Combinatorial Explosion Problem Research Articles

Modelling and evaluation of multi-state reliability of repairable non-series manufacturing system with finite buffers

The capacity and capability of flexible manufacturing system varies with different market demands. To satisfy the requirements of performance expressions, avoid the problem of combinatorial explosion and consider the influence of intermediate buffer stations, a new reliability modelling and evaluating methodology for repairable non-series hybrid flexible manufacturing systems with finite buffers is proposed using an extended vector universal generating function technique. For repairable modular machines, the Markov models of modular machines are established using stochastic process analysis and the corresponding theoretical steady-state probability in various states is obtained. Furthermore, the original system in combination with multi-state reliability measures of buffer stations is equivalent to a system with independent machines which can be expressed by vector u-functions. Based on the probability distributions of the states of subsystems, the composition operators for series connections and parallel connections are defined. Consequently, the entire system is simplified to one component represented by the polynomial universal generating function. In particular, reliability indicators and measurement models are given to assess the system’s reliability through promoting the basic ones. Finally, a practical case of engine head machining line is utilized to verify the effectiveness of the method. The results demonstrate that the use of vector universal generating functions can describe the system structure and states more appropriately while providing efficient assessment.

Noise-precision tradeoff in predicting combinations of mutations and drugs.

Many biological problems involve the response to multiple perturbations. Examples include response to combinations of many drugs, and the effects of combinations of many mutations. Such problems have an exponentially large space of combinations, which makes it infeasible to cover the entire space experimentally. To overcome this problem, several formulae that predict the effect of drug combinations or fitness landscape values have been proposed. These formulae use the effects of single perturbations and pairs of perturbations to predict triplets and higher order combinations. Interestingly, different formulae perform best on different datasets. Here we use Pareto optimality theory to quantitatively explain why no formula is optimal for all datasets, due to an inherent bias-variance (noise-precision) tradeoff. We calculate the Pareto front of log-linear formulae and find that the optimal formula depends on properties of the dataset: the typical interaction strength and the experimental noise. This study provides an approach to choose a suitable prediction formula for a given dataset, in order to best overcome the combinatorial explosion problem.

Indirect disjunctive belief rule base modeling using limited conjunctive rules: Two possible means

A traditional Belief Rule Base (BRB) is constructed under the conjunctive assumption (conjunctive BRB), which requires covering the traversal combinations of the referenced values for the attributes. Consequentially, a traditional conjunctive BRB may have to face the combinatorial explosion problem when there are too many attributes and/or referenced values for the attributes. It is difficult or at least expensive to construct a complete conjunctive BRB, while it is easy to derive one or several conjunctive rules. Comparatively, a BRB under the disjunctive assumption (disjunctive BRB) requires only covering the referenced values for the attributes instead of the traversal combination of them. Thus, the combinatorial explosion problem can be avoided. However, it is difficult to directly obtain a disjunctive BRB from either historical data or experts' knowledge. To combine the advantages of both conjunctive and disjunctive BRBs, a new approach is proposed to construct a disjunctive BRB using a limited number of conjunctive rules (insufficient to construct a complete conjunctive BRB). In the new disjunctive BRB modeling approach, each disjunctive rule is derived by quantifying its correlation with one or multiple conjunctive rules. To do so, two means for belief generation are proposed, namely, equal probability and self-organizing mapping (SOM). Two cases are studied for validating the efficiency of the proposed approach. The results by the disjunctive BRB show consistency with those derived by the conjunctive BRB as well as other approaches, which validates the efficiency of the proposed approach considering that the disjunctive BRB is constructed with only a limited number of conjunctive rules.

Visual Feature Integration of Three Attributes in Stimulus-Response Mapping Is Distinct From That of Two.

