A simple and robust Monte Carlo hybrid local search algorithm for the facility location problem

In this article, a new Monte Carlo hybrid local search algorithm (Hyb-LS) is proposed for solving the uncapacitated facility location problem. Hyb-LS is based on repeated sampling using two local search strategies based on best improvement and randomized neighbourhood search. A major advantage of Hyb-LS for its practical use is that the number of restarts is its only parameter to tune. The algorithm is also simple to reimplement, scalable and robust to changes in coefficients within a problem instance. The stopping criterion for local search is learned automatically. Experimental results are presented for four representative and contrasting cost and distance models. The results obtained by Hyb-LS are compared to the optimal or near-optimal solutions found by a mixed integer linear programming (MILP) solver with a generous time limit. For three out of the four models, Hyb-LS obtains better solutions than the upper bound found by the MILP solver for at least one instance.     

Genetic algorithms and Monte Carlo simulation for optimal plant design

We present an approach to the optimal plant design (choice of system layout and components) under conflicting safety and economic constraints, based upon the coupling of a Monte Carlo evaluation of plant operation with a Genetic Algorithms-maximization procedure. The Monte Carlo simulation model provides a flexible tool, which enables one to describe relevant aspects of plant design and operation, such as standby modes and deteriorating repairs, not easily captured by analytical models. The effects of deteriorating repairs are described by means of a modified Brown–Proschan model of imperfect repair which accounts for the possibility of an increased proneness to failure of a component after a repair. The transitions of a component from standby to active, and vice versa, are simulated using a multiplicative correlation model. The genetic algorithms procedure is demanded to optimize a profit function which accounts for the plant safety and economic performance and which is evaluated, for each possible design, by the above Monte Carlo simulation.In order to avoid an overwhelming use of computer time, for each potential solution proposed by the genetic algorithm, we perform only few hundreds Monte Carlo histories and, then, exploit the fact that during the genetic algorithm population evolution, the fit chromosomes appear repeatedly many times, so that the results for the solutions of interest (i.e. the best ones) attain statistical significance.     

Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review

Monte Carlo methods have attracted constant and even increasing attention in structural reliability analysis with a wide variety of developments seamlessly presented over decades. Along the way, a number of specialized reviews and benchmark studies have been provided from time to time, aiming at summarizing and comparing selected few approaches in detail, mainly from an implementation point of view. In contrast, the aim of the present survey is to play a comprehensive role as a methodological guidebook on Monte Carlo simulation and its related, especially variance reduction, techniques through a covering of 444 references in the relevant literature. To achieve this goal, we present an extensive review of formulations and techniques along with insightful summaries of developments of existing numerical methods, ranging from the general formulation, sub-categories and variants, to their combined uses with other simulation techniques and surrogate models, as well as the key advantages and assumptions.     

结构物理参数识别的贝叶斯估计马尔可夫蒙特卡罗方法

从结构动力特征方程出发,以结构主模态参数为观测量,推得结构物理参数线性回归模型。对该模型应用贝叶斯估计理论得到物理参数后验联合分布,再结合马尔可夫蒙特卡罗抽样方法给出各个物理参数的边缘概率分布和最优估计值,而提出了基于结构主模态参数的结构物理参数识别贝叶斯估计马尔可夫蒙特卡罗方法。对五层剪切型结构的数值研究表明,此方法能够利用少数主模态参数给出结构质量和刚度参数的概率分布和最优识别值,而且在主模态参数较准确时识别误差很小。     

Reducing the computational cost of local search in the hybrid evolutionary algorithm with application to electronic imaging

This article focuses on the efficiency problems associated with the use of local search in the hybrid evolutionary algorithm. A two-phase cyclic local search is proposed that alternates the random search and the downhill simplex method (DSM), and helps prevent the algorithm from converging to a sub-optimal solution in multidimensional optimization. The algorithm utilizes a novel micro-model of image local response, in order to reduce the number of fitness evaluations during the local DSM search, with the application to the global optimization problem arising in electronic imaging. The problem is stated as the search for the feasible transformation parameters that minimize the difference between two images. Image local response is defined as the variation of the fitness function that occurs because of a small variation of the parameters, and is computed over a small pixel area. The computed response coefficients specify a contraction transformation applied to the vector of the regular DSM coefficients that control the movement and the shape of the simplex. The transformation adjusts the length of the vector, making the step size of the simplex adaptive to the local properties of the fitness landscape. The computational experiments with two-dimensional grayscale images provide the experimental support and justification of the analytical model of image local response and its utilization for the reduction of the computational cost of local search, without the loss of the quality of the final solution.     

