Deterministic Annealing Algorithm Research Articles

A linearly decreasing deterministic annealing algorithm for the multi-vehicle dial-a-ride problem.

Dial a ride problem (DARP) is a complex version of the pick-up and delivery problem with many practical applications in the field of transportation. This study proposes an enhanced deterministic annealing algorithm for the solution of large-scale multi-vehicle DARPs. The proposed method always explores the feasible search space; therefore, a feasible solution is guaranteed at any point of termination. This method utilises advanced local search operators to accelerate the search for optimal solutions and it relies on a linearly decreasing deterministic annealing schedule to limit poor jumps during the course of search. This study puts forward a systematic series of experiments to compare the performance of solution methods from various angles. The proposed method is compared with the most efficient methods reported in the literature i.e., the Adaptive Large Neighbourhood Search (ALNS), Evolutionary Local Search (ELS), and Deterministic Annealing (DA) using standard benchmarks. The results suggest that the proposed algorithm is on average faster than the state-of-the-art algorithms in reaching competitive objective values across the range of benchmarks.

A deterministic annealing local search for the electric autonomous dial-a-ride problem

This paper investigates the Electric Autonomous Dial-A-Ride Problem (E-ADARP), which consists in designing a set of minimum-cost routes that accommodates all customer requests for a fleet of Electric Autonomous Vehicles (EAVs). Problem-specific features of the E-ADARP include: (i) the employment of EAVs and a partial recharging policy; (ii) the weighted-sum objective function that minimizes the total travel time and the total excess user ride time. In this work, we propose a Deterministic Annealing (DA) algorithm and provide the first heuristic results for the static E-ADARP. Partial recharging (i) is handled by an exact route evaluation scheme of linear time complexity. To tackle (ii), we propose a new method that allows effective computations of minimum excess user ride time by introducing a fragment-based representation of paths. These two methods compose an exact and efficient optimization of excess user ride time for a generated E-ADARP route. To validate the performance of the DA algorithm, we compare our algorithm results to the best-reported Branch-and-Cut (B&C) algorithm results on existing instances. Our algorithm provides 25 new best solutions and 45 equal solutions on 84 existing instances. To test the algorithm performance on larger-sized instances, we establish new instances with up to 8 vehicles and 96 requests, and we provide 19 new solutions for these instances. Our final investigation extends the state-of-the-art model and explores the effect of allowing multiple visits to recharging stations. This relaxation can efficiently improve the solution’s feasibility and quality.

A Linearly Decreasing Deterministic Annealing Algorithm for the Multivehicle Dial-a-Ride Problem

A Linearly Decreasing Deterministic Annealing Algorithm for the Multivehicle Dial-a-Ride Problem

An approximation lagrangian-based algorithm for the maximum clique problem via deterministic annealing neural network

The maximum clique problem is an NP hard combinatorial optimization problem, which is widely used in industrial and management processes. In order to approach the solution of the maximum clique problem, a deterministic annealing algorithm is proposed. When the barrier parameter is reduced from a large positive number to zero, the algorithm can track the minimum path of the obstacle problem to obtain a high-quality solution, which is a continuous method. The global convergence iteration of the Lagrange multiplier can be performed to obtain the minimum point of the obstacle problem in the feasible descent direction for any given positive value of the barrier parameter and has a desired property that it automatically satisfies the upper and lower bounds of variables if the steplength is a number that is between 0 and 1. Numerical results are provided to illustrate the efficiency of the proposed algorithm.

System Design for Pose Determination of Spacecraft Using Time-of-Flight Sensors

The pose determination between nanosatellites and the cooperative spacecraft is essential for swarm in-orbit services. Time-of–flight (ToF) sensors are one of the most promising sensors to achieve the tasks. This paper presented an end-to-end assessment of how these sensors were used for pose estimation. First, an embedded system was designed based on the ToF camera with lasers as a driven light source. Gray and depth images were collected to detect and match the cooperative spacecraft in real time, obtaining the pose information. A threshold-based segmentation was proposed to find a small set of the pixels belonging to reflector markers. Only operating on the defined active pixel set reduced computational resources. Then, morphological detection combined with an edge following-based ellipse detection extracted the centroid coordinate of the circular marker, while the center-of-heart rate was calculated as the recognition condition. Next, the marker matching was completed using a deterministic annealing algorithm, obtaining two sets of 3D coordinates. A singular value decomposition (SVD) algorithm estimated the relative pose between the nanosatellite and the spacecraft. In the experiments, the pose calculated by the TOF camera reached an accuracy of 0.13 degrees and 2 mm. It accurately identified the markers and determined the pose, verifying the feasibility of the ToF camera for rendezvous and docking.