In the human visual system, different attributes of an object are processed separately and are thought to be then temporarily bound by attention into an integrated representation to produce a specific response. However, if such representations existed in the brain for arbitrary multi-attribute objects, a combinatorial explosion problem would be unavoidable. Here, we show that attention may bind features of different attributes only in pairs and that bound feature pairs, rather than integrated object representations, are associated with responses for unfamiliar objects. We found that in a mapping task from three-attribute stimuli to responses, presenting three attributes in pairs (two attributes in each window) did not significantly complicate feature integration and response selection when the stimuli were not very familiar. We also found that repeated presentation of the same triple conjunctions significantly improved performance on the stimulus-response task when the correct responses were determined by the combination of three attributes, but this familiarity effect was not observed when the response could be determined by two attributes. These findings indicate that integration of three or more attributes is a distinct process from that of two, requiring long-term learning or some serial process. This suggests that integrated object representations are not formed or are formed only for a limited number of very familiar objects, which resolves the computational difficulty of the binding problem.

Ant colony optimization with an automatic adjustment mechanism for detecting epistatic interactions

Single Nucleotide polymorphisms (SNPs) are usually used as biomarkers for research and analysis of genome-wide association study (GWAS). Moreover, the epistatic interaction of SNPs is an important factor in determining the susceptibility of individuals to complex diseases. Nowadays, the detection of epistatic interactions not only attracts attention of many researchers but also brings new challenges. It is of great significance to mine epistatic interactions from large-scale data for the combinatorial explosion problem of loci. Hence, it is necessary to improve an efficient algorithm for solving the problem. In this article, a novel ant colony optimization based on automatic adjustment mechanism (AA-ACO) is proposed. The mechanism automatically adjusts the behaviour of artificial ants according to the real-time feedback information so that the algorithm can run at its best. This study also compares AA-ACO with ACO, AntEpiSeeker, AntMiner, MACOED and epiACO in a set of simulated data sets and a real genome-wide data. As shown by the experimental results, the proposed algorithm is superior to the other algorithms.

Optimization qualitative and quantitative for dependability analysis

Systems that are not dependable and insecure may be rejected by their users. For many systems controlled by computer, the most important system property is the dependability of the system. For this reason in this paper, we propose a complete approach for dependability analysis. The proposed approach is based on optimization qualitative and quantitative for dependability analysis, qualitative optimization is based on causality relations between the events deduced from the Truth Table Method combined with Karnaugh Table for deriving minimal feared states, q uantitative optimization is based on Reduced Markov Graph this graph is directly composed by a minimal feared state deduced from the qualitative optimization , to avoid the problem of combinatorial explosion in the number of states in the Markov graph modelling. The representation of the Markov graph will be particularly interesting to study dependability.

High Utility Itemset Mining over Uncertain Datasets Based on a Quantum Genetic Algorithm

The discovered high potential utility itemsets (HPUIs) have significant influence on a variety of areas, such as retail marketing, web click analysis, and biological gene analysis. Thus, in this paper, we propose an algorithm called HPUIM-QGA (Mining high potential utility itemsets based on a quantum genetic algorithm) to mine HPUIs over uncertain datasets based on a quantum genetic algorithm (QGA). The proposed algorithm not only can handle the problem of the non-downward closure property by developing an upper bound of the potential utility (UBPU) (which prunes the unpromising itemsets in the early stage) but can also handle the problem of combinatorial explosion by introducing a QGA, which finds optimal solutions quickly and needs to set only very few parameters. Furthermore, a pruning strategy has been designed to avoid the meaningless and redundant itemsets that are generated in the evolution process of the QGA. As proof of the HPUIM-QGA, a substantial number of experiments are performed on the runtime, memory usage, analysis of the discovered itemsets and the convergence on real-life and synthetic datasets. The results show that our proposed algorithm is reasonable and acceptable for mining meaningful HPUIs from uncertain datasets.

Evolutionary design of high signal integrity interconnection based on eye-diagram

Frequency of the digital signal in PCBs has remained at about 1 GHz, while that in VLSIs become more than several GHz. The frequency gap comes from signal integrity (SI) deterioration in PCB in GHz-domain. To overcome this problem, we have already proposed segmental transmission line, in which genetic algorithm is used to solve the combinatorial explosion problem in the design. In this paper, we propose a novel fitness based on the eye-diagram, which is widely and generally used for SI evaluation in the high-speed interconnection design field. And we also propose a high-speed eye-diagram calculation method based on virtual eye-diagram. This eye-diagram is constructed by superposing the single-shot pulse responses and can reduce the simulation time. The simulation experiments demonstrate that our proposed fitness increases the eye height and eye width by 3.07 and 1.06 times, respectively, compared with the conventional one.

