An Evolutionary Computation Approach to Resource Allocation in Container-based Clouds

<p>A container-based cloud is a new trend in cloud computing that introduces more granular management of cloud resources. Compared with VM-based clouds, container-based clouds can further improve energy efficiency with a finer granularity resource allocation in data centers. The current allocation approaches for VM-based clouds cannot be used in container-based clouds. The first reason is that existing research lacks appropriate models that can represent the interaction of allocation features. Many critical features, such as VM overhead, are also not considered in the current models. The second reason is that current allocation approaches do not perform well to the three frequently encountered allocation scenarios, offline allocation, on-line allocation, and multi-objective allocation. Current approaches for these scenarios are mostly based on greedy heuristics that can be easily stuck at local optimum, or meta-heuristics that consider a simplified one-level allocation problem. Evolutionary Computation (EC) is particularly good at solving combinatorial optimization problems for both off-line and on-line scenarios. The overall goal of this thesis is to propose an EC approach to the three allocation scenarios in order to improve the performance of container-based clouds. Specifically, we aim to optimize energy consumption in all the scenarios. An additional objective, availability of the application, is considered for the multi-objective scenario. First, this thesis investigates two promising representations, vector-based and group-based. We propose two novel vector-based (e.g., Single- chromosome Genetic Algorithm (SGA) and Dual-chromosome GA (DGA)) and a group-based GA approaches for the off-line allocation scenario. Cor- responding genetic operators and decoding processes are also developed and evaluated. Two contributions have been made. Firstly, a novel offline model has been proposed based on current models with additional features. It can be used to evaluate allocation algorithms. Secondly, two types of problem representation, vector-based and group-based, are investigated and three novel approaches are proposed. The three approaches are compared with state-of-the-art approaches. The results show that all solutions produced by these approaches are better than the state-of-the-art approaches and group-based GA is the best approach. Second, this thesis proposes a novel genetic programming hyper-heuristic (GPHH) and a cooperative coevolution (CCGP)-based approach for the on-line allocation scenario. These hyper-heuristic methods can automatically generate allocation rules. For the GPHH-based approach, we develop a novel training procedure to generate reservation-based rules for allocating containers to VM instances. For the CCGP-based approach, we introduce a new terminal set and develop a training procedure to generate allocation rules for two-level allocations. We analyze both human-designed rules and generated rules to provide insights for algorithm designers. Two contributions have been proposed for the on-line problem. First, the on-line model for the on-line allocation scenario is developed. Second, a novel terminal set and training procedures are developed. The automatically generated heuristics perform significantly better than the manually designed heuristics. Third, this thesis proposes a multi-objective approach that generates a set of trade-off solutions for the cloud providers to choose from. Our novel approach, namely Nondominated Sorting-Group GA (NS-GGA), combines the group-based representation and the NSGA-II framework. The experimental results are compared with existing approaches. The results show that our proposed NS-GGA approach outperforms all other approaches. We propose two novelties. The first novelty is the multi-objective model including objectives of energy consumption and availability. The second novelty is the NS-GGA approach that combines the group-based representation with NSGA-II. The allocation solutions found by NS-GGA dominate the solutions found by other existing approaches.</p>

An Evolutionary Computation Approach to Resource Allocation in Container-based Clouds

<p>A container-based cloud is a new trend in cloud computing that introduces more granular management of cloud resources. Compared with VM-based clouds, container-based clouds can further improve energy efficiency with a finer granularity resource allocation in data centers. The current allocation approaches for VM-based clouds cannot be used in container-based clouds. The first reason is that existing research lacks appropriate models that can represent the interaction of allocation features. Many critical features, such as VM overhead, are also not considered in the current models. The second reason is that current allocation approaches do not perform well to the three frequently encountered allocation scenarios, offline allocation, on-line allocation, and multi-objective allocation. Current approaches for these scenarios are mostly based on greedy heuristics that can be easily stuck at local optimum, or meta-heuristics that consider a simplified one-level allocation problem. Evolutionary Computation (EC) is particularly good at solving combinatorial optimization problems for both off-line and on-line scenarios. The overall goal of this thesis is to propose an EC approach to the three allocation scenarios in order to improve the performance of container-based clouds. Specifically, we aim to optimize energy consumption in all the scenarios. An additional objective, availability of the application, is considered for the multi-objective scenario. First, this thesis investigates two promising representations, vector-based and group-based. We propose two novel vector-based (e.g., Single- chromosome Genetic Algorithm (SGA) and Dual-chromosome GA (DGA)) and a group-based GA approaches for the off-line allocation scenario. Cor- responding genetic operators and decoding processes are also developed and evaluated. Two contributions have been made. Firstly, a novel offline model has been proposed based on current models with additional features. It can be used to evaluate allocation algorithms. Secondly, two types of problem representation, vector-based and group-based, are investigated and three novel approaches are proposed. The three approaches are compared with state-of-the-art approaches. The results show that all solutions produced by these approaches are better than the state-of-the-art approaches and group-based GA is the best approach. Second, this thesis proposes a novel genetic programming hyper-heuristic (GPHH) and a cooperative coevolution (CCGP)-based approach for the on-line allocation scenario. These hyper-heuristic methods can automatically generate allocation rules. For the GPHH-based approach, we develop a novel training procedure to generate reservation-based rules for allocating containers to VM instances. For the CCGP-based approach, we introduce a new terminal set and develop a training procedure to generate allocation rules for two-level allocations. We analyze both human-designed rules and generated rules to provide insights for algorithm designers. Two contributions have been proposed for the on-line problem. First, the on-line model for the on-line allocation scenario is developed. Second, a novel terminal set and training procedures are developed. The automatically generated heuristics perform significantly better than the manually designed heuristics. Third, this thesis proposes a multi-objective approach that generates a set of trade-off solutions for the cloud providers to choose from. Our novel approach, namely Nondominated Sorting-Group GA (NS-GGA), combines the group-based representation and the NSGA-II framework. The experimental results are compared with existing approaches. The results show that our proposed NS-GGA approach outperforms all other approaches. We propose two novelties. The first novelty is the multi-objective model including objectives of energy consumption and availability. The second novelty is the NS-GGA approach that combines the group-based representation with NSGA-II. The allocation solutions found by NS-GGA dominate the solutions found by other existing approaches.</p>

