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Pareto Optimal Synthesis of the Linear Array Geometry for Minimum Side lobe Level and Null Control During Beam Scanning

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INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING 2010年第5期20卷 557-566页

作者： Gunes, F. Tokan, F. Yildiz Tech Univ Dept Elect & Commun Engn Fac Elect & Elect TR-34349 Istanbul Turkey

In this work, synthesis of the linear array geometry is put forward as a constrained vector optimization problem whose components are to meet the minimum sidelobe level (SU) and control of the wide/narrow null placement during beam scanning whose range can vary from zero to the wide bands. As these synthesis objectives generally conflict with each other, nondominated solutions are acquired using the Nondominated Sorting Genetic Algorithm- II (NSGA-II) as a fast nondominated genetic sorting algorithm. Then, the Pareto frontiers are obtained using these trade-off solution sets between the maximum SLI,, null control, and scanning range to provide a view of all design options. Thus, the pattern features resulted from these Pardo frontiers are valid for any chosen main beam direction within its full prescribed beam scanning range. The same Pareto optimal synthesis procedure can be applied to a thinned linear antenna array. A thinned linear antenna array is obtained by a simple genetic optimization by rounding the excitation amplitudes either to I or 0 to minimize the maximum of side lobe level (MSLL) during the beam scanning within the prescribed region as stated in the multiobjective function. Finally, some typical Pardo optimal radiation patterns of the scanning arrays are synthesized with only perturbating the positions of the array elements, and their full electromagnetic wave simulations are also completed to examine the resulted mutual coupling effects between the elements of the arrays. It can be concluded that the Pareto optimal synthesis procedure gives the scanning linear antenna arrays with successful radiation performance. (C) 2010 Wiley Periodicals, Inc Int J RF and Microwave CAE 20 557-566.2010

关键词： linear array sidelobe suppression. null control beam scanmilit constrained multiobjective optimization pareto-optimal solutions nondominated sorting genetic algorithm

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Multistate-constrained multiobjective Differential Evolution Algorithm With Variable Neighborhood Strategy

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第7期53卷 4459-4472页

作者： Hou, Ying Wu, Yilin Han, Honggui Beijing Univ Technol Fac Informat Technol Engn Res Ctr Digital Commun Beijing Lab Urban Mass TransitMinist Educ Beijing 100124 Peoples R China Beijing Univ Technol Fac Informat Technol Engn Res Ctr Intelligent Percept & Autonomous Con Beijing Key Lab Computat Intelligence & Intellige Beijing 100124 Peoples R China

multiobjective differential evolution (DE) algorithm (MODE) has been widely used in multiobjective optimization problems. However, due to the complex feasible regions, the optimization efficiency of MODE may decrease when solving constrained multiobjective problems. It is challenging to promote the evolution of population with few feasible solutions. In this article, a multistate-constrained MODE with variable neighborhood strategy (MSCMODE-VNS) is proposed to enhance the optimization effectiveness with complex feasible regions. First, a variable neighborhood DE strategy, based on a specially designed convergence indicator, is designed to accelerate the generation of feasible solutions. Second, a multistate population updating strategy with a comprehensive solution evaluation mechanism is devised to update the population of the next generation to improve the performance of solutions. Third, the convergence analysis, based on the probability theory, is derived to verify the effectiveness of the proposed MSCMODE-VNS algorithm. Finally, experimental results indicate that MSCMODE-VNS can achieve a satisfactory performance on three benchmark test suites and two real-world-constrained multiobjective problems.

关键词： Statistics Sociology optimization Convergence Evolutionary computation Vehicle routing Linear programming Comprehensive solution evaluation mechanism constrained multiobjective optimization evolutionary state multiobjective differential evolution (DE) algorithm (MODE) variable neighborhood DE strategy

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An external penalty-type method for multicriteria

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TOP 2016年第2期24卷 493-513页

作者： Fukuda, Ellen H. Grana Drummond, L. M. Raupp, Fernanda M. P. Kyoto Univ Dept Appl Math & Phys Grad Sch Informat Kyoto 6068501 Japan Univ Fed Rio de Janeiro Fac Business & Adm BR-22290240 Rio De Janeiro RJ Brazil Natl Lab Sci Comp BR-25651075 Petropolis RJ Brazil

We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued method uses an auxiliary function, which can be chosen among large classes of "monotonic" real-valued mappings. We analyze the properties of the auxiliary functions in those classes and exhibit some examples. The convergence results are similar to those of the scalar-valued method, and depending on the kind of auxiliary function used in the implementation, under standard assumptions, the generated infeasible sequences converge to weak Pareto or Pareto optimal points. We also propose an implementable local version of the external penalization method and study its convergence results.

