bisection becomes lost amongst other random small bisections. It also remains open whether hillclimbing (i.e., annealing at temperature 0) solves the same problem; towards the latter result, Juels has recently extended our analysis and shown that random hillclimbing finds the minimum bisection with constant probability, when p − R = Ω(1) (corresponding to Δ=2). This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations. The deterministic annealing approach to clustering and its extensions has demonstrated substantial performance improvement over standard supervised and unsupervised learning methods in a variety of important applications including compression, estimation, pattern recognition and classification, and statistical regression. The application-specific cost is minimized subject to a constraint on the randomness of the solution, which is gradually lowered. We emphasize the intuition gained from analogy to statistical physics. Alternatively the method is derived within rate-distortion theory, where the annealing process is equivalent to computation of Shannon's rate-distortion function, and the annealing temperature is inversely proportional to the slope of the curve. The basic algorithm is extended by incorporating structural constraints to allow optimization of numerous popular structures including vector quantizers, decision trees, multilayer perceptrons, radial basis functions, and mixtures of experts.