A more efficient deterministic annealing neural network algorithm for the max-bisection problem

The max-bisection problem has extensive applications in network engineering, making it imperative to develop effective methods to solve this problem. However, the efficient computation on this problem remains challenging due to its NP-hard computational complexity. To address this question, in this paper, we transform the max-bisection problem to an artificial linearly constrained optimization problem and develop a modified deterministic annealing neural network algorithm by introducing a barrier function. The barrier parameter of this function acts as the temperature in the annealing process and decreases from a large positive number to zero. The initial value of the barrier parameter promises that the artificial problem is convex and can be easily solved at the beginning of the descending process. The solution to the original max-bisection problem is finally obtained through a descent algorithm, in which the bound limit of the solution is always satisfied as long as the iteration step length is less than one. We have proved the theoretical convergence of the proposed algorithm. Numerical results demonstrate that the proposed algorithm has several advantages over both the approximation algorithms and metaheuristic methods.

Adaptive parameter estimation of GMM and its application in clustering

Parameter estimation of Gaussian mixture model (GMM) has begun to gain attention in the field of science and engineering, and it has gradually become one of the most popular research topics. In particular, the rapid development of theoretical progress on globally optimal convergence promotes the widespread application of Gaussian mixtures in data clustering. So this paper introduces a novel parameter estimation algorithm called TDAVBEM, which combines the Tsallis entropy and a deterministic annealing (DA) algorithm on the basis of the variational bayesian expected maximum (VBEM) to simultaneously implement the parameter estimation and select the optimal components of GMM. We experimentally certified the effectiveness and robustness of our proposed algorithm passes through comparing it with several parameter evaluation methods and its application in data clustering.

On the Persistence of Clustering Solutions and True Number of Clusters in a Dataset

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the clustering solutions with different number of clusters. This article quantifies a notion of persistence of clustering solutions that enables comparing solutions with different number of clusters. The persistence relates to the range of dataresolution scales over which a clustering solution persists; it is quantified in terms of the maximum over two-norms of all the associated cluster-covariance matrices. Thus we associate a persistence value for each element in a set of clustering solutions with different number of clusters. We show that the datasets where natural clusters are a priori known, the clustering solutions that identify the natural clusters are most persistent - in this way, this notion can be used to identify solutions with true number of clusters. Detailed experiments on a variety of standard and synthetic datasets demonstrate that the proposed persistence-based indicator outperforms the existing approaches, such as, gap-statistic method, X-means, Gmeans, PG-means, dip-means algorithms and informationtheoretic method, in accurately identifying the clustering solutions with true number of clusters. Interestingly, our method can be explained in terms of the phase-transition phenomenon in the deterministic annealing algorithm, where the number of distinct cluster centers changes (bifurcates) with respect to an annealing parameter.

Fast pore matching method based on deterministic annealing algorithm

High-resolution fingerprint identification system (HRFIS) has become a hot topic in the field of academic research. Compared to traditional automatic fingerprint identification system, HRFIS reduces the risk of being faked by using level 3 features, such as pores, which cannot be detected in lower resolution images. However, there is a serious problem in HRFIS: there are hundreds of sweat pores in one fingerprint image, which will spend a considerable amount of time for direct fingerprint matching. The authors propose a method to match pores in two fingerprint images based on deterministic annealing algorithm. In this method, fingerprints are aligned using singular points. Then minutiae are matched based on the alignment result. To reduce the impact of deformation, they build a convex hull for each of these fingerprints. Pores in these convex hulls are used for matching. In the experiments, their method is compared with random sample consensus method, minutia and ICP-based method, and direct pore matching method. The results show that the proposed method is more efficient.