关键词： constrained multiobjective optimization External penalty method Pareto optimality Scalar representation

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An extended extremal principle with applications to multiobjective optimization

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SIAM JOURNAL ON optimization 2003年第2期14卷 359-379页

作者： Mordukhovich, BS Treiman, JS Zhu, QJJ Wayne State Univ Dept Math Detroit MI 48202 USA Western Michigan Univ Dept Math Kalamazoo MI 49008 USA

We develop an extended version of the extremal principle in variational analysis that can be treated as a variational counterpart to the classical separation results in the case of non-convex sets and which plays an important role in the generalized differentiation theory and its applications to optimization-related problems. The main difference between the conventional extremal principle and the extended version developed below is that, instead of the translation of sets involved in the extremal systems, we allow deformations. The new version seems to be more flexible in various applications and covers, in particular, multiobjective optimization problems with general preference relations. In this way we obtain new necessary optimality conditions for constrained problems of multiobjective optimization with nonsmooth data and also for multiplayer multiobjective games.

关键词： variational analysis extended extremal principle generalized differentiation constrained multiobjective optimization multiplayer games necessary optimality conditions

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On Economic Equilibrium Type Problems with Applications

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SET-VALUED AND VARIATIONAL ANALYSIS 2011年第3期19卷 417-456页

作者： Naniewicz, Zdzislaw Cardinal Stefan Wyszynski Univ Coll Sci Fac Math & Nat Sci PL-01938 Warsaw Poland

The existence solution for a class of economic equilibrium type problems in reflexive Banach space is considered. New results concerning the variational inequality approach to Arrow-Debreu model of economic equilibrium introduced in Naniewicz (Math Oper Res 32:436-466, 2007) are found and applied to ensure the existence of Pareto optimal solutions for a class of multiobjective optimization problems with so-called budget-like constraints. To achieve this goal, the theory of pseudo-monotone multivalued mappings combined with some fixed point technique for multivalued mappings with nonconvex values is used.

关键词： Economic equilibrium constrained multiobjective optimization Variational inequalities Pseudo-monotone multivalued operators Ky Fan inequality Fixed point

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A multiobjective Evolutionary Algorithm for Distribution System Reconfiguration Problems 12

A Multiobjective Evolutionary Algorithm for Distribution Sys...

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Joint 12th International Conference on Soft Computing and Intelligent Systems / 23rd International Symposium on Advanced Intelligent Systems (SCIS and ISIS)

作者： Sekizaki, Shinya Nishizaki, Ichiro Hayasida, Tomohiro Hiroshima Univ Grad Sch Adv Sci & Engn Higashihiroshima Japan

ISBN: (纸本)9781665499248

Real-world multiobjective optimization problems (MOPs) are generally constrained and multiobjective evolutionary algorithms (MOEAs) have been proposed for solving constrained MOPs (CMOPs). When solving CMOPs observed in the real world, which are computationally demanding and have severe constraints, finding a well-converged population to constrained Pareto front is not easy. In such cases, infeasible nondominated solutions with slight constraint violations can provide useful information for decision makers. In this paper, we propose a MOEA that can provide decision makers with trade-off information between constraint violations and objective values of those untractable CMOPs. The proposed MOEA partitions the objective space of a CMOP, with objectives to minimize constraint violations, into multiple subspaces and maintains the diversity of the population by preserving feasible and infeasible solutions in the subspaces. Solutions with slight constraint violations and small objective values are preserved in the population using different selection pressures for the feasible and infeasible populations. Computational experiments for solving a distribution system reconfiguration problem, which is a computationally demanding and severely constrained CMOP in the real world, are performed to demonstrate the effectiveness of the proposed MOEA.

关键词： multiobjective evolutionary algorithm constrained multiobjective optimization Distribution system reconfiguration

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The Effect of Feasible Region on Imbalanced Problem in constrained Multi-objective optimization 13

The Effect of Feasible Region on Imbalanced Problem in Const...

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13th International Conference on Computational Intelligence and Security (CIS)

作者： Lin, Jiabin Liu, Hai-Lin Peng, Chaoda Guangdong Univ Technol Fac Appl Math Guangzhou Guangdong Peoples R China

ISBN: (纸本)9781538648223

The decomposition-based multi-objective evolutionary algorithm, i.e. MOEA/D-M2M, has shown to be an efficient algorithm to solve unconstrained imbalanced multi-objective optimization problems. However, the use in constrained imbalanced multi-objective optimization problems has not been fully explored. In this paper, we study the factors that impact the constrained imbalanced multi-objective optimization problems. To begin with, a series of constrained imbalanced multi-objective optimization problems are constructed. Then three kinds of representative algorithms, i.e. NSGA-II, MOEA/D and MOEA/D-M2M, combined with the constraint domination principle respectively, are utilized to solve them. The experimental results demonstrate that MOEA/D-M2M works better than the other two compared algorithms on constrained imbalanced multi-objective optimization problems in terms of the reliability and stability of finding a set of well distributed non-domination solutions.

