Convergence concepts on quasi-probability space

Abstract. Quasi-probability is a kind of fuzzy measure, its properties will be further discussed in this paper. New convergence concepts for quasi-random variables are then introduced and the relationships among the convergence concepts are investigated. All obtained results are natural extensions of the classical convergence theory to the case where the measure tool is fuzzy. AMS Classification: 60F05, 28E1

Approximating Pareto frontier using a hybrid line search approach

This is the post-print version of the final paper published in Information Sciences. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that this technique sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new approach for multicriteria optimization, which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point. Once the first Pareto solution is obtained, a simplified version of the former one is used in the context of Pareto dominance to obtain a set of efficient points, which will assure a thorough distribution of solutions on the Pareto frontier. In the current form, the proposed technique is well suitable for problems having multiple objectives (it is not limited to bi-objective problems) and require the functions to be continuous twice differentiable. In order to assess the effectiveness of this approach, some experiments were performed and compared with two recent well known population-based metaheuristics namely ParEGO and NSGA II. When compared to ParEGO and NSGA II, the proposed approach not only assures a better convergence to the Pareto frontier but also illustrates a good distribution of solutions. From a computational point of view, both stages of the line search converge within a short time (average about 150 ms for the first stage and about 20 ms for the second stage). Apart from this, the proposed technique is very simple, easy to implement and use to solve multiobjective problems.CNCSIS IDEI 2412, Romani

CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features

In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring. Our aim is the optimization of the balance between exploration and exploitation in the search process. In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis. With this set of functions we can extract conclusions in function of the problem at hand. We analyze the results using ANOVA and multiple comparison statistical tests. As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks. The results obtained are above the performance of standard methods

Demand Response Strategy Based on Reinforcement Learning and Fuzzy Reasoning for Home Energy Management

As energy demand continues to increase, demand response (DR) programs in the electricity distribution grid are gaining momentum and their adoption is set to grow gradually over the years ahead. Demand response schemes seek to incentivise consumers to use green energy and reduce their electricity usage during peak periods which helps support grid balancing of supply-demand and generate revenue by selling surplus of energy back to the grid. This paper proposes an effective energy management system for residential demand response using Reinforcement Learning (RL) and Fuzzy Reasoning (FR). RL is considered as a model-free control strategy which learns from the interaction with its environment by performing actions and evaluating the results. The proposed algorithm considers human preference by directly integrating user feedback into its control logic using fuzzy reasoning as reward functions. Q-learning, a RL strategy based on a reward mechanism, is used to make optimal decisions to schedule the operation of smart home appliances by shifting controllable appliances from peak periods, when electricity prices are high, to off-peak hours, when electricity prices are lower without affecting the customer’s preferences. The proposed approach works with a single agent to control 14 household appliances and uses a reduced number of state-action pairs and fuzzy logic for rewards functions to evaluate an action taken for a certain state. The simulation results show that the proposed appliances scheduling approach can smooth the power consumption profile and minimise the electricity cost while considering user’s preferences, user’s feedbacks on each action taken and his/her preference settings. A user-interface is developed in MATLAB/Simulink for the Home Energy Management System (HEMS) to demonstrate the proposed DR scheme. The simulation tool includes features such as smart appliances, electricity pricing signals, smart meters, solar photovoltaic generation, battery energy storage, electric vehicle and grid supply.Peer reviewe