The simulation-driven metaheuristic algorithms have been successful in solving numerous problems compared to their deterministic counterparts. Despite this advantage, the stochastic nature of such algorithms resulted in a spectrum of solutions by a certain number of trials that may lead to the uncertainty of quality solutions. Therefore, it is of utmost importance to use a correct tool for measuring the performance of the diverse set of metaheuristic algorithms to derive an appropriate judgment on the superiority of the algorithms and also to validate the claims raised by researchers for their specific objectives. The performance of a randomized metaheuristic algorithm can be divided into efficiency and effectiveness measures. The efficiency relates to the algorithm’s speed of finding accurate solutions, convergence, and computation. On the other hand, effectiveness relates to the algorithm’s capability of finding quality solutions. Both scopes are crucial for continuous and discrete problems either in single- or multi-objectives. Each problem type has different formulation and methods of measurement within the scope of efficiency and effectiveness performance. One of the most decisive verdicts for the effectiveness measure is the statistical analysis that depends on the data distribution and appropriate tool for correct judgments.

Performance assessment of the metaheuristic optimization algorithms: an exhaustive review

As an important part of power system planning and the basis of economic operation of power systems, the main work of power load forecasting is to predict the time distribution and spatial distribution of future power loads. The accuracy of load forecasting will directly influence the reliability of the power system. In this paper, a novel short-term Empirical Mode Decomposition-Grey Relational Analysis-Modified Particle Swarm Optimization-Least Squares Support Vector Machine (EMD-GRA-MPSO-LSSVM) load forecasting model is proposed. The model uses the de-noising method combining empirical mode decomposition and grey relational analysis to process the original load series and forecasts the processed subsequences by the algorithm of modified particle swarm optimization and least square support vector machine. Then, the final forecasting results can be obtained after reconstructing the forecasting series. This paper takes the Jibei area as an example to produce an empirical analysis for load forecasting. The model input includes the hourly load one week before the forecasting day and the daily maximum temperature, daily minimum temperature, daily average temperature, relative humidity, wind force, date type of the forecasting day. The model output is the hourly load of the forecasting day. The models of BP neural network, SVM (Support vector machine), LSSVM (Least squares support vector machine), PSO-LSSVM (Particle swarm optimization-Least squares support vector machine), MPSO-LSSVM (Modified particle swarm optimization-Least squares support vector machine), EMD-MPSO-LSSVM are selected to compare with the model of EMD-GRA-MPSO-LSSVM using the same sample. The comparison results verify that the short-term load forecasting model of EMD-GRA-MPSO-LSSVM proposed in this paper is superior to other models and has strong generalization ability and robustness. It can achieve good forecasting effect with high forecasting accuracy, providing a new idea and reference for accurate short-term load forecasting.

/pdf/a-short-term-load-forecasting-model-with-a-modified-particle-51qikzd61b.pdf

A Short-Term Load Forecasting Model with a Modified Particle Swarm Optimization Algorithm and Least Squares Support Vector Machine Based on the Denoising Method of Empirical Mode Decomposition and Grey Relational Analysis

Firstly this article presents a thorough discussion of semantics formalization related issues in model driven engineering (MDE). Then motivated for the purpose of software implementation, and attempts to overcome the shortcomings of incompleteness and context-sensitivity in the existing models, we propose to study formalization of semantics from a cognitive background. Issues under study cover the broad scope of overlap vs. incomplete vs. complete, closed world assumption (CWA) vs. open world assumption (OWA), Y(Yes)/N(No) vs. T(True)/F(False), subjective (SUBJ) vs. objective (OBJ), static vs. dynamic, unconsciousness vs. conscious, human vs. machine aspects, etc. A semantics formalization approach called EID-SCE (Existence Identification Dualism-Semantics Cosmos Explosion) is designed to meet both the theoretical investigation and implementation of the proposed formalization goals. EID-SCE supports the measure/evaluation in a {complete, no overlap} manner whether a given concept or feature is an improvement. Some elementary cases are also shown to demonstrate the feasibility of EID-SCE.

