Random Walk Search Research Articles

Semi-empirical method for evaluating the robustness of QRWS algorithm for different coin sizes and functional dependence between coin phases

In this work we study the quantum random walk search algorithm when the walk coin is constructed by generalized Householder reflection and a phase multiplier. We focus on the algorithm’s robustness against errors in the phases – how the probability to find solution decreases with increasing the errors in those phases. The robustness depends on the functional dependence between the reflection phase φ and the phase multiplier ζ. Here we use interpolations by non-linear logistic regression functions to study a particular functional dependence between angles ζ = -2φ + 3π + α sin(2φ) for different coin sizes and parameters alpha. The obtained results in this work are discussed, together with their limitations.

Optimizing the walk coin in the quantum random walk search algorithm

This paper examines quantum random walk search algorithm with walk coin constructed by generalized Householder reflection and additional phase shift factor. The results from numerical simulations with neural network show that, with such a construction of the walk coin, the algorithm is more robust to inaccuracies in the specific values of its parameters, as long as it is possible to control the phase difference between the phase shift factor and the phase involved in the Householder reflection. This paper explicitly shows how achieving a properly designed phase difference would make quantum random walk search on a hypercube more robust for coin register consisting of one, two and three qubits.

A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins

In this work, the quantum random walk search algorithm with a walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with an arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are used to find walk coins that make the quantum algorithm more robust to deviations in the coin’s parameters. This is achieved by introducing functional dependence between these parameters. The functions that give the best performance of the algorithm are studied in detail by numerical statistical methods. A thorough comparison between our modification and an algorithm, with coins made using only Householder reflection, shows significant advantages of the former. By applying a deep neural network, we make a prediction for the parameters of an optimal coin with an arbitrary size and estimate the algorithm’s stability for such a coin.

Reducing number of gates in quantum random walk search algorithm via modification of coin operators

This paper examines a way to simplify the circuit of quantum random walk search algorithm, when the traversing coin is constructed by both generalized Householder reflection and an additional phase multiplier. If an appropriate relation between corresponding parameters is realized, our algorithm becomes more robust to deviations in the phases. In this modification marking coin is not needed, and all advantages from above mentioned optimization to the stability, are preserved. It is shown explicitly how to construct such walk coin in order to obtain more robust quantum algorithm.

Approaching the bi-objective critical node detection problem with a smart initialization-based evolutionary algorithm.

Determining the critical nodes in a complex network is an essential computation problem. Several variants of this problem have emerged due to its wide applicability in network analysis. In this article we study the bi-objective critical node detection problem (BOCNDP), which is a new variant of the well-known critical node detection problem, optimizing two objectives at the same time: maximizing the number of connected components and minimizing the variance of their cardinalities. Evolutionary multi-objective algorithms (EMOA) are a straightforward choice to solve this type of problem. We propose three different smart initialization strategies which can be incorporated into any EMOA. These initialization strategies take into account the basic properties of the networks. They are based on the highest degree, random walk (RW) and depth-first search. Numerical experiments were conducted on synthetic and real-world network data. The three different initialization types significantly improve the performance of the EMOA.

A Theoretical Framework for Studying Random Walk Planning

Random walks are a relatively new component used in several state of the art satisficing planners. Empirical results have been mixed: while the approach clearly outperforms more systematic search methods such as weighted A* on many planning domains, it fails in many others. So far, the explanations for these empirical results have been somewhat ad hoc. This paper proposes a formal framework for comparing the performance of random walk and systematic search methods. Fair homogenous graphs are proposed as a graph class that represents characteristics of the state space of prototypical planning domains, and is simple enough to allow a theoretical analysis of the performance of both random walk and systematic search algorithms. This gives well-founded insights into the relative strength and weaknesses of these approaches. The close relation of the models to some well-known planning domains is shown through simplified but semi-realistic planning domains that fulfill the constraints of the models. One main result is that in contrast to systematic search methods, for which the branching factor plays a decisive role, the performance of random walk methods is determined to a large degree by the Regress Factor, the ratio between the probabilities of progressing towards and regressing away from a goal with an action. The performance of random walk and systematic search methods can be compared by considering both branching and regress factors of a state space.

