Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

Waste collection routing-limited multiple landfills and heterogeneous fleet

This article deals with a real-life waste collection routing problem. To efficiently plan waste collection, large municipalities may be partitioned into convenient sectors and only then can routing problems be solved in each sector. Three diverse situations are described, resulting in three different new models. In the first situation, there is a single point of waste disposal from where the vehicles depart and to where they return. The vehicle fleet comprises three types of collection vehicles. In the second, the garage does not match any of the points of disposal. The vehicle is unique and the points of disposal (landfills or transfer stations) may have limitations in terms of the number of visits per day. In the third situation, disposal points are multiple (they do not coincide with the garage), they are limited in the number of visits, and the fleet is composed of two types of vehicles. Computational results based not only on instances adapted from the literature but also on real cases are presented and analyzed. In particular, the results also show the effectiveness of combining sectorization and routing to solve waste collection problems.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.

Analyzing Multiple Outcomes: Is it Really Worth the use of Multivariate Linear Regression?

In health related research it is common to have multiple outcomes of interest in a single study. These outcomes are often analysed separately, ignoring the correlation between them. One would expect that a multivariate approach would be a more efficient alternative to individual analyses of each outcome. Surprisingly, this is not always the case. In this article we discuss different settings of linear models and compare the multivariate and univariate approaches. We show that for linear regression models, the estimates of the regression parameters associated with covariates that are shared across the outcomes are the same for the multivariate and univariate models while for outcome-specific covariates the multivariate model performs better in terms of efficiency.

A Multiple Criteria Utility-based Approa h for the Unit Commitment with Wind Power and Pumped Storage Hydro

The integration of wind power in eletricity generation brings new challenges to unit commitment due to the random nature of wind speed. For this particular optimisation problem, wind uncertainty has been handled in practice by means of conservative stochastic scenario-based optimisation models, or through additional operating reserve settings. However, generation companies may have different attitudes towards operating costs, load curtailment, or waste of wind energy, when considering the risk caused by wind power variability. Therefore, alternative and possibly more adequate approaches should be explored. This work is divided in two main parts. Firstly we survey the main formulations presented in the literature for the integration of wind power in the unit commitment problem (UCP) and present an alternative model for the wind-thermal unit commitment. We make use of the utility theory concepts to develop a multi-criteria stochastic model. The objectives considered are the minimisation of costs, load curtailment and waste of wind energy. Those are represented by individual utility functions and aggregated in a single additive utility function. This last function is adequately linearised leading to a mixed-integer linear program (MILP) model that can be tackled by general-purpose solvers in order to find the most preferred solution. In the second part we discuss the integration of pumped-storage hydro (PSH) units in the UCP with large wind penetration. Those units can provide extra flexibility by using wind energy to pump and store water in the form of potential energy that can be generated after during peak load periods. PSH units are added to the first model, yielding a MILP model with wind-hydro-thermal coordination. Results showed that the proposed methodology is able to reflect the risk profiles of decision makers for both models. By including PSH units, the results are significantly improved.