A radial estimation of distribution algorithm for the job-shop scheduling problem

The job-shop environment has been widely studied under different approaches. It is due to its practical characteristic that makes its research interesting. Therefore, the job-shop scheduling problem continues being attracted to develop new evolutionary algorithms. In this paper, we propose a new estimation of distribution algorithm coupled with a radial probability function. The aforementioned radial function comes from the hydrogen element. This approach is proposed in order to build a competitive evolutionary algorithm for the job-shop scheduling problem. The key point is to exploit the radial probability distribution to construct offspring, and to tackle the inconvenient of the EDAs, i.e., lack of diversity of the solutions and poor ability of exploitation. Various instances and numerical experiments are presented to illustrate, and to validate this novel research. The results, obtained from this research, permits to conclude that using radial probability distributions is an emerging field to develop new and efficient EDAs.

A Survey on Recent Progress in the Theory of Evolutionary Algorithms for Discrete Optimization

The theory of evolutionary computation for discrete search spaces has made significant progress since the early 2010s. This survey summarizes some of the most important recent results in this research area. It discusses fine-grained models of runtime analysis of evolutionary algorithms, highlights recent theoretical insights on parameter tuning and parameter control, and summarizes the latest advances for stochastic and dynamic problems. We regard how evolutionary algorithms optimize submodular functions, and we give an overview over the large body of recent results on estimation of distribution algorithms. Finally, we present the state of the art of drift analysis, one of the most powerful analysis technique developed in this field.

An Adaptive Covariance Scaling Estimation of Distribution Algorithm

Optimization problems are ubiquitous in every field, and they are becoming more and more complex, which greatly challenges the effectiveness of existing optimization methods. To solve the increasingly complicated optimization problems with high effectiveness, this paper proposes an adaptive covariance scaling estimation of distribution algorithm (ACSEDA) based on the Gaussian distribution model. Unlike traditional EDAs, which estimate the covariance and the mean vector, based on the same selected promising individuals, ACSEDA calculates the covariance according to an enlarged number of promising individuals (compared with those for the mean vector). To alleviate the sensitivity of the parameters in promising individual selections, this paper further devises an adaptive promising individual selection strategy for the estimation of the mean vector and an adaptive covariance scaling strategy for the covariance estimation. These two adaptive strategies dynamically adjust the associated numbers of promising individuals as the evolution continues. In addition, we further devise a cross-generation individual selection strategy for the parent population, used to estimate the probability distribution by combing the sampled offspring in the last generation and the one in the current generation. With the above mechanisms, ACSEDA is expected to compromise intensification and diversification of the search process to explore and exploit the solution space and thus could achieve promising performance. To verify the effectiveness of ACSEDA, extensive experiments are conducted on 30 widely used benchmark optimization problems with different dimension sizes. Experimental results demonstrate that the proposed ACSEDA presents significant superiority to several state-of-the-art EDA variants, and it preserves good scalability in solving optimization problems.

Single-stage to orbit ascent trajectory optimisation with reliable evolutionary initial guess

In this paper, the ascent trajectory optimization of a lifting body Single-Stage To Orbit (SSTO) reusable launch vehicle is investigated. The work is carried out using a Direct Multiple Shooting method to solve the Optimal Control problem. The crucial initialisation of the optimisation process is performed by using a combination of two evolutionary algorithms, namely a Multi-Objective Parzen-based Estimation of Distribution (MOPED) algorithm and a Multi-Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA). Multi-Objective Parzen-based Estimation of Distribution (MOPED) belongs to the class of Estimation of Distribution Algorithms (EDAs) and it is used in the first phase of the initial guess research to explore the search space, then Multi-Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA) is used to refine the obtained results, and better fulfill the imposed constraints. The initial guesses obtained with this evolutionary framework were tested on different multiple shooting configurations. The importance of the continuity properties of the employed mathematical models was also quantitatively addressed.

A Hybrid Estimation of Distribution Algorithm for the Quay Crane Scheduling Problem

The aim of the quay crane scheduling problem (QCSP) is to identify the best sequence of discharging and loading operations for a set of quay cranes. This problem is solved with a new hybrid estimation of distribution algorithm (EDA). The approach is proposed to tackle the drawbacks of the EDAs, i.e., the lack of diversity of solutions and poor ability of exploitation. The hybridization approach, used in this investigation, uses a distance based ranking model and the moth-flame algorithm. The distance based ranking model is in charge of modelling the solution space distribution, through an exponential function, by measuring the distance between solutions; meanwhile, the heuristic moth-flame determines who would be the offspring, with a spiral function that identifies the new locations for the new solutions. Based on the results, the proposed scheme, called QCEDA, works to enhance the performance of those other EDAs that use complex probability models. The dispersion results of the QCEDA scheme are less than the other algorithms used in the comparison section. This means that the solutions found by the QCEDA are more concentrated around the best value than other algorithms, i.e., the average of the solutions of the QCEDA converges better than other approaches to the best found value. Finally, as a conclusion, the hybrid EDAs have a better performance, or equal in effectiveness, than the so called pure EDAs.

Differential Evolution with Estimation of Distribution for Worst-Case Scenario Optimization

Worst-case scenario optimization deals with the minimization of the maximum output in all scenarios of a problem, and it is usually formulated as a min-max problem. Employing nested evolutionary algorithms to solve the problem requires numerous function evaluations. This work proposes a differential evolution with an estimation of distribution algorithm. The algorithm has a nested form, where a differential evolution is applied for both the design and scenario space optimization. To reduce the computational cost, we estimate the distribution of the best worst solution for the best solutions found so far. The probabilistic model is used to sample part of the initial population of the scenario space differential evolution, using a priori knowledge of the previous generations. The method is compared with a state-of-the-art algorithm on both benchmark problems and an engineering application, and the related results are reported.