Simplified bacterial foraging optimization with quorum sensing for global optimization

Bacterial foraging optimization (BFO) has been exploited for function optimization, owing to its innovative ideas gleaned from the microbiological system. This paper first discusses its three crucial limitations: high computational cost, difficulty in parameter settings, and premature convergence. To alleviate the above problems, simplified BFO with quorum sensing (QS) is proposed. First, a novel computational framework is provided to reduce the computational complexity, leading to a simplified version. Second, the concept of “QS,” bacterial reciprocal behavior, is integrated into the simplified version by utilizing a new position updating equation coupled with a dynamic communication topology. Each bacterium adjusts its search trajectory based on both biased random walk and promising search directions provided by its communicatees. The communicatees are selected via a dynamic communication topology, where a rank-based communication strategy and two information mutation schemes are used for global exploration of the search space. Finally, a parameter automation strategy is introduced to promote the exploitation of promising regions. Further, the effectiveness and efficiency of the proposed algorithm are empirically confirmed on 30 benchmark functions, by comparing it with the four variants of BFO and four other advanced algorithms.

Chaotic search algorithm for detection of discontinuities using guided waves and beamforming data

The goal of inspection and continuous health monitoring of engineering structures is to detect defects particularly during their early stages of development. In this work, a method using an optimization scheme for localization of a target using ultrasonic guided waves in a thin plate and data sampled from a beamforming is studied. The proposed optimization scheme finds the target by using a search algorithm based on random and chaotic walk search to reduce the number of evaluation points within the search space. The data used for the scheme is extracted from the using only a reduced number of evaluation points from the energy reconstruction map of a delay and sum beamforming algorithm. The proposed approach is numerically studied and implemented experimentally for discontinuity detection in a plate using guided Lamb waves. The combined experimental and numerical analysis indicates that the searching algorithm was able to find an acoustic target generated by a discontinuity in a plate even when the signals were contaminated by noise.

Mean Shift Cluster Recognition Method Implementation in the Nested Sampling Algorithm.

Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a series of values sets called live points that evolve towards the region of interest, i.e., where the likelihood function is maximal. In presence of several local likelihood maxima, the algorithm converges with difficulty. Some systematic errors can also be introduced by unexplored parameter volume regions. In order to avoid this, different methods are proposed in the literature for an efficient search of new live points, even in presence of local maxima. Here we present a new solution based on the mean shift cluster recognition method implemented in a random walk search algorithm. The clustering recognition is integrated within the Bayesian analysis program NestedFit. It is tested with the analysis of some difficult cases. Compared to the analysis results without cluster recognition, the computation time is considerably reduced. At the same time, the entire parameter space is efficiently explored, which translates into a smaller uncertainty of the extracted value of the Bayesian evidence.

A stochastic modelling framework to accommodate the inter-annual variability of habitat conditions for Peary caribou (Rangifer tarandus pearyi) populations

Climate variability and a wide range of anthropogenic disturbances in the Canadian Arctic Archipelago (CAA) have a negative impact on Peary caribou (Rangifer tarandus pearyi) populations by encumbering seasonal migration patterns, forage accessibility, and calving processes. Increasing Arctic temperatures and precipitation along with the higher frequency of extreme weather events (winter cyclones, rain-on-snow) are responsible for spatiotemporal shifts in floral and faunal phenology, changes in species overlap, and functional alterations of trophic relationships. Building upon empirical estimates of the Peary caribou population rates of change on the Canadian Arctic Archipelago, we introduce a two-pronged approach aiming to characterize year-to-year variability of habitat conditions across the Canadian Arctic Archipelago from 2000 to 2013. Our explanatory variables are based on meteorological (surface snow melt, precipitation, temperature, wind speed) variables, landscape features (fraction of rockland), and resource competition with muskoxen (Ovibos moschatus). These habitat suitability estimates form the basis of a stochastic algorithm to recreate the population growth rates and identify locations, where Peary caribou could experience >10%, 25%, or 50% decrease relative to the population levels at the beginning of our study period. Our analysis identifies the Boothia island complex as a high-risk area, where the low Peary caribou population size is suggestive of their increased susceptibility to extirpation after episodic weather-related events, disease outbreaks, or even elevated incidental predation. In Banks island complex, we provide evidence that the volunteered curtailment of hunting, achieved through co-management between Indigenous communities and regional biologists, moderated (and possibly reversed) the declining trends as established during the pre-2000 period. Our random-walk search also suggests that the prevailing habitat conditions in Melville and Bathurst island complexes were generally favorable and could partly explain the recent Peary caribou population increase. We conclude by identifying unaccounted factors that are critical for building an empirical modelling framework with quasi-mechanistic foundation in order to evaluate the impact of climate change on the integrity of Peary caribou populations within any location of the Canadian Arctic.

