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The importance of the time-cost-quality trade-off problem in construction projects has been widely recognized. Its goal is to minimize time and cost and maximize quality. In this paper, the bonus-penalty mechanism is introduced to improve the traditional time-cost model, and considering the nonlinear relationship between quality and time, a nonlinear time-cost quality model is established. Meanwhile, in order to better solve the time-cost-quality trade-off problem, a multi-objective immune wolf colony optimization algorithm has been proposed. The hybrid method combines the fast convergence of the wolf colony algorithm and the excellent diversity of the immune algorithm to improve the accuracy of the wolf colony search process. Finally, a railway construction project is taken as an example to prove the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Q-learning is a classical reinforcement learning algorithm and one of the most important methods of mobile robot path planning without a prior environmental model. Nevertheless, Q-learning is too simple when initializing Q-table and wastes too much time in the exploration process, causing a slow convergence speed. This paper proposes a new Q-learning algorithm called the Paired Whale Optimization Q-learning Algorithm (PWOQLA) which includes four improvements. Firstly, to accelerate the convergence speed of Q-learning, a whale optimization algorithm is used to initialize the values of a Q-table. Before the exploration process, a Q-table which contains previous experience is learned to improve algorithm efficiency. Secondly, to improve the local exploitation capability of the whale optimization algorithm, a paired whale optimization algorithm is proposed in combination with a pairing strategy to speed up the search for prey. Thirdly, to improve the exploration efficiency of Q-learning and reduce the number of useless explorations, a new selective exploration strategy is introduced which considers the relationship between current position and target position. Fourthly, in order to balance the exploration and exploitation capabilities of Q-learning so that it focuses on exploration in the early stage and on exploitation in the later stage, a nonlinear function is designed which changes the value of ε in ε-greedy Q-learning dynamically based on the number of iterations. Comparing the performance of PWOQLA with other path planning algorithms, experimental results demonstrate that PWOQLA achieves a higher level of accuracy and a faster convergence speed than existing counterparts in mobile robot path planning. The code will be released at https://github.com/wanghanyu0526/improveQL.git. [ABSTRACT FROM AUTHOR]

The mayfly algorithm (MA), as a newly proposed intelligent optimization algorithm, is found that easy to fall into the local optimum and slow convergence speed. To address this, an improved mayfly algorithm based on dynamic elite strategy (DESMA) is proposed in this paper. Specifically, it first determines the specific space near the best mayfly in the current population, and dynamically sets the search radius. Then generating a certain number of elite mayflies within this range. Finally, the best one among the newly generated elite mayflies is selected to replace the best mayfly in the current population when the fitness value of elite mayfly is better than that of the best mayfly. Experimental results on 28 standard benchmark test functions from CEC2013 show that our proposed algorithm outperforms its peers in terms of accuracy speed and stability. [ABSTRACT FROM AUTHOR]

Because of the No Free Lunch (NFL) rule, we are still under the way developing new algorithms and improving the capabilities of the existed algorithms. Under consideration of the simple and steady convergence capability of the sine cosine algorithm (SCA) and the fast convergence rate of the Harris Hawk optimization (HHO) algorithms, we hereby propose a new hybridization algorithm of the SCA and HHO algorithm in this paper, called the CSCAHHO algorithm henceforth. The energy parameter is introduced to balance the exploration and exploitation procedure for individuals in the new swarm, and chaos is introduced to improve the randomness. Updating equations is redefined and combined of the equations in the SCA and HHO algorithms. Simulation experiments on 27 benchmark functions and CEC 2014 competitive functions, together with 3 engineering problems are carried out. Comparisons have been made with the original SCA, HHO, Archimedes optimization algorithm (AOA), Seagull optimization algorithm (SOA), Sooty Tern optimization algorithm (STOA), Arithmetic optimizer (AO) and Chimp optimization algorithm (ChOA). Simulation experiments on either unimodal or multimodal, benchmark or CEC2014 functions, or real engineering problems all verified the better performance of the proposed CSAHHO, such as faster convergence rate, low residual errors, and steadier capability. Matlab code of this algorithm is shared in Gitee with the following address: https://gitee.com/yuj-zhang/cscahho. [ABSTRACT FROM AUTHOR]

While the classical knapsack problem has been the object to be solved by optimization algorithm proposals for many years, another version of this problem, discounted {0-1} knapsack problem, is gaining a lot of attention recently. The original knapsack problem requires selecting specific items from an item set to maximize the total benefit while ensuring that the total weight does not exceed the knapsack capacity. Meanwhile, discounted {0-1} knapsack problem has more stringent requirements in which items are divided into groups, and only up to one item from a particular group can be selected. This constraint, which does not exist in the original knapsack problem, makes discounted {0-1} knapsack problem even more challenging. In this paper, we propose a new algorithm based on salp swarm algorithm in the form of four different variants to resolve the discounted {0-1} knapsack problem. In addition, we also make use of an effective data modeling mechanism and a greedy repair operator that helps overcome local optima when finding the global optimal solution. Experimental and statistical results show that our algorithm is superior to currently available algorithms in terms of solution quality, convergence, and other statistical criteria. [ABSTRACT FROM AUTHOR]

Several lifetime distributions have played an important role to fit survival data. However, for some of these models, the computation of maximum likelihood estimators is quite difficult due to presence of flat regions in the search space, among other factors. Several well-known derivative-based optimization tools are unsuitable for obtaining such estimates. To circumvent this problem, we introduce the AdequacyModel computational library version 2.0.0 for the R statistical environment with two major contributions: a general optimization technique based on the Particle Swarm Optimization (PSO) method (with a minor modification of the original algorithm) and a set of statistical measures for assessment of the adequacy of the fitted model. This library is very useful for researchers in probability and statistics and has been cited in various papers in these areas. It serves as the basis for the Newdistns library (version 2.1) published in an impact journal in the area of computational statistics, see . It is also the basis of the Wrapped library (version 2.0), see . A third package making use of the AdequacyModel library can be found in . In addition, the proposed library has proved to be very useful for maximizing log-likelihood functions with complex search regions. The library provides a greater control of the optimization process by introducing a stop criterion based on a minimum number of iterations and the variance of a given proportion of optimal values. We emphasize that the new library can be used not only in statistics but in physics and mathematics as proved in several examples throughout the paper. [ABSTRACT FROM AUTHOR]

