On Using Populations of Sets in Multiobjective Optimization

Bader, Johannes; Brockhoff, Dimo; Welten, Samuel; Zitzler, Eckart

doi:10.1007/978-3-642-01020-0_15

Cited by 24 publications

(8 citation statements)

References 16 publications

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“…Compared with the traditional MOEAs, set-based MOEAs have two advantages: (i) the new objectives are used to measure a solution set and (ii) each individual of the set-based evolutionary optimization is a solution set consisting of several solutions of the original problem. Researchers have carried out studies on set-based MOEAs, including the frameworks, the methods of transforming objectives, the approaches for comparing set-based individuals, and so on The first set-based MOEA was proposed by Bader et al [35]. In their work, solutions in a population are firstly divided into a number of solution sets of the same size, and then the hypervolume indicator is adopted to assess the performance of those sets.…”

Section: Related Workmentioning

confidence: 99%

“…In the method proposed by Zitzler et al [36], not only is the preference relation between a pair of set-based individuals defined, but the representation of preferences, the design of the algorithm, and the performance evaluation are also incorporated into a framework. Bader et al [35] presented a set-based Pareto dominance relation and designed a fitness function reflecting the decision maker's preference to effectively solve MaOPs. A comparison of results with traditional MOEAs shows that the proposed method is effective.…”

Section: Related Workmentioning

confidence: 99%

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An Improved Nondominated Sorting Genetic Algorithm III Method for Solving Multiobjective Weapon-Target Assignment Part I: The Value of Fighter Combat

You

Kou

2018

International Journal of Aerospace Engineering

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Multiobjective weapon-target assignment is a type of NP-complete problem, and the reasonable assignment of weapons is beneficial to attack and defense. In order to simulate a real battlefield environment, we introduce a new objective-the value of fighter combat on the basis of the original two-objective model. The new three-objective model includes maximizing the expected damage of the enemy, minimizing the cost of missiles, and maximizing the value of fighter combat. To solve the problem with complex constraints, an improved nondominated sorting algorithm III is proposed in this paper. In the proposed algorithm, a series of reference points with good performances in convergence and distribution are continuously generated according to the current population to guide the evolution; otherwise, useless reference points are eliminated. Moreover, an online operator selection mechanism is incorporated into the NSGA-III framework to autonomously select the most suitable operator while solving the problem. Finally, the proposed algorithm is applied to a typical instance and compared with other algorithms to verify its feasibility and effectiveness. Simulation results show that the proposed algorithm is successfully applied to the multiobjective weapon-target assignment problem, which effectively improves the performance of the traditional NSGA-III and can produce better solutions than the two multiobjective optimization algorithms NSGA-II and MPACO.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

An Improved Nondominated Sorting Genetic Algorithm III Method for Solving Multiobjective Weapon-Target Assignment Part I: The Value of Fighter Combat

You

Kou

2018

International Journal of Aerospace Engineering

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“…At present, a lot of MOEAs adopted the global optimum selection strategy based on the nondominated sorting [10, 11] or Pareto dominance [32] or hypervolume [33, 34] or niche [35, 36] and so on. But they all have some problems of high selection pressure or low selection pressure.…”

Section: Related Work and Motivationmentioning

confidence: 99%

AMOBH: Adaptive Multiobjective Black Hole Algorithm

et al. 2017

Computational Intelligence and Neuroscience

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This paper proposes a new multiobjective evolutionary algorithm based on the black hole algorithm with a new individual density assessment (cell density), called “adaptive multiobjective black hole algorithm” (AMOBH). Cell density has the characteristics of low computational complexity and maintains a good balance of convergence and diversity of the Pareto front. The framework of AMOBH can be divided into three steps. Firstly, the Pareto front is mapped to a new objective space called parallel cell coordinate system. Then, to adjust the evolutionary strategies adaptively, Shannon entropy is employed to estimate the evolution status. At last, the cell density is combined with a dominance strength assessment called cell dominance to evaluate the fitness of solutions. Compared with the state-of-the-art methods SPEA-II, PESA-II, NSGA-II, and MOEA/D, experimental results show that AMOBH has a good performance in terms of convergence rate, population diversity, population convergence, subpopulation obtention of different Pareto regions, and time complexity to the latter in most cases.

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“…Furthermore, the representation of preferences, the design of the algorithm, and the performance evaluation are incorporated into a framework. Bader et al [24] first divided solutions in a population into a number of sets of the same size, and then transformed the problem into a single-objective optimization problem whose objective is hyper-volume. In addition, they developed a scheme for recombining sets based on the hyper-volume.…”

Section: Set-based Many-objective Optimizationmentioning

confidence: 99%

“…As a result, MaOPs are very challenging and have received a lot of attention in the evolutionary optimization community in recent years [4][5][6][7][8][9][10]. At present, approaches for solving MaOPs can be grouped into the following four categories: (1) increasing the selection pressure via novel Pareto dominance relations [5][6][7][8][9]; (2) deleting redundant objectives according to certain principles [11][12][13][14]; (3) transforming an MaOP into one or several single-objective optimization problems by weighting or decomposing objectives [15][16][17][18][19][20]; (4) utilizing a certain performance indicator to evaluate individuals [21,22]; (5) taking a set of solutions and performance indicators as the variable and objectives of a new optimization problem, respectively, and utilizing set-based evolutionary operators to solve the new problem [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

A mutation operator guided by preferred regions for set-based many-objective evolutionary optimization

Sun

Gong

et al. 2017

Complex Intell. Syst.

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Many-objective optimization problems (MaOPs) are vital and challenging in real-world applications. Existing evolutionary algorithms mostly produce an approximate Pareto-optimal set using new dominance relations, dimensionality reduction, objective decomposition, and set-based evolution. In this paper, we propose a mutation operator guided by preferred regions to improve an existing setbased evolutionary many-objective optimization algorithm that integrates preferences. In the proposed mutation operator, optimal solutions in a preferred region are first chosen to form a reference set; then for each solution within the individual to be mutated, an optimal solution from the reference set is specified as its reference point; finally, the solution is mutated towards the preferred region via an adaptive Gaussian disturbance to accelerate the evolution, and thus an approximate Pareto-optimal set with high performances is obtained. We apply the proposed method to 21 instances of seven benchmark MaOPs, and the experimental results empirically demonstrate its superiority.

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On Using Populations of Sets in Multiobjective Optimization

Cited by 24 publications

References 16 publications

An Improved Nondominated Sorting Genetic Algorithm III Method for Solving Multiobjective Weapon-Target Assignment Part I: The Value of Fighter Combat

An Improved Nondominated Sorting Genetic Algorithm III Method for Solving Multiobjective Weapon-Target Assignment Part I: The Value of Fighter Combat

AMOBH: Adaptive Multiobjective Black Hole Algorithm

A mutation operator guided by preferred regions for set-based many-objective evolutionary optimization

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