Sustainability Assessment of Constructive Solutions for Urban Spain: A Multi-Objective Combinatorial Optimization Problem

Industrial areas are set up on plots of roads and associated infrastructure. These use materials and machinery that have environmental impacts, and thus require constructive solutions throughout their lifecycles. In turn, these solutions and their components cause environmental impacts that can be measured by sustainability indicators. The concept of sustainability is closely tied to sustainable development, which is defined as “development that meets the needs of the present, without compromising the ability of future generations to meet their own needs”. The large number of possible and available solutions means that identifying the best one for a given road section must employ a set of heuristic techniques, which conceptualize the issue as a combinatorial optimization problem that is purely discrete and non-differential. The system chosen can be based on a genetic algorithm method that differentiates individuals based on three sustainability indicators: CO2 emissions, embedded energy (also known as embodied energy, defined as the energy expended to manufacture a product), and economic cost. In this paper, we supplement traditional cost analyses using a three-objective multi-objective genetic algorithm that considers the aforementioned criteria, thus addressing sustainability in aggregate planning. The procedure is applied to three objective functions—CO2 emissions, economic cost and embedded energy—for each possible solution. We used the non-dominated sorting genetic algorithm (NSGA-II) to implement multi-objective optimization in MATLAB. Additional results for a random walk and multi-objective search algorithm are shown. This study involved 26 design variables, with different ranks of variation, and the application of the algorithm generates results for the defined Pareto fronts. Our method shows that the optimal approach effectively solves a real-world multi-objective project planning problem, as our solution is one of the Pareto-optimal solutions generated by the NSGA-II.

A random walk perspective on hide-and-seek games

We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of vertices of a random graph. Vertices at which items are hidden in the network are chosen at random as well, though with probabilities that may depend on degree. We pitch various hide and seek strategies against each other, and determine the efficiency of search strategies by computing the average number of hidden items that a searcher will uncover in a random walk of n steps. Our analysis is based on the cavity method for finite single instances of the problem, and generalises previous work of De Bacco et al (2015 J. Phys. A: Math. Theor. 48 205004) so as to cover degree-biased random walks. We also extend the analysis to deal with the thermodynamic limit of infinite system size. We study a broad spectrum of functional forms for the degree bias of both the hiding and the search strategy and investigate the efficiency of families of search strategies for cases where their functional form is either matched or unmatched to that of the hiding strategy. Our results are in excellent agreement with those of numerical simulations. We propose two simple approximations for predicting efficient search strategies. One is based on an equilibrium analysis of the random walk search strategy. While not exact, it produces correct orders of magnitude for parameters characterising optimal search strategies. The second exploits the existence of an effective drift in random walks on networks, and is expected to be efficient in systems with low concentration of small degree nodes.

Proton Wire Dynamics in the Green Fluorescent Protein.