Focusing on the problem incurred during particle swarm optimization (PSO) that tends to fall into local optimization when solving Nash equilibrium solutions of games, as well as the problem of slow convergence when solving higher order game pay off matrices, this paper proposes an improved Predator-Prey particle swarm optimization (IPP-PSO) algorithm based on a Predator-Prey particle swarm optimization (PP-PSO) algorithm. First, the convergence of the algorithm is advanced by improving the distribution of the initial predator and prey. By improving the inertia weight of both predator and prey, the problem of "precocity" of the algorithm is improved. By improving the formula used to represent particle velocity, the problems of local optimizations and slowed convergence rates are solved. By increasing pathfinder weight, the diversity of the population is increased, and the global search ability of the algorithm is improved. Then, by solving the Nash equilibrium solution of both a zero-sum game and a non-zero-sum game, the convergence speed and global optimal performance of the original PSO, the PP-PSO and the IPP-PSO are compared. Simulation results demonstrated that the improved Predator-Prey algorithm is convergent and effective. The convergence speed of the IPP-PSO is significantly higher than that of the other two algorithms. In the simulation, the PSO does not converge to the global optimal solution, and PP-PSO approximately converges to the global optimal solution after about 40 iterations, while IPP-PSO approximately converges to the global optimal solution after about 20 iterations. Furthermore, the IPP-PSO is superior to the other two algorithms in terms of global optimization and accuracy. [ABSTRACT FROM AUTHOR]

The Sine-Cosine algorithm (SCA) is a population-based metaheuristic algorithm utilizing sine and cosine functions to perform search. To enable the search process, SCA incorporates several search parameters. But sometimes, these parameters make the search in SCA vulnerable to local minima/maxima. To overcome this problem, a new Multi Sine-Cosine algorithm (MSCA) is proposed in this paper. MSCA utilizes multiple swarm clusters to diversify & intensify the search in-order to avoid the local minima/maxima problem. Secondly, during update MSCA also checks for better search clusters that offer convergence to global minima effectively. To assess its performance, we tested the MSCA on unimodal, multimodal and composite benchmark functions taken from the literature. Experimental results reveal that the MSCA is statistically superior with regards to convergence as compared to recent state-of-the-art metaheuristic algorithms, including the original SCA. [ABSTRACT FROM AUTHOR]

This paper proposes a new dynamic multi-objective optimization algorithm by integrating a new fitting-based prediction (FBP) mechanism with regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) for multi-objective optimization in changing environments. The prediction-based reaction mechanism aims to generate high-quality population when changes occur, which includes three subpopulations for tracking the moving Pareto-optimal set effectively. The first subpopulation is created by a simple linear prediction model with two different stepsizes. The second subpopulation consists of some new sampling individuals generated by the fitting-based prediction strategy. The third subpopulation is created by employing a recent sampling strategy, generating some effective search individuals for improving population convergence and diversity. Experimental results on a set of benchmark functions with a variety of different dynamic characteristics and difficulties illustrate that the proposed algorithm has competitive effectiveness compared with some state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In the EMO (evolutionary multi-objective, EMO) algorithm, MaOPs (many objective optimization problems, MaOPs) are sometimes difficult to keep the balance of convergence and diversity. The decomposition based EMO developed for MaOPs has been proved to be effective, and BBO/Complex (the biogeography based optimization for complex system, BBO/Complex) algorithm is a low complexity algorithm. In this paper, a decomposition and adaptive weight adjustment based BBO/Complex algorithm (DAWA-BBO/Complex) for MaOPs is proposed. First, a new method based on crowding distance is designed to generate a set of weight vectors with good uniformly. Second, an adaptive weight adjustment method is used to solve MaOPs with complex Pareto optimal front. Subsystem space obtains a non-dominated solution by a new selection strategy. The experimental results show that the algorithm is superior to other new algorithms in terms of convergence and diversity in DTLZ benchmark problems. Finally, the algorithm is used to solve the problem of NC (numerical control machine, NC) cutting parameters, and the final optimization result is obtained by AHP (Analytic Hierarchy Process, AHP) method. The results show that the cutting speed is 10.8m/min, back cutting depth is 0.13mm, the cutting time is 504s and the cutting cost is 22.15yuan. The proposed algorithm can effectively solve the practical optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, a novel, effective meta-heuristic, population-based Hybrid Firefly Particle Swarm Optimization (HFPSO) algorithm is applied to solve different non-linear and convex optimal power flow (OPF) problems. The HFPSO algorithm is a hybridization of the Firefly Optimization (FFO) and the Particle Swarm Optimization (PSO) technique, to enhance the exploration, exploitation strategies, and to speed up the convergence rate. In this work, five objective functions of OPF problems are studied to prove the strength of the proposed method: total generation cost minimization, voltage profile improvement, voltage stability enhancement, the transmission lines active power loss reductions, and the transmission lines reactive power loss reductions. The particular fitness function is chosen as a single objective based on control parameters. The proposed HFPSO technique is coded using MATLAB software and its effectiveness is tested on the standard IEEE 30-bus test system. The obtained results of the proposed algorithm are compared to simulated results of the original Particle Swarm Optimization (PSO) method and the present state-of-the-art optimization techniques. The comparison of optimum solutions reveals that the recommended method can generate optimum, feasible, global solutions with fast convergence and can also deal with the challenges and complexities of various OPF problems. [ABSTRACT FROM AUTHOR]