Sensor Deployment With Limited Communication Range in Homogeneous and Heterogeneous Wireless Sensor Networks

We study the heterogeneous wireless sensor networks (WSNs) and propose the necessary condition of the optimal sensor deployment. Similar to that in homogeneous WSNs, the necessary condition implies that every sensor node location should coincide with the centroid of its own optimal sensing region. Moreover, we discuss the dynamic sensor deployment in both the homogeneous and the heterogeneous WSNs with limited communication range for the sensor nodes. The purpose of sensor deployment is to improve sensing performance, reflected by distortion and coverage. We model the sensor deployment problem as a source coding problem with distortion reflecting sensing accuracy. However, when the communication range is limited, a WSN is divided into several disconnected sub-graphs under certain conditions as we will discuss in this paper. In such a scenario, neither the conventional distortion nor the coverage represents the sensing performance as the collected data in disconnected sub-graphs cannot be communicated with the access point. By defining an appropriate sensing performance measure, we propose a Restrained Lloyd (RL) algorithm and a deterministic annealing (DA) algorithm to optimize sensor deployment in both the homogeneous and heterogeneous WSNs. Our simulation results show that both the DA and the RL algorithms outperform the existing algorithms when communication range is limited.

A computational approach inspired by simulated annealing to study the stability of protein interaction networks in cancer and neurological disorders

Molecular networks provide a powerful tool for the study of biomedical systems, in particular several studies have detected alterations of the network structure associated to disease states. Here we propose that diseases cannot only alter the structure of the network but also its stability. To evaluate network stability we have developed a new methodological framework. Our approach is an adaptation of the classical Deterministic Simulated Annealing algorithm to work with discrete states. Adjusted energy values are used to compare the network stability in disease and control states. The results show that cancer networks are less stable than the Alzheimer's disease (AD) ones. These results can be interpreted in terms of our previous observations on cancer and AD inverse comorbidity, i.e. AD patients have lower than expected risk to suffer cancer.

Aggregation of Graph Models and Markov Chains by Deterministic Annealing

We consider the problem of simplifying large weighted directed graphs by aggregating nodes and edges. This problem is recast as a clustering/resource allocation problem, and a solution method that incorporates features of the deterministic annealing (DA) algorithm is proposed. The novelty in our method is a quantitive measure of dissimilarity that allows us to compare directed graphs of possibly different sizes (i.e., the original and the aggregated graphs). The approach we propose is insensitive to initial conditions and less likely to converge to poor local minima than Lloyd-type algorithms. We apply our graph-aggregation (clustering) method to Markov chains, where low-order Markov chains that approximate high-order chains are obtained through appropriate aggregation of state transition matrices. We further develop a decentralized computational scheme to improve tractability of the algorithm.

Clustering and Coverage Control for Systems With Acceleration-Driven Dynamics

In this technical note, we consider the dynamic coverage control problem from a clustering perspective, to which we apply control-theoretic methods to identify and track the cluster center dynamics. To the authors' knowledge, this is the first work to consider tracking cluster centers when the dynamics of the system elements involve acceleration fields. We show that a dynamic control design is necessary to achieve dynamic coverage under these acceleration fields. We pose the goal of maximizing the instantaneous coverage as a combinatorial optimization problem, and propose a framework that extends the concepts of the deterministic annealing algorithm to the dynamic setting. The resulting Lagrangian is used as a control Lyapunov function for designing coverage control. The algorithms we propose guarantee asymptotic tracking of cluster group dynamics, and we further establish continuity and boundedness of the corresponding control laws. Simulations are provided to corroborate these results.

Bi-objective optimization of drayage operations in the service area of intermodal terminals

A full truckload vehicle routing problem in drayage operations around intermodal container terminals is studied. Loaded and empty containers need to be transported in a small geographical area. Either the origin or the destination of empty container transports is unknown in advance. The problem is formulated as an asymmetric multiple vehicle Traveling Salesman Problem with Time Windows (am-TSPTW). For the first time, this type of problem is considered from a bi-objective perspective. Three solution algorithms are proposed and compared with each other. Best results are obtained by a two-phase hybrid deterministic annealing and tabu search algorithm.

A deterministic annealing algorithm for approximating a solution of the linearly constrained nonconvex quadratic minimization problem

A deterministic annealing algorithm is proposed for approximating a solution of the linearly constrained nonconvex quadratic minimization problem. The algorithm is derived from applications of a Hopfield-type barrier function in dealing with box constraints and Lagrange multipliers in handling linear equality constraints, and attempts to obtain a solution of good quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter. For any given value of the barrier parameter, the algorithm searches for a minimum point of the barrier problem in a feasible descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. At each iteration, the feasible descent direction is found by updating Lagrange multipliers with a globally convergent iterative procedure. For any given value of the barrier parameter, the algorithm converges to a stationary point of the barrier problem. Preliminary numerical results show that the algorithm seems effective and efficient.