A Dualism Based Semantics Formalization Mechanism for Model Driven Engineering

The fundamental objective in value-based software engineering is to integrate consistent stakeholder value propositions into the full extent of software engineering principles and practices so as to increase the value for software assets. In such a value-based setting, artifacts in software development such as requirement specifications, use cases, test cases, or defects, are not treated as equally important during the development process. Instead, they will be differentiated according to how much they are contributing, directly or indirectly, to the stakeholder value propositions. The higher the contributions, the more important the artifacts become. In turn, development activities involving more important artifacts should be given higher priorities and greater considerations in the development process. In this paper, a value-based framework is proposed for carrying out software evolutionary testing with a focus on test data generation through genetic algorithms. The proposed framework incorporates general principles in value-based software testing and makes it possible to prioritize testing decisions that are rooted in the stakeholder value propositions. It allows for a cost-effective way to fulfill most valuable testing objectives first and a graceful degradation when planned testing process has to be shortened.

A Value-Based Framework for Software Evolutionary Testing

Two independent laws of measure theoretically defined randomness, one in the interval (α, β) and the other in the interval (β, γ),are necessary and sufficient to define a normal fuzzy number (α, β, γ), the membership function of which is the distribution function with reference to the law of randomness defined in (α, β) and is the complementary distribution function with reference to the law of randomness defined in (β, γ). Thus to construct a normal fuzzy number (α, β, γ), we need to define two probability measures, one in (α, β) and the other in (β, γ).

Construction of Normal Fuzzy Numbers Using the Mathematics of Partial Presence

To control particles flying inside the limited search space and deal with the problem of slow search speed and premature convergence, this paper applies the theory of topology, and proposes a novel quotient space-based boundary condition by using the properties of quotient space and homeomorphism. In this new method, named QsaBC, Search space-zoomed factor and Attractor are introduced to enhance the performance of PSO according to analyzing the dynamic behavior and stability of particles. QsaBC proposed in this paper not only reduces the subjective interference and enforces the capability of global search, but also enhance the power of local search and escaping from an inferior local optimum. Four CEC'2008 benchmark functions are selected to evaluate the performance of QsaBC. Comparative experiments show that QsaBC is more effective to do with the boundary condition, furthermore, can get the satisfactory solution with fast convergence speed, easy calculation and good robustness than other experienced methods.

Quotient space-based boundary condition for particle swarm optimization algorithm

By the comparison study on several commonly used population diversity measures, we find that the conclusions derived from these diversity measures are not in keeping with the knowledge accepted by many scholars, and the relationship between population diversity and the evolutionary process of PSO is questionable. To deal with the above mentioned problems, a novel population diversity measure based on the optimal point is proposed in this paper, where the outliers are discarded, and the measure results are easy to understand the evolutionary state of the PSO algorithm. Furthermore, the optimal point-based diversity (O-diversity) measure is studied to control the population diversity and improve the optimization performance of PSO algorithm. The study results verify that the O-diversity measure is effective and useful to assess and control the population diversity, and it is meaningful to guide to better optimization performance of the advanced PSO algorithm.

An efficient population diversity measure for improved particle swarm optimization algorithm

To control particles to fly inside the limited search space and deal with the problems of slow search speed and premature convergence of particle swarm optimization algorithm, this paper applies the theory of topology, and proposed a quotient space-based boundary condition named QsaBC by using the properties of quotient space and homeomorphism. In QsaBC, Search space-zoomed factor and Attractor are introduced according to the dynamic behavior and stability of particles, which not only reduce the subjective interference and enforce the capability of global search, but also enhance the power of local search and escaping from an inferior local optimum. Four CEC'2008 benchmark functions are selected to evaluate the performance of QsaBC. Comparative experiments show that QsaBC can achieve the satisfactory optimization solution with fast convergence speed. Furthermore, QsaBC is more effective with errant particles, and has easier calculation and better robustness than other methods.

Quotient Space-Based Boundary Condition for Particle Swarm Optimization Algorithm

Standard particle swarm optimization (PSO) introduced in 2007, here called 2007-sPSO, is chosen as a starting algorithm in this paper. To solve the problems of the swarm's velocity slowing down towards zero and stagnant phenomena in the later evolutionary process of 2007-sPSO, elastic boundary for PSO (EBPSO) is proposed, where search space boundary is not fixed, but adapted to the condition whether the swarm is flying inside the current elastic search space or not. When some particles are stagnant, they are activated to speed up in the range of the current elastic boundary, and personal cognition is cleared. Experimental results show that EBPSO improves the optimization performance of 2007-sPSO, and performs better than comparison algorithms.

Elastic boundary for particle swarm optimization

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Quotient space-based boundary condition for particle swarm optimization algorithm

An efficient population diversity measure for improved particle swarm optimization algorithm

Quotient Space-Based Boundary Condition for Particle Swarm Optimization Algorithm

Elastic boundary for particle swarm optimization