In this research, we have investigated doubly singular ordinary differential equations and a real application problem of studying the temperature profile in a porous fin model. We have suggested a novel soft computing strategy for the training of unknown weights involved in the feed-forward artificial neural networks (ANNs). Our neuroevolutionary approach is used to suggest approximate solutions to a highly nonlinear doubly singular type of differential equations. We have considered a real application from thermodynamics, which analyses the temperature profile in porous fins. For this purpose, we have used the optimizer, namely, the fractional-order particle swarm optimization technique (FO-DPSO), to minimize errors in solutions through fitness functions. ANNs are used to design the approximate series of solutions to problems considered in this paper. We find the values of unknown weights such that the approximate solutions to these problems have a minimum residual error. For global search in the domain, we have initialized FO-DPSO with random solutions, and it collects best so far solutions in each generation/ iteration. In the second phase, we have fine-tuned our algorithm by initializing FO-DPSO with the collection of best so far solutions. It is graphically illustrated that this strategy is very efficient in terms of convergence and minimum mean squared error in its best solutions. We can use this strategy for the higher-order system of differential equations modeling different important real applications. [ABSTRACT FROM AUTHOR]

This paper presents a novel method on the optimization of bi-objective Flexible Job-shop Scheduling Problem (FJSP) under stochastic processing times. The robust counterpart model and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are used to solve the bi-objective FJSP with consideration of the completion time and the total energy consumption under stochastic processing times. The case study on GM Corporation verifies that the NSGA-II used in this paper is effective and has advantages to solve the proposed model comparing with HPSO and PSO+SA. The idea and method of the paper can be generalized widely in the manufacturing industry, because it can reduce the energy consumption of the energy-intensive manufacturing enterprise with less investment when the new approach is applied in existing systems. [ABSTRACT FROM AUTHOR]

Combinatorial test design is a plan of test that aims to reduce the amount of test cases systematically by choosing a subset of the test cases based on the combination of input variables. The subset covers all possible combinations of a given strength and hence tries to match the effectiveness of the exhaustive set. This mechanism of reduction has been used successfully in software testing research with t-way testing (where t indicates the interaction strength of combinations). Potentially, other systems may exhibit many similarities with this approach. Hence, it could form an emerging application in different areas of research due to its usefulness. To this end, more recently it has been applied in a few research areas successfully. In this paper, we explore the applicability of combinatorial test design technique for Fractional Order (FO), Proportional-Integral-Derivative (PID) parameter design controller, named as FOPID, for an automatic voltage regulator (AVR) system. Throughout the paper, we justify this new application theoretically and practically through simulations. In addition, we report on first experiments indicating its practical use in this field. We design different algorithms and adapted other strategies to cover all the combinations with an optimum and effective test set. Our findings indicate that combinatorial test design can find the combinations that lead to optimum design. Besides this, we also found that by increasing the strength of combination, we can approach to the optimum design in a way that with only 4-way combinatorial set, we can get the effectiveness of an exhaustive test set. This significantly reduced the number of tests needed and thus leads to an approach that optimizes design of parameters quickly. [ABSTRACT FROM AUTHOR]

Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation. [ABSTRACT FROM AUTHOR]

The unrivaled computing capabilities of modern GPUs meet the demand of processing massive amounts of data seen in many application domains. While traditional HPC systems support applications as standalone entities that occupy entire GPUs, there are GPU-based DBMSs where multiple tasks are meant to be run at the same time in the same device. To that end, system-level resource management mechanisms are needed to fully unleash the computing power of GPUs in large data processing, and there were some researches focusing on it. In our previous work, we explored the single compute-bound kernel modeling on GPUs under NVidia’s CUDA framework and provided an in-depth anatomy of the NVidia’s concurrent kernel execution mechanism (CUDA stream). This paper focuses on resource allocation of multiple GPU applications towards optimization of system throughput in the context of systems. Comparing to earlier studies of enabling concurrent tasks support on GPU such as MultiQx-GPU, we use a different approach that is to control the launching parameters of multiple GPU kernels as provided by compile-time performance modeling as a kernel-level optimization and also a more general pre-processing model with batch-level control to enhance performance. Specifically, we construct a variation of multi-dimensional knapsack model to maximize concurrency in a multi-kernel environment. We present an in-depth analysis of our model and develop an algorithm based on dynamic programming technique to solve the model. We prove the algorithm can find optimal solutions (in terms of thread concurrency) to the problem and bears pseudopolynomial complexity on both time and space. Such results are verified by extensive experiments running on our microbenchmark that consists of real-world GPU queries. Furthermore, solutions identified by our method also significantly reduce the total running time of the workload, as compared to sequential and MultiQx-GPU executions. [ABSTRACT FROM AUTHOR]

The process of inferring parameter values from experimental data can be a cumbersome task. In addition, the collection of experimental data can be time consuming and costly. This paper covers both these issues by addressing the following question: “Which experimental outputs should be measured to ensure that unique model parameters can be calculated?”. Stated formally, we examine the topic of minimal output sets that guarantee a model’s structural identifiability. To that end, we introduce an algorithm that guides a researcher as to which model outputs to measure. Our algorithm consists of an iterative structural identifiability analysis and can determine multiple minimal output sets of a model. This choice in different output sets offers researchers flexibility during experimental design. Our method can determine minimal output sets of large differential equation models within short computational times. [ABSTRACT FROM AUTHOR]

