We study three-dimensional isogeometric analysis (IGA) and the solution of the resulting system of linear equations via a direct solver. IGA uses highly continuous $C^{p-1}$Cp-1 basis functions, which provide multiple benefits in terms of stability and convergence properties. However, smooth basis significantly deteriorate the direct solver performance and its parallel scalability. As a partial remedy for this, refined Isogeometric Analysis (rIGA) method improves the sequential execution of direct solvers. The refinement strategy enriches traditional highly-continuous $C^{p-1}$Cp-1 IGA spaces by introducing low-continuity $C^0$C0-hyperplanes along the boundaries of certain pre-defined macro-elements. In this work, we propose a solution strategy for rIGA for parallel distributed memory machines and compare the computational costs of solving rIGA versus IGA discretizations. We verify our estimates with parallel numerical experiments. Results show that the weak parallel scalability of the direct solver improves approximately by a factor of $p^2$p2 when considering rIGA discretizations rather than highly-continuous IGA spaces.

Evolutionary algorithms are (meta-)heuristic techniques used in the case of search, optimization, and adaptation problems, which cannot be solved with the use of traditional methods. Sexual selection mechanism helps to maintain the population diversity in evolutionary algorithms. In this paper the agent-based realization of multi-objective evolutionary algorithm with sexual selection mechanism is presented. The system is evaluated with the use of Zitzler’s test problems and compared to “classical” multi-objective evolutionary algorithms.

Evolutionary Multi-Agent System approach for optimization (for multi-objective optimization in particular) is a promising computational model. Its computational as well as implemental simplicity cause that approaches based on EMAS model can be widely used for solving optimization tasks. It turns out that introducing some additional mechanisms into basic EMAS-such as presented in the course of this paper elitist extensions cause that results obtained with the use of proposed elEMAS (elitist Evolutionary Multi-Agent System) approach are as high-quality results as results obtained by such famous and commonly used algorithms as NSGA-II or SPEA2. Apart from the computational simplicity especially important and interesting aspects of EMAS-based algorithms it is characteristic for them a kind of soft selection which can be additionally easily adjusted depending on a particular situation-in particular it is possible to introduce auto-adapting selection into such systems. Such a kind of selection seems to be especially important and valuable in solving optimization tasks in uncertain or ldquonoisedrdquo environments. In the course of this paper the model and experimental results obtained by elEMAS system in solving noisy multi-objective optimization problems are presented and the general conclusion is as follows: EMAS-based optimization system seems to be more effective alternative than classical (i.e. non agent-based) evolutionary algorithms for multi-objective optimization, in particular, in uncertain environment, it seems to be better alternative than NSGA-II algorithm.

Introducing elitism into evolutionary multi-agent system for multi-objective optimization proofed to be smooth both conceptually and in realization. Simultaneously it allowed for obtaining results with comparable high quality to such referenced algorithms as Non-dominated Sorting Genetic Algorithm (NSGA-II) or Strength Pareto Evolutionary Algorithm (SPEA2). What is more, applying mentioned agent-based computational paradigm for solving multi-criteria optimization tasks in ldquonoisyrdquo environments mainly because of-characteristic for EMAS-based approach-a kind of soft selection allowed for obtaining better solutions than mentioned referenced algorithms. From the above observations the following conclusion can be drown: evolutionary multi-agent system (EMAS) (and being the subject of this paper elitist evolutionary multi-agent system (elEMAS) in particular) seems to be promising computational model in the context of multi-criteria optimization tasks. In previous works however the possibility of applying elEMAS for solving constrained multi-objective optimization task has not been investigated. It is obvious however that in almost all real-life problems constraints are a crucial part of multi-objective optimization problem (MOOP) definition and it is nothing strange that among (evolutionary) algorithms for multi-objective optimization a special attention is paid to techniques and algorithms for constrained multi-objective optimization and a variety-more or less effective-algorithms have been proposed. Thus, the question appears if effective constrained multi-objective optimization with the use of elitist evolutionary multi-agent system is possible. In the course of this paper preliminary answer for that question is given.

Evolutionary multi-agent system approach for optimization (especially for multi-objective optimization) is a very promising computational model. Its computational as well as implemental simplicity causes that approaches based on EMAS model can be widely used for solving optimization tasks. It turns out that introducing some additional mechanisms into basic EMAS - causes that EMAS-based system can be successfully applied for solving constrained multi-objective optimization tasks - and what is important results obtained by proposed approach are better/not worse than results obtained by NSGA-II or SPEA2 algorithms. In the course of this paper some extensions that can be introduced into EMAS in order to constrained multi-objective optimization are presented. What is important - any new additional mechanisms do not have to be introduced into EMAS to solve constrained optimization tasks - the only extensions causing that EMAS-based model becomes an efficient and simple both in conception as well as in implementation - is an appropriate strategy regarding the flow among agents crucial non-renewable resource which is usually called life energy. In this paper, both the idea as well as preliminary results of constrained evolutionary multi-agent system (conEMAS) for multi-objective optimization are presented.

It has been already proofed and discussed in our previous works that thanks to its computational as well as implemental simplicity evolutionary multi-agent system (EMAS) approach can be easily adjusted and widely used for solving almost any type of multi-objective optimization task. Unfortunately, results obtained by distributed and decentralized agent-based evolutionary heuristic approach applied for solving multi-objective optimization problems (MOOPs) can be limited by such factors, as stagnation of agents' evolution or problems with distributing agents evenly over the whole approximation of the Pareto frontier. In the course of this paper three main shortcomings of EMAS-based approach are diagnosed and ideas of possible solutions of identified problems with the use of "flock-based" mechanisms are presented. Next, one of many possible realization of flock-based ideas i.e. so-called densityplus realization of floEMAS paradigm is discussed. Finally, experimental results obtained by floEMAS system in solving noisy multi-objective optimization tasks are presented. The goal of this paper is: to discuss shortcomings identified in applying EMAS for solving MOOPs, to present flock-based mechanisms allowing for overcoming such shortcomings, to discuss one of possible realization of floEMAS approach and to present the behavior of proposed floEMAS realization in noisy environment - since in the case of EMAS-based approaches there is no need to introduce any additional mechanisms to solve efficiently noisy problems.

Co-evolutionary techniques for evolutionary algorithms are aimed at overcoming their limited adaptive capabilities and allow for the application of such algorithms to problems for which it is difficult or even impossible to formulate explicit fitness function. Sexual selection resulting from sexual conflict and co-evolution of female mate choice and male displayed trait is considered to be one of the ecological interactions responsible for maintaining population diversity. In this paper the idea of co-evolutionary multi-agent system with sexual selection mechanism for multi-objective optimization is introduced. In presented system the Pareto frontier is located by the population of agents as a result of co-evolutionary interactions between sexes. Also, results from runs of presented system against test functions and comparison to classical multi-objective evolutionary algorithms are presented.