Biophysical attributes that affect CaMKII activation deduced with a novel spatial stochastic simulation approach.

Calcium/calmodulin-dependent protein kinase II (CaMKII) holoenzymes play a critical role in decoding Ca2+ signals in neurons. Understanding how this occurs has been the focus of numerous studies including many that use models. However, CaMKII is notoriously difficult to simulate in detail because of its multi-subunit nature, which causes a combinatorial explosion in the number of species that must be modeled. To study the Ca2+-calmodulin-CaMKII reaction network with detailed kinetics while including the effect of diffusion, we have customized an existing stochastic particle-based simulator, Smoldyn, to manage the problem of combinatorial explosion. With this new method, spatial and temporal aspects of the signaling network can be studied without compromising biochemical details. We used this new method to examine how calmodulin molecules, both partially loaded and fully loaded with Ca2+, choose pathways to interact with and activate CaMKII under various Ca2+ input conditions. We found that the dependence of CaMKII phosphorylation on Ca2+ signal frequency is intrinsic to the network kinetics and the activation pattern can be modulated by the relative amount of Ca2+ to calmodulin and by the rate of Ca2+ diffusion. Depending on whether Ca2+ influx is saturating or not, calmodulin molecules could choose different routes within the network to activate CaMKII subunits, resulting in different frequency dependence patterns. In addition, the size of the holoenzyme produces a subtle effect on CaMKII activation. The more extended the subunits are organized, the easier for calmodulin molecules to access and activate the subunits. The findings suggest that particular intracellular environmental factors such as crowding and calmodulin availability can play an important role in decoding Ca2+ signals and can give rise to distinct CaMKII activation patterns in dendritic spines, Ca2+ channel nanodomains and cytoplasm.

Research and analysis of video image target tracking algorithm based on significance

A target tracking algorithm based on joint probabilistic data association encounters the problems of target loss and combinatorial explosion in cluttered and target-intensive tracking environments. In order to address these challenges, this paper proposes a video target tracking algorithm based on significance joint probabilistic data association. This algorithm detects the moving target in a video sequence through significance calculation. The detection results are classified, and the returned classes are then used as valid echoes for data association. Meanwhile, the validation matrix and joint probability in the joint probabilistic data association algorithm are redefined based on the significance information and a validation matrix and association probability based on significance is proposed. The association results are compensated and corrected using the colour association probability. Experiments in real scenes demonstrate that the proposed algorithm can suppress clutter in the background, simplify interconnected events, and solve the problem of computational combinatorial explosion.

Research and analysis of video image target tracking algorithm based on significance

A target tracking algorithm based on joint probabilistic data association encounters the problems of target loss and combinatorial explosion in cluttered and target-intensive tracking environments. In order to address these challenges, this paper proposes a video target tracking algorithm based on significance joint probabilistic data association. This algorithm detects the moving target in a video sequence through significance calculation. The detection results are classified, and the returned classes are then used as valid echoes for data association. Meanwhile, the validation matrix and joint probability in the joint probabilistic data association algorithm are redefined based on the significance information and a validation matrix and association probability based on significance is proposed. The association results are compensated and corrected using the colour association probability. Experiments in real scenes demonstrate that the proposed algorithm can suppress clutter in the background, simplify interconnected events, and solve the problem of computational combinatorial explosion.

Fault Diagnosis of Discrete-Event systems Based on the Symbolic Observation Graph

Fault diagnosis of discrete-event systems (DESs) has received a lot of attention in industry and academia during the last two decades. In DES based diagnosis, the two main discussed topics are offline diagnosability analysis and online diagnosis. A pioneering approach that led to the development of various techniques is based on the so-called diagnose. However, this approach suffers from the combinatorial explosion problem due to the exponential complexity of construction. To partially overcome this problem, an efficient approach to construct a symbolic diagnoser is proposed in this paper. The proposed approach consists in constructing a diagnoser based on the symbolic observation graph (SOG), which combines symbolic and enumarative representations. The construction of the diagnoser as well as the verification of diagnosability are performed simultaneously on the fly, which can considerably reduce the state space of the diagnoser and thus the overall running time. To evaluate the efficiency and the scalability of the approach, some experimental results are presented and discussed based on a DES benchmark.