The problem that passengers are hard to take taxis while empty driving rate is high widely exists under the traditional taxi operation mode. The implementation of taxi carpooling mode can alleviate the problem in a certain extent. The objective of this study is to optimize the taxi carpooling path. Firstly, the taxi carpooling path optimization model with single objective and its extended model with multiple objectives are built respectively. Then, the single objective path optimization model of taxi carpooling is solved based on the improved single objective genetic algorithm, and the multiple-objective path optimization model of taxi carpooling is solved based on the improved multiple-objective genetic algorithm. Finally, a case study is carried out based on a road network with 24 nodes. The case study results show the path optimization models and algorithms of taxi carpooling proposed in the paper can quickly get the taxi carpooling path, and can increase the income of taxi driver while reduce the cost for passengers. [ABSTRACT FROM AUTHOR]

For railway operators, one of many important goals is to improve the utilization efficiency of electric multiple units (EMUs). When operators design EMU circulation plans, EMU type restrictions are critical factors when assigning EMUs to the correct depots for maintenance. However, existing studies only consider that EMUs are maintained at their home depots. However, targeting that problem, in this paper, an optimization model for the EMU circulation planning problem that allows depots to be selected for EMU maintenance is proposed. This model aims at optimizing the number of used EMUs and the number of EMU maintenance tasks and simultaneously incorporates other important constraints, including type restrictions, on EMU maintenance and night accommodation capacity at depots. In order to solve the model, a branch-and-price algorithm is also developed. A case study of a real-world high-speed railway was conducted to compare and analyze the effects of different maintenance location constraints. The results show that the number of EMUs used will decrease under the maintenance sharing scheme, the number of EMU maintenance tasks can be reduced, and the time occupied in EMU maintenance will be released. In addition, the scheme of maintenance resources sharing and increases to mileage limits can effectively decrease the number of EMU maintenance tasks significantly. The model and algorithm can be used as an effective quantitative analysis tool for railway operators' decision-making processes in the EMU circulation planning problem. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of makespan minimization on unrelated parallel machines with sequence dependent setup times. The symbiotic organisms search (SOS) algorithm is a new and popular global optimization technique that has received wide acceptance in recent years from researchers in continuous and discrete optimization domains. An improved SOS algorithm is developed to solve the parallel machine scheduling problem. Since the standard SOS algorithm was originally developed to solve continuous optimization problems, a new solution representation and decoding procedure is designed to make the SOS algorithm suitable for the unrelated parallel machine scheduling problem (UPMSP). Similarly, to enhance the solution quality of the SOS algorithm, an iterated local search strategy based on combining variable numbers of insertion and swap moves is incorporated into the SOS algorithm. More so, to further improve the SOS optimization speed and performance, the longest processing time first (LPT) rule is used to design a machine assignment heuristic that assigns processing machines to jobs based on the machine dynamic load-balancing mechanism. Subsequently, the machine assignment scheme is incorporated into SOS algorithms and used to solve the UPMSP. The performances of the proposed methods are evaluated by comparing their solutions with other existing techniques from the literature. A number of statistical tests were also conducted to determine the variations in performance for each of the techniques. The experimental results showed that the SOS with LPT (SOS-LPT) heuristic has the best performance compared to other tested method, which is closely followed by SOS algorithm, indicating that the two proposed algorithms’ solution approaches are reasonable and effective for solving large-scale UPMSPs. [ABSTRACT FROM AUTHOR]

In this paper, a new color watermarking algorithm based on differential evolution is proposed. A color host image is first converted from RGB space to YIQ space, which is more suitable for the human visual system. Then, apply three-level discrete wavelet transformation to luminance component Y and generate four different frequency sub-bands. After that, perform singular value decomposition on these sub-bands. In the watermark embedding process, apply discrete wavelet transformation to a watermark image after the scrambling encryption processing. Our new algorithm uses differential evolution algorithm with adaptive optimization to choose the right scaling factors. Experimental results show that the proposed algorithm has a better performance in terms of invisibility and robustness. [ABSTRACT FROM AUTHOR]

The vehicle routing problem (VRP) has a wide range of applications in the field of logistics distribution. In order to reduce the cost of logistics distribution, the distance-constrained and capacitated VRP with split deliveries by order (DCVRPSDO) was studied. We show that the customer demand, which can’t be split in the classical VRP model, can only be discrete split deliveries by order. A model of double objective programming is constructed by taking the minimum number of vehicles used and minimum vehicle traveling cost as the first and the second objective, respectively. This approach contains a series of constraints, such as single depot, single vehicle type, distance-constrained and load capacity limit, split delivery by order, etc. DCVRPSDO is a new type of VRP. A new tabu search algorithm is designed to solve the problem and the examples testing show the efficiency of the proposed algorithm. This paper focuses on constructing a double objective mathematical programming model for DCVRPSDO and designing an adaptive tabu search algorithm (ATSA) with good performance to solving the problem. The performance of the ATSA is improved by adding some strategies into the search process, including: (a) a strategy of discrete split deliveries by order is used to split the customer demand; (b) a multi-neighborhood structure is designed to enhance the ability of global optimization; (c) two levels of evaluation objectives are set to select the current solution and the best solution; (d) a discriminating strategy of that the best solution must be feasible and the current solution can accept some infeasible solution, helps to balance the performance of the solution and the diversity of the neighborhood solution; (e) an adaptive penalty mechanism will help the candidate solution be closer to the neighborhood of feasible solution; (f) a strategy of tabu releasing is used to transfer the current solution into a new neighborhood of the better solution. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel algorithm—parallel adaptive quantum genetic algorithm—which can rapidly determine the minimum control nodes of arbitrary networks with both control nodes and state nodes. The corresponding network can be fully controlled with the obtained control scheme. We transformed the network controllability issue into a combinational optimization problem based on the Popov-Belevitch-Hautus rank condition. A set of canonical networks and a list of real-world networks were experimented. Comparison results demonstrated that the algorithm was more ideal to optimize the controllability of networks, especially those larger-size networks. We demonstrated subsequently that there were links between the optimal control nodes and some network statistical characteristics. The proposed algorithm provides an effective approach to improve the controllability optimization of large networks or even extra-large networks with hundreds of thousands nodes. [ABSTRACT FROM AUTHOR]