A statistical method for verifying mesh convergence in Monte Carlo simulations with application to fragmentation

A novel method is presented for assessing the convergence of a sequence of statistical distributions generated by direct Monte Carlo sampling. The primary application is to assess the mesh or grid convergence, and possibly divergence, of stochastic outputs from non‐linear continuum systems. Example systems include those from fluid or solid mechanics, particularly those with instabilities and sensitive dependence on initial conditions or system parameters. The convergence assessment is based on demonstrating empirically that a sequence of cumulative distribution functions converges in the L_infty norm. The effect of finite sample sizes is quantified using confidence levels from the Kolmogorov–Smirnov statistic. The statistical method is independent of the underlying distributions. The statistical method is demonstrated using two examples: (1) the logistic map in the chaotic regime, and (2) a fragmenting ductile ring modeled with an explicit‐dynamics finite element code. In the fragmenting ring example the convergence of the distribution describing neck spacing is investigated. The initial yield strength is treated as a random field. Two different random fields are considered, one with spatial correlation and the other without. Both cases converged, albeit to different distributions. The case with spatial correlation exhibited a significantly higher convergence rate compared with the one without spatial correlation. Copyright © 2011 John Wiley & Sons, Ltd.     

A semi-analytical Monte Carlo simulation method for system's reliability with load sharing and damage accumulation

A novel approach for assessing a systems' reliability with dependency structures, load sharing, and damage accumulation and reversal is proposed in this paper. It is a blend of analytical reliability analysis performed at the component level, and is based on understanding the failure mechanism of the components, and a Monte Carlo simulation for the entire system to assess the reliability at the system level incorporating the dynamics of the system behavior as the components interact, share loads, and age over time. Model reduction is deployed to reduce the complexity and accelerate the simulation and convergence of the analytical methods such as FORM and SORM performed at the component level. Numerical examples are provided to illustrate the usability and performance of the method.     

Monte Carlo method implemented in a finite element code with application to dynamic vacuum in particle accelerators

Modern particle accelerators require UHV conditions during their operation. In the accelerating cavities, breakdowns can occur, releasing large amount of gas into the vacuum chamber. To determine the pressure profile along the cavity as a function of time, the time-dependent behaviour of the gas has to be simulated. To do that, it is useful to apply accurate three-dimensional method, such as Test Particles Monte Carlo. In this paper, a time-dependent Test Particles Monte Carlo is used. It has been implemented in a Finite Element code, CASTEM. The principle is to track a sample of molecules during time. The complex geometry of the cavities can be created either in the FE code or in a CAD software (CATIA in our case). The interface between the two softwares to export the geometry from CATIA to CASTEM is given. The algorithm of particle tracking for collisionless flow in the FE code is shown. Thermal outgassing, pumping surfaces and electron and/or ion stimulated desorption can all be generated as well as different surface properties. The method is used to determine the pressure profile after breakdown in the Compact Linear Collider accelerating structures. Preliminary results are presented in this paper.     

Polymer solutions confined in slit-like pores with attractive walls: An off-lattice Monte Carlo study of static properties and chain dynamics

Summary Using a bead spring model of flexible polymer chains, the density profiles and chain configurational properties of polymer solutions confined between parallel plates were studied. A wide range of density , chain length N, and strength of a short-range attractive wall potential was investigated. Both a temperature T in the good solvent regime (T > , being the Theta temperature where a chain in unconfined bulk three-dimensional solution would behave ideally) and a temperature in the bad solvent regime (T < ) were considered. It is shown that phase separation in a polymer-rich and polymer-poor solution in the slit competes with polymer adsorption at the walls. A qualitative connection to the wetting behavior of semi-infinite polymer solutions is drawn. The acceptance rate for monomer motions was studied for various conditions, and profiles of monomer mobility across the slit were recorded. Also, average chain relaxation times were extracted from the time dependence of mean-square displacements. Although with increasing density the chain radii (at T > ) show a crossover from two-dimensional excluded volume behavior (R_g N² with = 3/4) to ideal random walk behavior ( = 1/2), the relaxation times show effective exponents Z_eff ( N^{Z eff}) that clearly deviate from the Rouse prediction in concentrated confined solutions.     