Evaluating Bees Algorithm for Sequence-based T-way Testing Test Data Generation

T-way testing is a testing technique that is used to detect faults due to parameter interactions or software configurations. In order to perform t-way testing, software testers need to prepare the test data. For a system with many configuration parameters, the test data could lead to combinatorial explosion problem, since all possible parameter combinations need to be considered. Therefore, test data generation for t-way testing need to be optimized. Many t-way test data generation strategies have been proposed in the literature to generate optimized t-way test data. However, very few strategies have been proposed for sequence-based t-way. This paper presents statistical analysis on the performance of Bees Algorithm against the other sequence t-way strategies, in order to generate test cases.

Fault diagnosis of discrete-event systems based on the symbolic observation graph

Fault diagnosis of discrete-event systems (DESs) has received a lot of attention in industry and academia during the last two decades. In DES based diagnosis, the two main discussed topics are offline diagnosability analysis and online diagnosis. A pioneering approach that led to the development of various techniques is based on the so-called diagnose. However, this approach suffers from the combinatorial explosion problem due to the exponential complexity of construction. To partially overcome this problem, an efficient approach to construct a symbolic diagnoser is proposed in this paper. The proposed approach consists in constructing a diagnoser based on the symbolic observation graph (SOG), which combines symbolic and enumarative representations. The construction of the diagnoser as well as the verification of diagnosability are performed simultaneously on the fly, which can considerably reduce the state space of the diagnoser and thus the overall running time. To evaluate the efficiency and the scalability of the approach, some experimental results are presented and discussed based on a DES benchmark.

Prediction of drug cocktail effects when the number of measurements is limited.

Cocktails of drugs can be more effective than single drugs, because they can potentially work at lower doses and avoid resistance. However, it is impossible to test all drug cocktails drawn from a large set of drugs because of the huge number of combinations. To overcome this combinatorial explosion problem, one can sample a relatively small number of combinations and use a model to predict the rest. Recently, Zimmer and Katzir et al. presented a model that accurately predicted the effects of cocktails at all doses based on measuring pairs of drugs. This model requires measuring each pair at several different doses and uses interpolation to reduce experimental noise. However, often, it is not possible to measure each pair at multiple doses (for example, in scarce patient-derived tumor material or in large screens). Here, we ask whether measurements at only a single dose can also predict high-order drug cocktails. To address this, we present a fully factorial experimental dataset on all drug cocktails built of 6 chemotherapy drugs on 2 cancer cell lines. We develop a formula that uses only pair measurements at a single dose to predict much of the variation up to 6-drug cocktails in the present data, outperforming commonly used Bliss independence and regression approaches. This model, called the pairs model, is an extension of the Bliss independence model to pairs: For M drugs, it equals the product of all pair effects to the power 1/(M−1). The pairs model also shows good agreement with previously published data on antibiotic triplets and quadruplets. The present model can only predict combinations at the same doses in which the pairs were measured and is not able to predict effects at other doses. This study indicates that pair-based approaches might be able to usefully predict and prioritize high-order combinations, even in large screens or when material for testing is limited.

Development of intervention programs for inland waterway networks using genetic algorithms

Inland waterways often consist of large numbers of man-made objects to ensure navigability. These objects are of many different types, ages and sizes, and deteriorate in uncountable of different ways. In order to ensure that the deterioration of the objects does not result in a loss of navigability, interventions must be executed. This, however, produces costs, in terms of both labour and material costs and costs of loss of service if the waterway is rendered non-navigable during intervention. In this paper, a methodology is presented to determine optimal multiple time period intervention programmes for inland waterways. The optimal intervention programme is the one that has highest net benefit, i.e. overall benefits minus overall costs, where benefits are the reduction in risk of failure. A genetic algorithm is used to overcome the problem of combinatorial explosion when many objects, in many states, over many time periods are to be considered. The exact formulation of the genome, as well as the genetic fitness function, are presented. They are used to determine an optimal intervention programme for a fictive inland waterway network. The results are presented and discussed, and an outlook is provided on further steps to improve this methodology.