Software test suites based on the concept of interaction testing are very useful for testing software components in an economical way. Test suites of this kind may be created using mathematical objects called covering arrays. A covering array, denoted by CA(N; t, k, v), is an N × k array over with the property that every N × t sub-array covers all t-tuples of at least once. Covering arrays can be used to test systems in which failures occur as a result of interactions among components or subsystems. They are often used in areas such as hardware Trojan detection, software testing, and network design. Because system testing is expensive, it is critical to reduce the amount of testing required. This paper addresses the Optimal Shortening of Covering ARrays (OSCAR) problem, an optimization problem whose objective is to construct, from an existing covering array matrix of uniform level, an array with dimensions of (N − δ) × (k − Δ) such that the number of missing t-tuples is minimized. Two applications of the OSCAR problem are (a) to produce smaller covering arrays from larger ones and (b) to obtain quasi-covering arrays (covering arrays in which the number of missing t-tuples is small) to be used as input to a meta-heuristic algorithm that produces covering arrays. In addition, it is proven that the OSCAR problem is NP-complete, and twelve different algorithms are proposed to solve it. An experiment was performed on 62 problem instances, and the results demonstrate the effectiveness of solving the OSCAR problem to facilitate the construction of new covering arrays. [ABSTRACT FROM AUTHOR]

With the recent technological developments a vast amount of high-throughput data has been profiled to understand the mechanism of complex diseases. The current bioinformatics challenge is to interpret the data and underlying biology, where efficient algorithms for analyzing heterogeneous high-throughput data using biological networks are becoming increasingly valuable. In this paper, we propose a software package based on the Prize-collecting Steiner Forest graph optimization approach. The PCSF package performs fast and user-friendly network analysis of high-throughput data by mapping the data onto a biological networks such as protein-protein interaction, gene-gene interaction or any other correlation or coexpression based networks. Using the interaction networks as a template, it determines high-confidence subnetworks relevant to the data, which potentially leads to predictions of functional units. It also interactively visualizes the resulting subnetwork with functional enrichment analysis. [ABSTRACT FROM AUTHOR]

In this paper, an anti-jamming method, which turns the single objective optimization problem into a multi-objective optimization problem by utilizing 2-norm, is proposed. The proposed jamming suppression method can reduce the wide nulls and wrong nulls problems, which are generated by the common adaptive nulling methods. Therefore a better signal-noise-ratio (SNR) can be achieved, especially when the jammers are close to satellite signals. It can also improve the robustness of the algorithm. The effectiveness of the proposed method is evaluated by simulation and practical outdoor experiments with the GPS L1 band C/A signals. The experimental results show that with the dedicated method, the nulls targeting at the corresponding jammers become narrower and the wrong nulls can be eliminated. [ABSTRACT FROM AUTHOR]

Due to its environmentally sustainable and energy-saving characteristics, railway transportation nowadays plays a fundamental role in delivering passengers and goods. Emerged in the area of transportation planning, the crew (workforce) sizing problem and the crew scheduling problem have been attached great importance by the railway industry and the scientific community. In this paper, we aim to solve the two problems by proposing a novel two-stage optimization approach in the context of the electric multiple units (EMU) depot shunting driver assignment problem. Given a predefined depot shunting schedule, the first stage of the approach focuses on determining an optimal size of shunting drivers. While the second stage is formulated as a bi-objective optimization model, in which we comprehensively consider the objectives of minimizing the total walking distance and maximizing the workload balance. Then we combine the normalized normal constraint method with a modified Pareto filter algorithm to obtain Pareto solutions for the bi-objective optimization problem. Furthermore, we conduct a series of numerical experiments to demonstrate the proposed approach. Based on the computational results, the regression analysis yield a driver size predictor and the sensitivity analysis give some interesting insights that are useful for decision makers. [ABSTRACT FROM AUTHOR]

To optimize the geometry of airfoils for a specific application is an important engineering problem. In this context genetic algorithms have enjoyed some success as they are able to explore the search space without getting stuck in local optima. However, these algorithms require the computation of aerodynamic properties for a significant number of airfoil geometries. Consequently, for low-speed aerodynamics, panel methods are most often used as the inner solver. In this paper we evaluate the performance of such an optimization algorithm on modern accelerators (more specifically, the Intel Xeon Phi 7120 and the NVIDIA K80). For that purpose, we have implemented an optimized version of the algorithm on the CPU and Xeon Phi (based on OpenMP, vectorization, and the Intel MKL library) and on the GPU (based on CUDA and the MAGMA library). We present timing results for all codes and discuss the similarities and differences between the three implementations. Overall, we observe a speedup of approximately 2.5 for adding an Intel Xeon Phi 7120 to a dual socket workstation and a speedup between 3.4 and 3.8 for adding a NVIDIA K80 to a dual socket workstation. [ABSTRACT FROM AUTHOR]

As a sustainable transportation mode, high-speed railway (HSR) has become an efficient way to meet the huge travel demand. However, due to the high acquisition and maintenance cost, it is impossible to build enough infrastructure and purchase enough train-sets. Great efforts are required to improve the transport capability of HSR. The utilization efficiency of train-sets (carrying tools of HSR) is one of the most important factors of the transport capacity of HSR. In order to enhance the utilization efficiency of the train-sets, this paper proposed a train-set circulation optimization model to minimize the total connection time. An innovative two-stage approach which contains segments generation and segments combination was designed to solve this model. In order to verify the feasibility of the proposed approach, an experiment was carried out in the Beijing-Tianjin passenger dedicated line, to fulfill a 174 trips train diagram. The model results showed that compared with the traditional Ant Colony Algorithm (ACA), the utilization efficiency of train-sets can be increased from 43.4% (ACA) to 46.9% (Two-Stage), and 1 train-set can be saved up to fulfill the same transportation tasks. The approach proposed in the study is faster and more stable than the traditional ones, by using which, the HSR staff can draw up the train-sets circulation plan more quickly and the utilization efficiency of the HSR system is also improved. [ABSTRACT FROM AUTHOR]