ON THE UPPER AND LOWER RESOLVING FUNCTIONS IN GAME PROBLEMS OF DYNAMICS

The quasi-linear conflict-controlled processes of general form are studied. The theme for investigation is the problem of the trajectories approaching a given cylindrical set. The research is based on the method of upper and lower resolving functions. The main attention is paid to the case when Pontryagin’s condition does not hold, moreover, the bodily part of the terminal set is non-convex. A scheme of the method is proposed, which allows, in the case of non-convexity of the body part, to fix some point in it, namely the aiming point, and to realize the process of approach. Sufficient conditions are obtained for solving the problem of approach for different classes of strategies. In so doing, the Hayek stroboscopic strategies that prescribe control by N.N. Krasovskii are applied. The process of approach goes on in two stages — active and passive. On the active stage the upper resolving function of second type is accumulated and after the moment of switching the lower resolving function of second type is used. These functions allow constructing a measurable control of second player on the basis of the theorems on measurable choice, in particular, the Filippov-Castaing theorem. The obtained results for generalized quasi-linear processes make it possible to encompass a wide range of functional-differential systems as well as the systems with fractional and partial derivatives. Possibilities for development of the offered technique are specified.

On a discrete game problem with non-convex control vectograms

In a normed space of finite dimension, a discrete game problem with fixed duration is considered. The terminal set is determined by the condition that the norm of the phase vector belongs to a segment with positive ends. In this paper, a set defined by this condition is called a ring. At each moment, the vectogram of the first player's controls is a certain ring. The controls of the second player at each moment are taken from balls with given radii. The goal of the first player is to lead a phase vector to the terminal set at a fixed time. The goal of the second player is the opposite. In this paper, necessary and sufficient termination conditions are found, and optimal controls of the players are constructed.

Structure, Activity and Function of the MLL2 (KMT2B) Protein Lysine Methyltransferase

The Mixed Lineage Leukemia 2 (MLL2) protein, also known as KMT2B, belongs to the family of mammalian histone H3 lysine 4 (H3K4) methyltransferases. It is a large protein of 2715 amino acids, widely expressed in adult human tissues and a paralog of the MLL1 protein. MLL2 contains a characteristic C-terminal SET domain responsible for methyltransferase activity and forms a protein complex with WRAD (WDR5, RbBP5, ASH2L and DPY30), host cell factors 1/2 (HCF 1/2) and Menin. The MLL2 complex is responsible for H3K4 trimethylation (H3K4me3) on specific gene promoters and nearby cis-regulatory sites, regulating bivalent developmental genes as well as stem cell and germinal cell differentiation gene sets. Moreover, MLL2 plays a critical role in development and germ line deletions of Mll2 have been associated with early growth retardation, neural tube defects and apoptosis that leads to embryonic death. It has also been involved in the control of voluntary movement and the pathogenesis of early stage childhood dystonia. Additionally, tumor-promoting functions of MLL2 have been detected in several cancer types, including colorectal, hepatocellular, follicular cancer and gliomas. In this review, we discuss the main structural and functional aspects of the MLL2 methyltransferase with particular emphasis on transcriptional mechanisms, gene regulation and association with diseases.

