Algorithms for the continuous nonlinear resource allocation problem---new implementations and numerical studies

Patriksson (2008) provided a then up-to-date survey on the continuous,separable, differentiable and convex resource allocation problem with a single resource constraint. Since the publication of that paper the interest in the problem has grown: several new applications have arisen where the problem at hand constitutes a subproblem, and several new algorithms have been developed for its efficient solution. This paper therefore serves three purposes. First, it provides an up-to-date extension of the survey of the literature of the field, complementing the survey in Patriksson (2008) with more then 20 books and articles. Second, it contributes improvements of some of these algorithms, in particular with an improvement of the pegging (that is, variable fixing) process in the relaxation algorithm, and an improved means to evaluate subsolutions. Third, it numerically evaluates several relaxation (primal) and breakpoint (dual) algorithms, incorporating a variety of pegging strategies, as well as a quasi-Newton method. Our conclusion is that our modification of the relaxation algorithm performs the best. At least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

Time out of mind: Subben's checklist revisited: A partial description of the development of quantitative OR papers over a period of 25 years

This short paper aims to investigate some of the historical developments of one classic, well-cited and highly esteemed scientific journal in the domain of quantitative operations research - namely the INFORMS journal Operations Research - over a period of 25 years between 1981 and 2006. As such this paper, and the journal in question, represents one representative attempt to analyze - for the purpose of possible future generalization - how research production has evolved, and evolves, over time. Among the general developments that we think we can trace are that (a) the historical overviews (i.e., literature surveys) in the articles, as well as the list of references, somewhat counter-intuitively shrink over time, while (b) the motivating and modelling parts grow. We also attempt to characterize - in some detail - the appearance and character, over time, of the most cited, as well as the least cited, papers over the years studied. In particular, we find that many of the least cited papers are quite imbalanced. For example, some of them include one main section only, and the least cited papers also have shorter reference lists. We also analyse the articles' utilization of important buzz words representing the constitutive parts of an OR journal paper, based on Subben's checklist (Larsson and Patriksson, 2014, 2016). Based on a word count of these buzz words we conclude through a citation study, utilizing a collection of particularly highly or little cited papers, that there is a quite strong positive correlation between a journal paper being highly cited and its degree of utilization of this checklist

Optimal scheduling of the next preventive maintenance activity for a wind farm

Global warming has been attributed to increased greenhouse gas emission concentrations in the atmosphere through the burning of fossil fuels. Renewable energy, as an alternative, is capable of displacing energy from fossil fuels. Wind power is abundant, renewable, and produces almost no greenhouse gas during operation. A large part of the cost of operations is due to the cost of maintaining the wind power equipment, especially for offshore wind farms. How to reduce the maintenance cost is what this article focus on. This article presents a binary linear optimisation model whose solution may suggest wind turbine owners which components, and when, should undergo the next preventive maintenance (PM). The scheduling strategy takes into account eventual failure events of the multi-component system, in that after the failed system is repaired, the previously scheduled PM plan should be updated treating the restored components to be as good as new. The optimisation model NextPM is tested through three numerical case studies. The first study addresses the illuminating case of a single component system. The second study analyses the case of seasonal variations of set-up costs, as compared to the constant set-up cost setting. Among other things, this analysis reveals a dramatic cost reduction achieved by the NextPM model as compared to the the pure CM strategy. In these two case studies, the cost are reduced by around 35%. The third case study compares the NextPM model with another optimisation model preventive maintenance scheduling problem with interval costs(PMSPIC) which was the major source of inspiration for this article. This comparison demonstrates that the NextPM model is accurate and much more effective. In conclusion, the NextPM model is both accurate and fast to solve. The algorithm stemming from the proposed model can be used as a key module in a maintenance scheduling app.Comment: 16 pages, 2 figures. Submitted to Wind Energy Scienc

Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment mode

Integration of expert knowledge into radial basis function surrogate models

A current application in a collaboration between Chalmers University of Technology and Volvo Group Trucks Technology concerns the global optimization of a complex simulation-based function describing the rolling resistance coefficient of a truck tyre. This function is crucial for the optimization of truck tyres selection considered. The need to explicitly describe and optimize this function provided the main motivation for the research presented in this article. Many optimization algorithms for simulation-based optimization problems use sample points to create a computationally simple surrogate model of the objective function. Typically, not all important characteristics of the complex function (as, e.g., non-negativity)—here referred to as expert knowledge—are automatically inherited by the surrogate model. We demonstrate the integration of several types of expert knowledge into a radial basis function interpolation. The methodology is first illustrated on a simple example function and then applied to a function describing the rolling resistance coefficient of truck tyres. Our numerical results indicate that expert knowledge can be advantageously incorporated and utilized when creating global approximations of unknown functions from sample points

The stochastic opportunistic replacement problem, part III: improved bounding procedures

We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51–75, 2015), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy

Efficient solution of many instances of a simulation-based optimization problem utilizing a partition of the decision space

This paper concerns the solution of a class of mathematical optimization problems with simulation-based objective functions. The decision variables are partitioned into two groups, referred to as variables and parameters, respectively, such that the objective function value is influenced more by the variables than by the parameters. We aim to solve this optimization problem for a large number of parameter settings in a computationally efficient way. The algorithm developed uses surrogate models of the objective function for a selection of parameter settings, for each of which it computes an approximately optimal solution over the domain of the variables. Then, approximate optimal solutions for other parameter settings are computed through a weighting of the surrogate models without requiring additional expensive function evaluations. We have tested the algorithm\u27s performance on a set of global optimization problems differing with respect to both mathematical properties and numbers of variables and parameters. Our results show that it outperforms a\ua0standard and often applied approach based on a surrogate model of the objective function over the complete space of variables and parameters