Protein β-sheet prediction using an efficient dynamic programming algorithm

Predicting the β-sheet structure of a protein is one of the most important intermediate steps towards the identification of its tertiary structure. However, it is regarded as the primary bottleneck due to the presence of non-local interactions between several discontinuous regions in β-sheets. To achieve reliable long-range interactions, a promising approach is to enumerate and rank all β-sheet conformations for a given protein and find the one with the highest score. The problem with this solution is that the search space of the problem grows exponentially with respect to the number of β-strands. Additionally, brute-force calculation in this conformational space leads to dealing with a combinatorial explosion problem with intractable computational complexity. The main contribution of this paper is to generate and search the space of the problem efficiently to reduce the time complexity of the problem. To achieve this, two tree structures, called sheet-tree and grouping-tree, are proposed. They model the search space by breaking it into sub-problems. Then, an advanced dynamic programming is proposed that stores the intermediate results, avoids repetitive calculation by repeatedly uses them efficiently in successive steps and reduces the space of the problem by removing those intermediate results that will no longer be required in later steps. As a consequence, the following contributions have been made. Firstly, more accurate β-sheet structures are found by searching all possible conformations, and secondly, the time complexity of the problem is reduced by searching the space of the problem efficiently which makes the proposed method applicable to predict β-sheet structures with high number of β-strands. Experimental results on the BetaSheet916 dataset showed significant improvements of the proposed method in both execution time and the prediction accuracy in comparison with the state-of-the-art β-sheet structure prediction methods Moreover, we investigate the effect of different contact map predictors on the performance of the proposed method using BetaSheet1452 dataset. The source code is available at http://www.conceptsgate.com/BetaTop.rar.

On‐the‐Fly and Incremental Technique for Fault Diagnosis of Discrete Event Systems Modeled by Labeled Petri Nets

AbstractIn this paper, we develop an on‐the‐fly and incremental technique for fault diagnosis of discrete event systems modeled by labeled Petri nets, in order to tackle the combinatorial explosion problem. K‐diagnosability, diagnosability, Kmin (the minimum K ensuring diagnosability) and on‐line diagnosis are solved on the basis of the on‐the‐fly and incremental building of two structures, called respectively fault marking graph and fault marking set graph, in parallel. We build on existing results, namely those establishing necessary and sufficient conditions for diagnosability, but we bring mechanisms to make the checking of such conditions potentially more efficient. We show that, in general, analyzing or even building the whole reachability graph is unnecessary to analyze diagnosability and build an on‐line diagnoser. Our technique was implemented in a prototype tool called OF‐PENDA, and a railway level crossing benchmark is used to make a comparative discussion pertaining to efficiency in terms of time and memory relative to some existing approaches.

Monotone Fuzzy Rule Relabeling for the Zero-Order TSK Fuzzy Inference System

To maintain the monotonicity property of a fuzzy inference system, a monotonically ordered and complete set of fuzzy rules is necessary. However, monotonically ordered fuzzy rules are not always available, e.g., errors in human judgments lead to nonmonotone fuzzy rules. The focus of this paper is on a new monotone fuzzy rule relabeling (MFRR) method that is able to relabel a set of nonmonotone fuzzy rules to meet the monotonicity property with reduced computation. Unlike the brute-force approach, which is susceptible to the combinatorial explosion problem, the proposed MFRR method explores within a reduced search space to find the solutions, therefore decreasing the computational requirements. The usefulness of the proposed method in undertaking failure mode and effect analysis problems is demonstrated using publicly available information. The results indicate that the MFRR method can produce optimal solutions with reduced computational time.

Prediction of multidimensional drug dose responses based on measurements of drug pairs

Finding potent multidrug combinations against cancer and infections is a pressing therapeutic challenge; however, screening all combinations is difficult because the number of experiments grows exponentially with the number of drugs and doses. To address this, we present a mathematical model that predicts the effects of three or more antibiotics or anticancer drugs at all doses based only on measurements of drug pairs at a few doses, without need for mechanistic information. The model provides accurate predictions on available data for antibiotic combinations, and on experiments presented here on the response matrix of three cancer drugs at eight doses per drug. This approach offers a way to search for effective multidrug combinations using a small number of experiments.