Integrated planning of loaded and empty container movements

Efficiently planning drayage operations is an important task for transportation companies since these operations constitute a large part of the cost of an intermodal transport. In this paper, a full truckload vehicle routing problem for transporting loaded and empty containers in drayage operations is studied. For empty container transports, either the origin or the destination is not predefined. The problem is formulated as an asymmetric multiple vehicle Travelling Salesman Problem with Time Windows (am-TSPTW). Two solution approaches are proposed: a sequential and an integrated approach. For both approaches, a single- and a two-phase deterministic annealing algorithm are presented. Results show that the proposed algorithms are able to find good quality solutions in a small amount of computation time. The integrated approach clearly outperforms the sequential one and the results confirm the advantage of using a two-phase algorithm for vehicle routing problems with hierarchical objectives. Finally, it is shown that the proposed integrated solution method improves previous results on a similar problem.

A Distributed Deterministic Annealing Algorithm for Limited-Range Sensor Coverage

This paper presents a distributed coverage algorithm for a network of mobile agents. Unlike previous work that uses a simple gradient descent algorithm, here we employ an existing deterministic annealing (DA) technique to achieve more optimal convergence values since typical coverage objective functions contain many local minima. We replicate the results of the classical DA algorithm while imposing a limited-range constraint to sensors. As the temperature is decreased, phase changes lead to a regrouping of agents, which is decided through a distributed task allocation algorithm. While simple gradient descent algorithms are heavily dependent on initial conditions for such non-convex coverage objective functions, annealing techniques are generally less prone to this phenomena. The results of our simulations confirm this fact, as we show in the manuscript.

A deterministic annealing algorithm for the minimum concave cost network flow problem

The existing algorithms for the minimum concave cost network flow problems mainly focus on the single-source problems. To handle both the single-source and the multiple-source problem in the same way, especially the problems with dense arcs, a deterministic annealing algorithm is proposed in this paper. The algorithm is derived from an application of the Lagrange and Hopfield-type barrier function. It consists of two major steps: one is to find a feasible descent direction by updating Lagrange multipliers with a globally convergent iterative procedure, which forms the major contribution of this paper, and the other is to generate a point in the feasible descent direction, which always automatically satisfies lower and upper bound constraints on variables provided that the step size is a number between zero and one. The algorithm is applicable to both the single-source and the multiple-source capacitated problem and is especially effective and efficient for the problems with dense arcs. Numerical results on 48 test problems show that the algorithm is effective and efficient.

3D dense reconstruction from 2D video sequence via 3D geometric segmentation

3D reconstruction is a major problem in computer vision. This paper considers the problem of reconstructing 3D structures, given a 2D video sequence. This problem is challenging since it is difficult to identify the trajectory of each object point/pixel over time. Traditional stereo 3D reconstruction methods and volumetric 3D reconstruction methods suffer from the blank wall problem, and the estimated dense depth map is not smooth, resulting in loss of actual geometric structures such as planes. To retain geometric structures embedded in the 3D scene, this paper proposes a novel surface fitting approach for 3D dense reconstruction. Specifically, we develop an expanded deterministic annealing algorithm to decompose 3D point cloud to multiple geometric structures, and estimate the parameters of each geometric structure. In this paper, we only consider plane structure, but our methodology can be extended to other parametric geometric structures such as spheres, cylinders, and cones. The experimental results show that the new approach is able to segment 3D point cloud into appropriate geometric structures and generate accurate 3D dense depth map.

On Semi-Supervised Learning Genetic-Based and Deterministic Annealing EM Algorithm for Dirichlet Mixture Models

We propose a genetic-based and deterministic annealing expectation-maximization (GA&DA-EM) algorithm for learning Dirichlet mixture models from multivariate data. This algorithm is capable of selecting the number of components of the model using the minimum description length (MDL) criterion. Our approach benefits from the properties of Genetic algorithms and deterministic annealing algorithm by combination of both into a single procedure. The population-based stochastic search of the GA&DA explores the search space more thoroughly than the EM method. Therefore, our algorithm enables escaping from local optimal solutions since the algorithm becomes less sensitive to its initialization. The GA&DA-EM algorithm is elitist which maintains the monotonic convergence property of the EM algorithm. We conducted experiments on the WebKB and 20NEWSGROUPS. The results show that show that 1) the GA&DA-EM outperforms the EM method since: Our approach identifies the number of components which were used to generate the underlying data more often than the EM algorithm. 2) the algorithm alternatives to EM that overcoming the challenges of local maxima.