Heterogeneous information networks (e.g. bibliographic networks and social media networks) that consist of multiple interconnected objects are ubiquitous. Clustering analysis is an effective method to understand the semantic information and interpretable structure of the heterogeneous information networks, and it has attracted the attention of many researchers in recent years. However, most studies assume that heterogeneous information networks usually follow some simple schemas, such as bi-typed networks or star network schema, and they can only cluster one type of object in the network each time. In this paper, a novel clustering framework is proposed based on sparse tensor factorization for heterogeneous information networks, which can cluster multiple types of objects simultaneously in a single pass without any network schema information. The types of objects and the relations between them in the heterogeneous information networks are modeled as a sparse tensor. The clustering issue is modeled as an optimization problem, which is similar to the well-known Tucker decomposition. Then, an Alternating Least Squares (ALS) algorithm and a feasible initialization method are proposed to solve the optimization problem. Based on the tensor factorization, we simultaneously partition different types of objects into different clusters. The experimental results on both synthetic and real-world datasets have demonstrated that our proposed clustering framework, STFClus, can model heterogeneous information networks efficiently and can outperform state-of-the-art clustering algorithms as a generally applicable single-pass clustering method for heterogeneous network which is network schema agnostic. [ABSTRACT FROM AUTHOR]

Artificial neural networks (ANNs) have been employed to solve a broad variety of tasks. The selection of an ANN model with appropriate weights is important in achieving accurate results. This paper presents an optimization strategy for ANN model selection based on the cuckoo search (CS) algorithm, which is rooted in the obligate brood parasitic actions of some cuckoo species. In order to enhance the convergence ability of basic CS, some modifications are proposed. The fraction Pa of the n nests replaced by new nests is a fixed parameter in basic CS. As the selection of Pa is a challenging issue and has a direct effect on exploration and therefore on convergence ability, in this work the Pa is set to a maximum value at initialization to achieve more exploration in early iterations and it is decreased during the search to achieve more exploitation in later iterations until it reaches the minimum value in the final iteration. In addition, a novel master-leader-slave multi-population strategy is used where the slaves employ the best fitness function among all slaves, which is selected by the leader under a certain condition. This fitness function is used for subsequent Lévy flights. In each iteration a copy of the best solution of each slave is migrated to the master and then the best solution is found by the master. The method is tested on benchmark classification and time series prediction problems and the statistical analysis proves the ability of the method. This method is also applied to a real-world water quality prediction problem with promising results. [ABSTRACT FROM AUTHOR]

Railway and metro transport systems (RS) are becoming one of the popular choices of transportation among people, especially those who live in urban cities. Urbanization and increasing population due to rapid development of economy in many cities are leading to a bigger demand for urban rail transit. Despite being a popular variant of Traveling Salesman Problem (TSP), it appears that the universal formula or techniques to solve the problem are yet to be found. This paper aims to develop an optimization algorithm for optimum route selection to multiple destinations in RS before returning to the starting point. Bee foraging behaviour is examined to generate a reliable algorithm in railway TSP. The algorithm is then verified by comparing the results with the exact solutions in 10 test cases, and a numerical case study is designed to demonstrate the application with large size sample. It is tested to be efficient and effective in railway route planning as the tour can be completed within a certain period of time by using minimal resources. The findings further support the reliability of the algorithm and capability to solve the problems with different complexity. This algorithm can be used as a method to assist business practitioners making better decision in route planning. [ABSTRACT FROM AUTHOR]

This paper presents a robust satisficing decision-making method for Unmanned Aerial Vehicles (UAVs) executing complex missions in an uncertain environment. Motivated by the info-gap decision theory, we formulate this problem as a novel robust satisficing optimization problem, of which the objective is to maximize the robustness while satisfying some desired mission requirements. Specifically, a new info-gap based Markov Decision Process (IMDP) is constructed to abstract the uncertain UAV system and specify the complex mission requirements with the Linear Temporal Logic (LTL). A robust satisficing policy is obtained to maximize the robustness to the uncertain IMDP while ensuring a desired probability of satisfying the LTL specifications. To this end, we propose a two-stage robust satisficing solution strategy which consists of the construction of a product IMDP and the generation of a robust satisficing policy. In the first stage, a product IMDP is constructed by combining the IMDP with an automaton representing the LTL specifications. In the second, an algorithm based on robust dynamic programming is proposed to generate a robust satisficing policy, while an associated robustness evaluation algorithm is presented to evaluate the robustness. Finally, through Monte Carlo simulation, the effectiveness of our algorithms is demonstrated on an UAV search mission under severe uncertainty so that the resulting policy can maximize the robustness while reaching the desired performance level. Furthermore, by comparing the proposed method with other robust decision-making methods, it can be concluded that our policy can tolerate higher uncertainty so that the desired performance level can be guaranteed, which indicates that the proposed method is much more effective in real applications. [ABSTRACT FROM AUTHOR]

