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

This article proposes a novel and computationally efficient explicit intertask information transfer strategy between optimization tasks by aligning the subspaces. In evolutionary multitasking, the tasks might have biases embedded in function landscapes and decision spaces, which often causes the threat of predominantly negative transfer. However, the complementary information among different tasks can give an enhanced performance of solving complicated problems when properly harnessed. In this article, we distill this insight by introducing an intertask knowledge transfer strategy implemented in the low-dimension subspaces via a learnable alignment matrix. Specifically, to unveil the significant features of the function landscapes, the task-specific low-dimension subspaces is established based on the distribution information of subpopulations possessed by tasks, respectively. Next, the alignment matrix between pairwise subspaces is learned by minimizing the discrepancies of the subspaces. Given the aligned subspaces by applying the alignment matrix to subspaces’ base vectors, the individuals from different tasks are then projected into aligned subspaces and reproduce therein. Moreover, since this method only considers the leading eigenvectors, it turns out to be intrinsically regularized and noise-insensitive. Comprehensive experiments are conducted on the synthetic and practical benchmark problems so as to assess the efficacy of the proposed method. According to the experimental results, the proposed method exhibits a superior performance compared with existing evolutionary multitask optimization algorithms.

Regularized Evolutionary Multitask Optimization: Learning to Intertask Transfer in Aligned Subspace

Satellite range scheduling plays a very important role in guaranteeing the normal operation and the real-time control of in-orbit satellites. Although there appears a stronger demand for multi-objective optimization of satellite monitoring departments, multiple scheduling criteria are rarely considered simultaneously. To address the multi-objective satellite range scheduling problem (MOSRSP), a general MOEA based memetic algorithm (MOEA-MA) framework is proposed, which optimizes the failure rate of ground-satellite communication requests and the load-balance degree of remote-tracking antennas. Based on a novel decision model for MOSRSP, the conflict-resolution and load-balance operators and the tabu search metaheuristic are designed to implement the local search operations in the MOEA-MA. Different types of the MOEAs, including the domination-based MOEAs, decomposition-based MOEAs and metric-based MOEAs are adopted to implement the evolutionary operations in the MOEA-MA. The highlight of this paper is the effective application of the MOEA-MAs to practical scheduling problems, where the two most concerning objectives are well addressed. The MOEA-MAs that adopt five well-known MOEAs are given and examined by the Benchmarks problems. Computational results indicate that the MOEA-MAs outperform the original MOEAs in terms of the metrics of coverage, hypervolume and spacing, which show good performance and application prospect for the MOSRSP.

MOEA based memetic algorithms for multi-objective satellite range scheduling problem

The Multi-satellite Tracking Telemetry and Command (TT&C) Scheduling, a multi-constrained and high-conflict complex combinatorial optimization problem, is a typical NP-hard problem. The effective utilization of existing TT&C resources has always played a key role in the satellite field. This paper first simplified the problem and established a corresponding mathematical model with the hybrid objective of maximizing the profit and task completion rate. Considering the significant effect of genetic algorithm in solving the problem of resource allocation, a population perturbation and elimination strategy based genetic algorithm (GA-PE) which focused on the Multi-Satellite TT&C Scheduling problem was proposed. For each case, a task scheduling sequence was first obtained through the GA-PE algorithm, and then a task planning algorithm will be used to determine which tasks can be scheduled. Compared with several efficient heuristic algorithms, a series of computational experiments have illustrated its better performance in both profit and task completion rates. The experiments of strategy and parameter sensitivity verification have investigated the performance of GA-PE in various aspects thoroughly.

A population perturbation and elimination strategy based genetic algorithm for multi-satellite TT&C scheduling problem

Up to now, different genetic algorithm (GA) based error correcting output codes (ECOC) algorithms have been proposed by setting accuracy as the optimization objective. However, it was demonstrated that diversity among learners is of great significance to a robust ensemble. In this paper, we propose a multi-objective GA with setting accuracy and diversity as two objectives. To further promote diversity in an ensemble, a new individual structure is designed to accommodate heterogeneous dichotomizers. Three multi-objective ranking strategies are deployed to balance two objectives respectively. A novel genetic operator is designed to produce ECOC-compatible offspring in the evolutionary process, and a local improvement algorithm is designed to promote individuals’ fitness values. To verify the performance of our GA, a single objective ranking strategy and the design of homogeneous learner based GA are also adopted. Ten widely used ECOC algorithms and three famous ensemble algorithms are deployed for performance comparisons based on a set of the UCI data and microarray data sets. Results show that compared with other algorithms, our GA obtains higher performance in most cases due to the trade-off between performance and diversity. Besides, the accommodation of heterogeneous dichotomizers in an ensemble provides higher generalization ability compared with homogeneous ensembles.

A novel multi-objective genetic algorithm based error correcting output codes

Satellite range scheduling is an important issue in the field of satellite mission planning, which greatly affects the development of satellite industry. This paper analyzed satellite range scheduling problem, constructed a multi-objective SRSP (MO-SRSP) model and proposed an improved multi-objective evolutionary algorithm (MOEA), called learning-guided nondominated sorting genetic algorithm II (LGNSGAII) that contains a learning mechanism. Learning mechanisms can speed up optimization process. Meanwhile, another algorithm called task-time window selection algorithm (TTSA) is also proposed. Specifically, it can select satellite ground stations time windows for tasks. TTSA includes three location selection methods and two location movement methods, both are used to select the appropriate execution location for tasks. Experiments show that the proposed algorithm can solve MO-SRSP better than several comparison algorithms. In other words, this algorithm we proposed has a broad practical application prospect.

Pei Wang

Papers

Learning-guided nondominated sorting genetic algorithm II for multi-objective satellite range scheduling problem