A method for constructing an optimal control strategy in a linear terminal problem

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances, where the control goal is to steer the system with guarantees into a given terminal set while minimising the terminal cost function. We define an optimal control strategy which takes into account the state of the system at one future time instant and propose an efficient numerical method for its construction. The results of numerical experiments show an improvement in performance under the optimal control strategy in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.

DIFFERENTIAL GAMES OF FRACTIONAL ORDER WITH DISTRIBUTED PARAMETERS

The article deals with the problem of pursuit in differential games of fractional order with distributed parameters. Partial fractional derivatives with respect to time and space variables are understood in the sense of Riemann - Liouville, and the Grunwald-Letnikov formula is used in the approximation. The problem of getting into some positive neighborhood of the terminal set is considered. To solve this problem, the finite difference method is used. The fractional Riemann-Liouville derivatives with respect to spatial variables on a segment are approximated using the Grunwald-Letnikov formula. Using a sufficient criterion for the existence of a fractional derivative, a difference approximation of the fractional-order derivative with respect to time is obtained. By approximating a differential game to an explicit difference game, a discrete game is obtained. The corresponding pursuit problem for a discrete game is formulated, which is obtained using the approximation of a continuous game. The concept of the possibility of completing the pursuit, a discrete game in the sense of an exact capture, is defined. Sufficient conditions are obtained for the possibility of completing the pursuit. It is shown that the order of approximation in time is equal to one, and in spatial variables is equal to two. It is proved that if in a discrete game from a given initial position it is possible to complete the pursuit in the sense of exact capture, then in a continuous game from the corresponding initial position it is possible to complete the pursuit in the sense of hitting a certain neighborhood. A structure for constructing pursuit controls is proposed, which will ensure the completion of the game in a finite time. The methods used for this problem can be used to study differential games described by more general equations of fractional order.

Feature selection in evolving job shop dispatching rules with genetic programming

Genetic Programming (GP) has been successfully used to automatically design dispatching rules in job shop scheduling. The goal of GP is to evolve a priority function that will be used to order the waiting jobs at each decision point, and decide the next job to be processed. To this end, the proper terminals (i.e. job shop features) have to be decided. When evolving the priority function, various job shop features can be included in the terminal set. However, not all the features are helpful, and some features are irrelevant to the rule. Including irrelevant features into the terminal set enlarges the search space, and makes it harder to achieve promising areas. Thus, it is important to identify the important features and remove the irrelevant ones to improve the GP-evolved rules. This paper proposes a domain-knowledge-free feature ranking and selection approach. As a result, the terminal set is significantly reduced and only the most important features are selected. The experimental results show that using only the selected features can lead to significantly better GP-evolved rules on both training and unseen test instances. © Mei 2016. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in 'GECCO '16: Proceedings of the Genetic and Evolutionary Computation Conference', https://doi.org/10.1145/2908812.2908822.

Feature selection in evolving job shop dispatching rules with genetic programming

Genetic Programming (GP) has been successfully used to automatically design dispatching rules in job shop scheduling. The goal of GP is to evolve a priority function that will be used to order the waiting jobs at each decision point, and decide the next job to be processed. To this end, the proper terminals (i.e. job shop features) have to be decided. When evolving the priority function, various job shop features can be included in the terminal set. However, not all the features are helpful, and some features are irrelevant to the rule. Including irrelevant features into the terminal set enlarges the search space, and makes it harder to achieve promising areas. Thus, it is important to identify the important features and remove the irrelevant ones to improve the GP-evolved rules. This paper proposes a domain-knowledge-free feature ranking and selection approach. As a result, the terminal set is significantly reduced and only the most important features are selected. The experimental results show that using only the selected features can lead to significantly better GP-evolved rules on both training and unseen test instances. © Mei 2016. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in 'GECCO '16: Proceedings of the Genetic and Evolutionary Computation Conference', https://doi.org/10.1145/2908812.2908822.

One Game Problem for Oscillatory Systems

The paper concerns the linear differential game of approaching a cylindrical terminal set. We study the case when classic Pontryagin’s condition does not hold. Instead, the modified considerably weaker condition, dealing with the function of time stretching, is used. The latter allows expanding the range of problems susceptible to analytical solution by the way of passing to the game with delayed information. Investigation is carried out in the frames of Pontryagin’s First Direct method that provides hitting the terminal set by a trajectory of the conflict-controlled process at finite instant of time. In so doing, the pursuer’s control, realizing the game goal, is constructed on the basis of the Filippov-Castaing theorem on measurable choice. The outlined scheme is applied to solving the problem of pursuit for two different second-order systems, describing damped oscillations. For this game, we constructed the function of time stretching and deduced conditions on the game parameters, ensuring termination of the game at a finite instant of time, starting from arbitrary initial states and under all admissible controls of the evader. Keywords: differential game, time-variable information delay, Pontryagin’s condition, Aumann’s integral, principle of time stretching, Minkowski’ difference, damped oscillations.