Inside proteins, protons move on proton wires (PWs). Starting from the highest resolution X-ray structure available, we conduct a 306 ns molecular dynamics simulation of the (A-state) wild-type (wt) green fluorescent protein (GFP) to study how its PWs change with time. We find that the PW from the chromophore via Ser205 to Glu222, observed in all X-ray structures, undergoes rapid water molecule insertion between Ser205 and Glu222. Sometimes, an alternate Ser205-bypassing PW exists. Side chain rotations of Thr203 and Ser205 play an important role in shaping the PW network in the chromophore region. Thr203, with its bulkier side chain, exhibits slower transitions between its three rotameric states. Ser205 experiences more frequent rotations, slowing down when the Thr203 methyl group is close by. The combined states of both residues affect the PW probabilities. A random walk search for PWs from the chromophore reveals several exit points to the bulk, one being a direct water wire (WW) from the chromophore to the bulk. A longer WW connects the "bottom" of the GFP barrel with a "water pool" (WP1) situated below Glu222. These two WWs were not observed in X-ray structures of wt-GFP, but their analogues have been reported in related fluorescent proteins. Surprisingly, the high-resolution X-ray structure utilized herein shows that Glu222 is protonated at low temperatures. At higher temperatures, we suggest ion pairing between anionic Glu222 and a proton hosted in WP1. Upon photoexcitation, these two recombine, while a second proton dissociates from the chromophore and either exits the protein using the short WW or migrates along the GFP-barrel axis on the long WW. This mechanism reconciles the conflicting experimental and theoretical data on proton motion within GFP.

Bayesian resource discovery in infrastructure-less networks

Resource discovery is one of the most important infrastructure-level facilities enabling the success of modern ad-hoc mobile communication networks, integrating services and capabilities provided by heterogeneous objects into the Future Internet environment. However, the highly dynamic and infrastructure-less nature of these organizations, where nodes continuously join and leave the network or change their attachment connections by moving between different coverage areas, makes resource discovery an extremely challenging tasks. In lack of specific knowledge about the availability of resources and their location over the network, flooding-based or pure probabilistic exploration approaches are the only feasible options to support search/discovery operations. By considering the high communication cost and the incomplete coverage problems respectively characterizing the aforementioned approaches we propose a novel adaptive random-walk search strategy, for resource discovery in ad-hoc networks, structured according to a selective stochastic query/response scheme where the exploration process is driven by posterior probability, using Bayesian inference and relying on the history of past discovery operations. This strategy, by also taking advantage of the scale-free properties characterizing the aforementioned ad-hoc organizations, is able to significantly contain the broadcast traffic without compromising the overall success of search operations by seamlessly accommodating to dynamic changes in resource location and network topology.

PS-LTE 환경에서 최적기지국 위치 선정

본 논문에서는 PS-LTE(Public Safety-Long Term Evolution) 환경에서 단독기지국의 설치에 있어서 전체 사용자의 데이터 처리량을 최대화하는 PSO(Particle Swarm Optimization)기반의 최적기지국 위치 선정 방법을 제안한다. 또한 전체 재난 지역을 탐색하여 최적의 위치를 찾는 완전탐색(Exhaustive Search) 방법, 임의보행(Random Walk) 이동모형을 적용하여 위치를 선정하는 방법, 기지국 균일 배치방법과의 성능을 비교하였다. 제안하는 방법의 경우 모든 지역을 탐색하여 최적위치를 찾는 완전탐색 방법과 유사한 최적위치 및 전체 사용자의 데이터 처리량(Throughput)을 갖지만, 최적해 수렴시간에 있어서 완전탐색의 경우 재난지역의 크기가 커질수록 증가하지만, 제안하는 방법 경우 빠른 수렴 시간 및 거의 일정한 수렴시간을 갖는 것을 알 수 있다. In this paper, we try to find the optimal locations of NeNB(Nomadic evolved NodeB)s for maximizing the overall throughput of the PS-LTE networks. Since finding optimal locations of all NeNBs in a given area is NP-hard(Non-deterministic Polynomial time-hard) problem, we proposed a PSO-based heuristic approach. In order to evaluate the performance, we conducted two experiments. We compared performance with other schemes such as Exhaustive Search, Random Walk Search, and locating neighboring NeNBs with the same NeNB-to-NeNB distance. The proposed method showed the similar results to the exhaustive search method in terms of locating optimal position and user's data throughput. The proposed method, however, has the fast and consistent convergence time.