关键词： Evolutionary Algorithm constrained multiobjective optimization Imbalanced Problem Decomposition

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A Hybrid Evolutionary Algorithm Based on Dominated Clustering for constrained Bi-Objective optimization Problems 12

A Hybrid Evolutionary Algorithm Based on Dominated Clusterin...

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12th International Conference on Computational Intelligence and Security (CIS)

作者： Fan, Lei Liang, Yanfang Liu, Xiyang Gu, Xin Xidian Univ Inst Software Engn Xian 710071 Peoples R China Xidian Univ Sch Software Xian 710071 Peoples R China

ISBN: (纸本)9781509048403

constrained optimization problems are with great difficulties to be solved for the complex influences of their constraints. However, many crossover operators in the constrained evolutionary algorithms have a disadvantage on bias search of the boundary. A novel uniform design based crossover operator coupled with a new space searching strategy aiming to overcome this disadvantage are proposed in this paper. Based on this, a hybrid evolutionary algorithm with domination clustering is constructed to solve constrained multiobjective optimization problems. Experiments on 13 benchmarks are made, and the results are conpared with existing algorithms to demonstrate the effectiveness and positiveness of the proposed algorithm.

关键词： hybrid evolutionary algorithm dominated clustering constrained multiobjective optimization hybrid crossover

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Extending Pareto Dominance for Multi-Constraints Satisfaction and Multi-Performance Enhancement in constrained Multi-Objective optimization

Extending Pareto Dominance for Multi-Constraints Satisfactio...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Yu, Fan Chen, Qun Zhou, Jinlong Cent South Univ Changsha Peoples R China

ISBN: (纸本)9798400704949

Multi-objective optimization problems (MOPs) in science and engineering frequently involve intricate multi-constraints. This paper extends the application of the Pareto dominance in MOPs on addressing complex multi-constraints and enhancing algorithmic conflicting multi-performance, such as convergence, diversity, and feasibility. The approach begins by identifying non-dominated constraints that closest approximate the actual constrained Pareto Front (CPF) through Pareto non-dominated sorting of every single constrained Pareto Front (SCPF). Subsequently, a Pareto non-dominated sorting multi-performance methodology is employed under the determined non-dominated constraints, considering convergence, diversity, and feasibility as competing objectives. Building upon extending the Pareto dominance approach for constrained multi-objective optimization (EPDCMO), this paper introduces a dual-population multi-archive optimization mechanism to optimize multiple constraints and performance simultaneously. The effectiveness of the proposed approach is validated through the evaluation of 23 constrained multi-objective problems (CMOPs) and practical applications in the domain of CMOPs. The results demonstrate the algorithm's capability to generate competitive solutions for MOPs characterized by multi-constraints.

关键词： Extending Pareto dominance constrained multiobjective optimization multi-constraints multi-performance

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Surrogate Assisted Simulated Annealing (SASA) for constrained Multi-objective optimization

Surrogate Assisted Simulated Annealing (SASA) for Constraine...

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2010 IEEE World Congress on Computational Intelligence

作者： Singh, Hemant Kumar Ray, Tapabrata Smith, Warren Univ New S Wales Australian Def Force Acad Sch Informat Technol & Engn Canberra ACT Australia

ISBN: (纸本)9781424481262

Real life optimization problems often involve a tradeoff between multiple objectives. They also comprise constraints, which may be due to various factors such as the strength of materials, stability and safety of design, limits on operational time, financial viability and many others. In recent years, Evolutionary Algorithms (EAs) have been a popular choice for solving such multi-objective, constrained problems for various reasons. Point to point search methods, such as Simulated Annealing (SA) have been largely unexplored for such problems. However, some recent studies have suggested that with certain enhancements, SA can also be an effective tool to deal with such problems. The ability of SA to accept uphill moves (unlike EAs) during the search makes it a less prone to getting trapped in a local minimum, and is therefore attractive for solving optimization problems. For many engineering design problems, evaluating a candidate solution can be computationally intensive. This can often put a restriction on the number of function evaluations to find a near optimum solution. To mitigate this problem, often suitable approximations (surrogates) are used in optimization instead of real function evaluations. Surrogate assisted approaches have so far been used in the paradigm of Evolutionary Algorithms (EA). In this paper, we extend the use of surrogates to another well known heuristic, Simulated Annealing (SA), for constrained, multi-objective problems. A comparison with currently prevalent EAs on a difficult set of constrained problems has been included in order to highlight the efficacy of the proposed approach.

关键词： constrained multiobjective optimization engineering design problem evolutionary algorithm evolutionary computation heuristic point to point search method simulated annealing surrogate assisted simulated annealing

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