Digital images have been extensively used in education, research, and entertainment. Many of these images, taken by consumer cameras, are compressed by the JPEG algorithm for effective storage and transmission. Blocking artifact is a well-known problem caused by this algorithm. Effective measurement of blocking artifacts plays an important role in the design, optimization, and evaluation of image compression algorithms. In this paper, we propose a no-reference objective blockiness measure, which is adaptive to high frequency component in an image. Difference of entropies across blocks and variation of block boundary pixel values in edge images are adopted to calculate the blockiness level in areas with low and high frequency component, respectively. Extensive experimental results prove that the proposed measure is effective and stable across a wide variety of images. It is robust to image noise and can be used for real-world image quality monitoring and control. Index Terms—JPEG, no-reference, blockiness measure [ABSTRACT FROM AUTHOR]

Sodium is an integral part of water, and its excessive amount in drinking water causes high blood pressure and hypertension. In the present paper, spatial distribution of sodium concentration in drinking water is modeled and optimized sampling designs for selecting sampling locations is calculated for three divisions in Punjab, Pakistan. Universal kriging and Bayesian universal kriging are used to predict the sodium concentrations. Spatial simulated annealing is used to generate optimized sampling designs. Different estimation methods (i.e., maximum likelihood, restricted maximum likelihood, ordinary least squares, and weighted least squares) are used to estimate the parameters of the variogram model (i.e, exponential, Gaussian, spherical and cubic). It is concluded that Bayesian universal kriging fits better than universal kriging. It is also observed that the universal kriging predictor provides minimum mean universal kriging variance for both adding and deleting locations during sampling design. [ABSTRACT FROM AUTHOR]

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately. [ABSTRACT FROM AUTHOR]

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. [ABSTRACT FROM AUTHOR]

Cloud computing system is a huge cluster of interconnected servers residing in a datacenter and dynamically provisioned to clients on-demand via a front-end interface. Scientific applications scheduling in the cloud computing environment is identified as NP-hard problem due to the dynamic nature of heterogeneous resources. Recently, a number of metaheuristics optimization schemes have been applied to address the challenges of applications scheduling in the cloud system, without much emphasis on the issue of secure global scheduling. In this paper, scientific applications scheduling techniques using the Global League Championship Algorithm (GBLCA) optimization technique is first presented for global task scheduling in the cloud environment. The experiment is carried out using CloudSim simulator. The experimental results show that, the proposed GBLCA technique produced remarkable performance improvement rate on the makespan that ranges between 14.44% to 46.41%. It also shows significant reduction in the time taken to securely schedule applications as parametrically measured in terms of the response time. In view of the experimental results, the proposed technique provides better-quality scheduling solution that is suitable for scientific applications task execution in the Cloud Computing environment than the MinMin, MaxMin, Genetic Algorithm (GA) and Ant Colony Optimization (ACO) scheduling techniques. [ABSTRACT FROM AUTHOR]

In this paper, an improved algorithm of wavelet packet-chaos model for life prediction of space relays based on volterra series is proposed. In the proposed method, the high and low frequency time sequence components of performance parameters are obtained by employing the improved wavelet packet transform to decompose the performance parameters of the relay into multiple scales. Then the optimization algorithm of parameters in volterra series is improved, and is used to construct a chaotic forecasting model for the high and low frequency time sequence components gained by the wavelet packet transform. At last, the chaotic forecasting results of the high and low frequency components are combined by taking the wavelet packet reconstruction approach, so as to predict the lifetime of the studied space relay. The algorithm can predict the life curve of the relay accurately and reflect the characteristics of the relay performance with sufficient accuracy. The proposed method is validated via a case study of a space relay. [ABSTRACT FROM AUTHOR]

Information carried by an image can be distorted due to different image processing steps introduced by different electronic means of storage and communication. Therefore, development of algorithms which can automatically assess a quality of the image in a way that is consistent with human evaluation is important. In this paper, an approach to image quality assessment (IQA) is proposed in which the quality of a given image is evaluated jointly by several IQA approaches. At first, in order to obtain such joint models, an optimisation problem of IQA measures aggregation is defined, where a weighted sum of their outputs, i.e., objective scores, is used as the aggregation operator. Then, the weight of each measure is considered as a decision variable in a problem of minimisation of root mean square error between obtained objective scores and subjective scores. Subjective scores reflect ground-truth and involve evaluation of images by human observers. The optimisation problem is solved using a genetic algorithm, which also selects suitable measures used in aggregation. Obtained multimeasures are evaluated on four largest widely used image benchmarks and compared against state-of-the-art full-reference IQA approaches. Results of comparison reveal that the proposed approach outperforms other competing measures. [ABSTRACT FROM AUTHOR]

The maximal information coefficient (MIC) captures dependences between paired variables, including both functional and non-functional relationships. In this paper, we develop a new method, ChiMIC, to calculate the MIC values. The ChiMIC algorithm uses the chi-square test to terminate grid optimization and then removes the restriction of maximal grid size limitation of original ApproxMaxMI algorithm. Computational experiments show that ChiMIC algorithm can maintain same MIC values for noiseless functional relationships, but gives much smaller MIC values for independent variables. For noise functional relationship, the ChiMIC algorithm can reach the optimal partition much faster. Furthermore, the MCN values based on MIC calculated by ChiMIC can capture the complexity of functional relationships in a better way, and the statistical powers of MIC calculated by ChiMIC are higher than those calculated by ApproxMaxMI. Moreover, the computational costs of ChiMIC are much less than those of ApproxMaxMI. We apply the MIC values tofeature selection and obtain better classification accuracy using features selected by the MIC values from ChiMIC. [ABSTRACT FROM AUTHOR]

This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality. [ABSTRACT FROM AUTHOR]