Resource location based on precomputed partial random walks in dynamic networks

The problem of finding a resource residing in a network node (the resource location problem) is a challenge in complex networks due to aspects as network size, unknown network topology, and network dynamics. The problem is especially difficult if no requirements on the resource placement strategy or the network structure are to be imposed, assuming of course that keeping centralized resource information is not feasible or appropriate. Under these conditions, random algorithms are useful to search the network. A possible strategy for static networks, proposed in previous work, uses short random walks precomputed at each network node as partial walks to construct longer random walks with associated resource information. In this work, we adapt the previous mechanisms to dynamic networks, where resource instances may appear in, and disappear from, network nodes, and the nodes themselves may leave and join the network, resembling realistic scenarios. We analyze the resulting resource location mechanisms, providing expressions that accurately predict average search lengths, which are validated using simulation experiments. Reduction of average search lengths compared to simple random walk searches are found to be very large, even in the face of high network volatility. We also study the cost of the mechanisms, focusing on the overhead implied by the periodic recomputation of partial walks to refresh the information on resources, concluding that the proposed mechanisms behave efficiently and robustly in dynamic networks.

Development of Unstructured Architecture for Voice and Data Services in Mobile Communication

The huge popularity of voice and data services in mobile communication facilitates ubiquitous infrastructure that has been mainly driven by the scalability of their architectures and the flexibility of their search facilities. Such systems are usually designed as unstructured point-to-point networks and support highly versatile search algorithms.Developing search algorithms is difficult in unstructured peer-to-peer networks. Flooding and Random Walk are two typical search algorithms. Flooding covers most of the nodes by searching randomly. In the unstructured network peers are interconnected randomly, they rely on Flooding query messages to discover objects of interest. It generates a large amount of query messages which produces network traffic. Random walk search algorithms are used in mobile networks because of their dynamic nature. But it only generates a fixed amount of query messages at each peer but would take longer search time. Thus we propose development of unstructured architecture for voice and data services in mobile communication. In this architecture we are focusing on interconnection of various mobile devices. One way is to improve the algorithm for selecting path, second way to modify the routing algorithm by considering new characteristics for less signaling overhead.

Optimized quantum random-walk search algorithm for multi-solution search**Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.

Levy Foraging in a Dynamic Environment – Extending the Levy Search

A common task for robots is the patrolling of an unknown area with inadequate information about target locations. Under these circumstances it has been suggested that animal foraging could provide an optimal or at least sub-optimal search methodology, namely the Levy flight search. Although still in debate, it seems that predators somehow follow this search pattern when foraging, because it avoids being trapped in a local search if the food is beyond the sensory range. A Levy flight is a particular case of the random walk. Its displacements on a 2-D surface are drawn from the Pareto-Levy probability distribution, characterized by power law tails. The Levy flight search has many applications in optical material, ladars, optics, large database search, earthquake data analysis, location of DNA sites, human mobility, stock return analysis, online auctions, astronomy, ecology and biology. Almost all studies and simulations concerning the Levy flight foraging examine static or slowly moving (with respect to the forager) uniformly distributed resources. Moreover, in recent works a small swarm of underwater autonomous vehicles has been used to test the standard Levy search in the underwater environment, with good results. In this paper we extend the classical Levy foraging framework taking into consideration a moving target allocated on a 2-D surface according to a radial probability distribution and comparing its performance with the random walk search. The metric used in the numerical simulations is the detection rate. Simulations include the sensor resolution, intended as the maximum detection distance of the forager from the target. Furthermore, contrarily to the usual Levy foraging framework, we use only one target. Results show that Levy flight outperforms the random walk if the sensor detection radius is not too small or too large. We also find the Levy flight in the velocity of the center of mass model of a fish school according the Kuramoto equation, a famous model of synchronization phenomena. Finally, a discussion about the controversy concerning the innate or evolutionary origin of the Levy foraging is given.

Decoherence in optimized quantum random-walk search algorithm**Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.