A Monte Carlo methodological approach to plant availability modeling with maintenance, aging and obsolescence

In this paper we present a Monte Carlo approach for the evaluation of plant maintenance strategies and operating procedures under economic constraints. The proposed Monte Carlo simulation model provides a flexible tool which enables one to describe many of the relevant aspects for plant management and operation such as aging, repair, obsolescence, renovation, which are not easily captured by analytical models. The maintenance periods are varied with the age of the components. Aging is described by means of a modified Brown–Proschan model of imperfect (deteriorating) repair which accounts for the increased proneness to failure of a component after it has been repaired. A model of obsolescence is introduced to evaluate the convenience of substituting a failed component with a new, improved one. The economic constraint is formalized in terms of an energy, or cost, function; optimization studies are then performed using the maintenance period as the control parameter.     

A combined global and local search method to deal with constrained optimization for continuous tabu search

Heuristic methods, such as tabu search, are efficient for global optimizations. Most studies, however, have focused on constraint‐free optimizations. Penalty functions are commonly used to deal with constraints for global optimization algorithms in dealing with constraints. This is sometimes inefficient, especially for equality constraints, as it is difficult to keep the global search within the feasible region by purely adding a penalty to the objective function. A combined global and local search method is proposed in this paper to deal with constrained optimizations. It is demonstrated by combining continuous tabu search (CTS) and sequential quadratic programming (SQP) methods. First, a nested inner‐ and outer‐loop method is presented to lead the search within the feasible region. SQP, a typical local search method, is used to quickly solve a non‐linear programming purely for constraints in the inner loop and provides feasible neighbors for the outer loop. CTS, in the outer loop, is used to seek for the global optimal. Finally, another local search using SQP is conducted with the results of CTS as initials to refine the global search results. Efficiency is demonstrated by a number of benchmark problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Biogeography-based particle swarm optimization with fuzzy elitism and its applications to constrained engineering problems

In evolutionary algorithms, elites are crucial to maintain good features in solutions. However, too many elites can make the evolutionary process stagnate and cannot enhance the performance. This article employs particle swarm optimization (PSO) and biogeography-based optimization (BBO) to propose a hybrid algorithm termed biogeography-based particle swarm optimization (BPSO) which could make a large number of elites effective in searching optima. In this algorithm, the whole population is split into several subgroups; BBO is employed to search within each subgroup and PSO for the global search. Since not all the population is used in PSO, this structure overcomes the premature convergence in the original PSO. Time complexity analysis shows that the novel algorithm does not increase the time consumption. Fourteen numerical benchmarks and four engineering problems with constraints are used to test the BPSO. To better deal with constraints, a fuzzy strategy for the number of elites is investigated. The simulation results validate the feasibility and effectiveness of the proposed algorithm.     

A variant space search method and its application to the optimization design of compressor profiles

Optimization methods have been widely used in practical engineering, with search efficiency and global search ability being the main evaluation criteria. In this article, the Bezier curve equivalent recursion is used in a genetic algorithm (GA) to realize the variant space search to improve the search efficiency and global search ability. The parameters related to this method are investigated by an optimization test of the simple curve approximation, which is then used for optimization designs of supersonic and transonic profiles. The results show that the GA can be improved if the variant space search method is added.     

A new hybrid real-coded genetic algorithm and its application to parameters identification of soils

Inverse analysis using an optimization method based on a genetic algorithm (GA) is a useful tool for obtaining soil parameters in geotechnical fields. However, the performance of the optimization in identifying soil parameters mainly depends on the search ability of the GA used. This study aims to develop a new efficient hybrid real-coded genetic algorithm (RCGA) being applied to identify parameters of soils. In this new RCGA, a new hybrid strategy is proposed by adopting two crossovers with outstanding ability, namely the Simulated Binary Crossover and the simplex crossover. In order to increase the convergence speed, a chaotic local search technique is used conditionally. The performance of the proposed RCGA is first validated by optimizing mathematical benchmark functions. The results demonstrate that the RCGA has an outstanding search ability and faster convergence speed compared to other hybrid RCGAs. The proposed new hybrid RCGA is then further evaluated by identifying soil parameters based on both laboratory tests and field tests, for different soil models. All the comparisons demonstrate that the proposed RCGA has an excellent performance of inverse analysis in identifying soil parameters, and is thus recommended for use based on all the evaluations carried out in this paper.