The differential evolution algorithm has been widely applied on unmanned aerial vehicle (UAV) path planning. At present, four random tuning parameters exist for differential evolution algorithm, namely, population size, differential weight, crossover, and generation number. These tuning parameters are required, together with user setting on path and computational cost weightage. However, the optimum settings of these tuning parameters vary according to application. Instead of trial and error, this paper presents an optimization method of differential evolution algorithm for tuning the parameters of UAV path planning. The parameters that this research focuses on are population size, differential weight, crossover, and generation number. The developed algorithm enables the user to simply define the weightage desired between the path and computational cost to converge with the minimum generation required based on user requirement. In conclusion, the proposed optimization of tuning parameters in differential evolution algorithm for UAV path planning expedites and improves the final output path and computational cost. [ABSTRACT FROM AUTHOR]

This paper presents a new size estimation method that can be used to estimate size level for software engineering projects. The Algorithmic Optimisation Method is based on Use Case Points and on Multiple Least Square Regression. The method is derived into three phases. The first phase deals with calculation Use Case Points and correction coefficients values. Correction coefficients are obtained by using Multiple Least Square Regression. New project is estimated in the second and third phase. In the second phase Use Case Points parameters for new estimation are set up and in the third phase project estimation is performed. Final estimation is obtained by using newly developed estimation equation, which used two correction coefficients. The Algorithmic Optimisation Method performs approximately 43% better than the Use Case Points method, based on their magnitude of relative error score. All results were evaluated by standard approach: visual inspection, goodness of fit measure and statistical significance. [ABSTRACT FROM AUTHOR]

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. [ABSTRACT FROM AUTHOR]

It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method. [ABSTRACT FROM AUTHOR]

Particle Swarm Optimization (PSO) is a meta-heuristic algorithm that has been shown to be successful in solving a wide variety of real and complicated optimization problems in engineering and computer science. This paper introduces a projection based PSO technique, named ProjPSO, to efficiently find different types of optimal designs, or nearly optimal designs, for mixture models with and without constraints on the components, and also for related models, like the log contrast models. We also compare the modified PSO performance with Fedorov's algorithm, a popular algorithm used to generate optimal designs, Cocktail algorithm, and the recent algorithm proposed by []. [ABSTRACT FROM AUTHOR]

Microbial strains optimization for the overproduction of desired phenotype has been a popular topic in recent years. The strains can be optimized through several techniques in the field of genetic engineering. Gene knockout is a genetic engineering technique that can engineer the metabolism of microbial cells with the objective to obtain desirable phenotypes. However, the complexities of the metabolic networks have made the process to identify the effects of genetic modification on the desirable phenotypes challenging. Furthermore, a vast number of reactions in cellular metabolism often lead to the combinatorial problem in obtaining optimal gene deletion strategy. Basically, the size of a genome-scale metabolic model is usually large. As the size of the problem increases, the computation time increases exponentially. In this paper, we propose Differential Bees Flux Balance Analysis (DBFBA) with OptKnock to identify optimal gene knockout strategies for maximizing the production yield of desired phenotypes while sustaining the growth rate. This proposed method functions by improving the performance of a hybrid of Bees Algorithm and Flux Balance Analysis (BAFBA) by hybridizing Differential Evolution (DE) algorithm into neighborhood searching strategy of BAFBA. In addition, DBFBA is integrated with OptKnock to validate the results for improving the reliability the work. Through several experiments conducted on Escherichia coli, Bacillus subtilis, and Clostridium thermocellum as the model organisms, DBFBA has shown a better performance in terms of computational time, stability, growth rate, and production yield of desired phenotypes compared to the methods used in previous works. [ABSTRACT FROM AUTHOR]

: Prediction and classification techniques have been well studied by machine learning researchers and developed for several real-word problems. However, the level of acceptance and success of prediction models are still below expectation due to some difficulties such as the low performance of prediction models when they are applied in different environments. Such a problem has been addressed by many researchers, mainly from the machine learning community. A second problem, principally raised by model users in different communities, such as managers, economists, engineers, biologists, and medical practitioners, etc., is the prediction models’ interpretability. The latter is the ability of a model to explain its predictions and exhibit the causality relationships between the inputs and the outputs. In the case of classification, a successful way to alleviate the low performance is to use ensemble classiers. It is an intuitive strategy to activate collaboration between different classifiers towards a better performance than individual classier. Unfortunately, ensemble classifiers method do not take into account the interpretability of the final classification outcome. It even worsens the original interpretability of the individual classifiers. In this paper we propose a novel implementation of classifiers combination approach that does not only promote the overall performance but also preserves the interpretability of the resulting model. We propose a solution based on Ant Colony Optimization and tailored for the case of Bayesian classifiers. We validate our proposed solution with case studies from medical domain namely, heart disease and Cardiotography-based predictions, problems where interpretability is critical to make appropriate clinical decisions. Availability: The datasets, Prediction Models and software tool together with supplementary materials are available at http://faculty.uaeu.ac.ae/salahb/ACO4BC.htm. [ABSTRACT FROM AUTHOR]

The part-based method has been a fast rising framework for object detection. It is attracting more and more attention for its detection precision and partial robustness to the occlusion. However, little research has been focused on the problem of occlusion overlapping of the part regions, which can reduce the performance of the system. This paper proposes a part-based probabilistic model and the corresponding inference algorithm for the problem of the part occlusion. The model is based on the Bayesian theory integrally and aims to be robust to the large occlusion. In the stage of the model construction, all of the parts constitute the vertex set of a fully connected graph, and a binary variable is assigned to each part to indicate its occlusion status. In addition, we introduce a penalty term to regularize the argument space of the objective function. Thus, the part detection is formulated as an optimization problem, which is divided into two alternative procedures: the outer inference and the inner inference. A stochastic tentative method is employed in the outer inference to determine the occlusion status for each part. In the inner inference, the gradient descent algorithm is employed to find the optimal positions of the parts, in term of the current occlusion status. Experiments were carried out on the Caltech database. The results demonstrated that the proposed method achieves a strong robustness to the occlusion. [ABSTRACT FROM AUTHOR]