The Grid 2: Blueprint for a New Computing Infrastructure

Constrained multiobjective optimization problems (CMOPs) are frequently encountered in real-world applications, which usually involve constraints in both the decision and objective spaces. However, current artificial CMOPs never consider constraints in the decision space (i.e., decision constraints) and constraints in the objective space (i.e., objective constraints) at the same time. As a result, they have a limited capability to simulate practical scenes. To remedy this issue, a set of CMOPs, named DOC, is constructed in this paper. It is the first attempt to consider both the decision and objective constraints simultaneously in the design of artificial CMOPs. Specifically, in DOC, various decision constraints (e.g., inequality constraints, equality constraints, linear constraints, and nonlinear constraints) are collected from real-world applications, thus making the feasible region in the decision space have different properties (e.g., nonlinear, extremely small, and multimodal). On the other hand, some simple and controllable objective constraints are devised to reduce the feasible region in the objective space and to make the Pareto front have diverse characteristics (e.g., continuous, discrete, mixed, and degenerate). As a whole, DOC poses a great challenge for a constrained multiobjective evolutionary algorithm (CMOEA) to obtain a set of well-distributed and well-converged feasible solutions. In order to enhance current CMOEAs’ performance on DOC, a simple and efficient two-phase framework, named ToP, is proposed in this paper. In ToP, the first phase is implemented to find the promising feasible area by transforming a CMOP into a constrained single-objective optimization problem. Then in the second phase, a specific CMOEA is executed to obtain the final solutions. ToP is applied to four state-of-the-art CMOEAs, and the experimental results suggest that it is quite effective.

Handling Constrained Multiobjective Optimization Problems With Constraints in Both the Decision and Objective Spaces

This paper provides an extensive review of the popular multi-objective optimization algorithm NSGA-II for selected combinatorial optimization problems viz. assignment problem, allocation problem, travelling salesman problem, vehicle routing problem, scheduling problem, and knapsack problem. It is identified that based on the manner in which NSGA-II has been implemented for solving the aforementioned group of problems, there can be three categories: Conventional NSGA-II, where the authors have implemented the basic version of NSGA-II, without making any changes in the operators; the second one is Modified NSGA-II, where the researchers have implemented NSGA-II after making some changes into it and finally, Hybrid NSGA-II variants, where the researchers have hybridized the conventional and modified NSGA-II with some other technique. The article analyses the modifications in NSGA-II and also discusses the various performance assessment techniques used by the researchers, i.e., test instances, performance metrics, statistical tests, case studies, benchmarking with other state-of-the-art algorithms. Additionally, the paper also provides a brief bibliometric analysis based on the work done in this study.

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A Comprehensive Review on NSGA-II for Multi-Objective Combinatorial Optimization Problems

Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.

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A survey on evolutionary computation for complex continuous optimization

The class imbalance problem has become a leading challenge. Although conventional imbalance learning methods are proposed to tackle this problem, they have some limitations: 1) undersampling methods suffer from losing important information and 2) cost-sensitive methods are sensitive to outliers and noise. To address these issues, we propose a hybrid optimal ensemble classifier framework that combines density-based undersampling and cost-effective methods through exploring state-of-the-art solutions using multi-objective optimization algorithm. Specifically, we first develop a density-based undersampling method to select informative samples from the original training data with probability-based data transformation, which enables to obtain multiple subsets following a balanced distribution across classes. Second, we exploit the cost-sensitive classification method to address the incompleteness of information problem via modifying weights of misclassified minority samples rather than the majority ones. Finally, we introduce a multi-objective optimization procedure and utilize connections between samples to self-modify the classification result using an ensemble classifier framework. Extensive comparative experiments conducted on real-world data sets demonstrate that our method outperforms the majority of imbalance and ensemble classification approaches.

Hybrid Classifier Ensemble for Imbalanced Data

Web service location allocation problem is an important problem in the modern IT industry. In this paper, the two major objectives, i.e. deployment cost and network latency, are considered simultaneously. In order to solve this new multi-objective problem effectively, we adopted the framework of binary Particle Swarm Optimization (PSO) due to its efficacy that has been demonstrated in many optimization problems. Specifically, we developed two PSO variants, one with weighted-sum fitness function (WSPSO) and the other with dominance-based fitness function. Concretely, it uses the fast Non-dominate Sorting scheme, and thus is called NSPSO. The experimental results showed that both PSO variants performed better than NSGA-II, which is the one of the most commonly used multi-objective genetic algorithms. Furthermore, we have found that NSPSO achieved a more diverse set of solutions than WSPSO, and thus covers the Pareto front better. This demonstrates the efficacy of using the dominance-based fitness function in solving multi-objective Web service location allocation problem.

Particle Swarm Optimization for Multi-Objective Web Service Location Allocation

Cloud container resource allocation aims to find container placements in cloud Virtual Machines (VM) and Physical Machines (PM) such that overall energy consumption is minimised. A resource allocation architecture where application containers are consolidated into cloud VMs in a container-VM-PM model is common practise in data centers. The VM layer may provide additional administrative or security features, but adds complexity to the optimization problem when deploying containers initially on a large scale. Research addressing this two-level resource allocation is limited, some of the recent work try to optimise consolidation of containers to VM layer separately from consolidation of VMs to PMs, which results in large portions of the search space remaining unexplored. A Grouping Genetic Algorithm (GGA) framework that can simultaneously optimize consolidation on both levels is promising. However, for large instances of the two-level optimisation, it may suffer from premature convergence and limited population diversity. In this work, we propose a new fixed-length crossover operator that is designed to improve population diversity and exploration in GGA for container resource allocation optimisation. We also propose problem-specific Best-Fit and Largest VM heuristic operators to aid local search by rearranging containers from the lower fitness PMs at the chromosome tail into existing VMs and PMs with better utilization when possible. We demonstrate that with the newly developed operators, the proposed GGA can significantly reduce energy consumption in large-scale test cases. 

Boxiong Tan

Papers

Particle Swarm Optimization for Multi-Objective Web Service Location Allocation

Hybrid Grouping Genetic Algorithm for Large-Scale Two-Level Resource Allocation of Containers in the Cloud

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