Solving optimization problems with linear-fractional objective functions and additional constraints on arrangements

The paper proposes an exact method to solve an optimization problem on arrangements with a linear-fractional objective function and additional linear constraints. The efficiency of the solution algorithm is analyzed by means of numerical experiments. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 79–85, September–October 2006.     

An approach to solving discrete vector optimization problems over a combinatorial set of permutations

Complex discrete multicriteria problems over a combinatorial set of permutations are analyzed. Some properties of an admissible domain for a combinatorial multicriteria problem embedded into an arithmetic Euclidian space are considered. Optimality conditions are obtained for different types of effective solutions. A new approach to solving the problems formulated is constructed and substantiated. This work was supported by the Fundamental Research Fund of Ukraine (project Φ251/094). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 158–172, May–June 2008.     

Analysis of mathematical models and methods of solving combinatorial optimization problems on game-type permutations

The paper is concerned with an optimization problem on game-type permutations, where one or both players have combinatorial constraints on their strategies. A mathematical model of such problems is constructed and analyzed. A modified graphical method is proposed to solve (2xn)-and (mx2)-dimensional problems. High-dimensional problems are reduced to linear programming and combinatorial optimization problems. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 103–114, November–December 2007.     

Solution of Euclidean combinatorial optimization problems by the method of construction of a lexicographic equivalence

A method of space partition based on an equivalence relation is considered. Based on a lexicographic exhaustive search for equivalence classes, algorithms are developed for solution of a new class of optimization problems, namely, linear conditional Euclidean problems of lexicographic combinatorial optimization.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 155–125, September–October 2004.     

Multiobjective combinatorial optimization problems with a cost and several bottleneck objective functions: An algorithm with reoptimization

This paper addresses multicriteria combinatorial optimization problems involving one cost and several bottleneck objective functions. An algorithm is developed which generates the minimal complete set of Pareto-optimal solutions. This algorithm runs in polynomial time as long as the single objective problem considering only the cost function can be solved polynomially. A reoptimization procedure is used to accelerate the convergence of the algorithm. Applications are given. Computational results on randomly generated instances and planar grid graphs concerning the minimum cost spanning tree and the shortest path problem are presented.     

求解约束优化问题的新方法

提出了用于解决约束优化问题的新的类电磁机制算法,针对约束优化问题,利用惩罚函数法,构造了新的适应度函数,将约束问题转化为无约束问题求解,结合类电磁机制算法的寻优特点,设计了适合于问题特点的局部搜索过程,并重新定义了粒子的电荷和力的计算公式,以使在算法实现过程中,引导不可行点逐步向可行点转化,并最终找到问题的最优解。数值模拟结果验证了算法的有效性。     

求解约束优化问题的改进果蝇优化算法及其工程应用

针对基本果蝇优化算法收敛速度慢、求解精度低、易于陷入局部极值以及算法候选解不能取负值等不足,提出一种用于解决约束优化问题的改进果蝇优化算法.该算法利用果蝇个体历史最佳记忆信息和种群全局历史最佳记忆信息构建多策略混合协同进化的搜索机制,以达到有效平衡算法的全局探索与局部开发的目的,同时也能够较好地避免算法的早熟收敛问题;...     

On non-linearity and affine equivalence of permutations over an arbitrary finite commutative ring with unity

Cryptographic properties of permutations viz non-linearity, affine equivalence, and mode transform have been studied in the literature, treating them as bijections on ?_n. In this article, the authors consider them as bijection on an arbitrary finite commutative ring with unity. Treating them this way, they achieve a generalization of the above mentioned properties. The authors also propose an algorithm for computing non-linearity in their generalized scenario, which is faster compared to the direct approach in many cases.     

A novel metric based on changes in pareto domination ratio for objective reduction of many-objective optimization problems

Abstract

Although many-objective optimisation can be simplified through reduction of redundant objectives, algorithms that perform this reduction still lack a convenient method of evaluation. In this paper, we address this deficiency by proposing a new method of evaluation, on the basis of changes in the Pareto-domination ratio after a reduction has occurred. Experimental results have shown that the proposed method can perform non- redundant objective set evaluation more accurately than existing evaluation methods, and also does not need the true Pareto front beforehand.     

A modified objective function method with feasible-guiding strategy to solve constrained multi-objective optimization problems

For constrained multi-objective optimization problems (CMOPs), how to preserve infeasible individuals and make use of them is a problem to be solved. In this case, a modified objective function method with feasible-guiding strategy on the basis of NSGA-II is proposed to handle CMOPs in this paper. The main idea of proposed algorithm is to modify the objective function values of an individual with its constraint violation values and true objective function values, of which a feasibility ratio fed back from current population is used to keep the balance, and then the feasible-guiding strategy is adopted to make use of preserved infeasible individuals. In this way, non-dominated solutions, obtained from proposed algorithm, show superiority on convergence and diversity of distribution, which can be confirmed by the comparison experiment results with other two CMOEAs on commonly used constrained test problems.     

求解一类不可微多目标优化问题的社会认知算法*

针对一类不可微多目标优化问题,给出了一个新的算法——极大熵社会认知算法。利用极大熵方法将带有约束的不可微多目标优化问题转化为无约束单目标优化问题,然后利用社会认知算法对其进行求解。该算法是基于社会认知理论,通过一系列的学习代理来模拟人类的社会性和智能性从而完成对目标的优化。利用两个测试算例对其进行测试并与其他算法进行比较,计算结果表明,该算法在求解的准确性和有效性方面均优于其他算法。     

求解约束化工优化问题的混合布谷鸟搜索算法

针对布谷鸟搜索算法存在收敛速度慢和易陷入局部最优等缺陷,提出一种基于Rosenbrock搜索和柯西变异的混合布谷鸟搜索算法用于求解约束化工优化问题。该算法首先采用佳点集方法对鸟窝位置进行初始化,为全局搜索的多样性奠定基础;然后利用Rosenbrock搜索算法对当前最优位置进行局部搜索,以提高算法的收敛速度;最后对当前最优解进行柯西变异以避免算法陷入局部最优。两个约束化工优化问题的实验结果表明了该混合算法的有效性。     

求解约束优化问题的改进灰狼优化算法

针对基本灰狼优化(GWO)算法存在求解精度低、收敛速度慢、局部搜索能力差的问题,提出一种改进灰狼优化(IGWO)算法用于求解约束优化问题。该算法采用非固定多段映射罚函数法处理约束条件,将原约束优化问题转化为无约束优化问题,然后利用IGWO算法对转换后的无约束优化问题进行求解。在IGWO算法中,引入佳点集理论生成初始种群,为算法全局搜索奠定基础;为了提高局部搜索能力和加快收敛,对当前最优灰狼个体执行Powell局部搜索。采用几个标准约束优化测试问题进行仿真实验,结果表明该算法不仅克服了基本GWO的缺点,而且性能优于差分进化和粒子群优化算法。     

Evolutionary algorithm with a directional local search for multiobjective optimization in combinatorial problems

Evolutionary algorithms (EAs) are often employed to multiobjective optimization, because they process an entire population of solutions which can be used as an approximation of the Pareto front of the tackled problem. It is a common practice to couple local search with evolutionary algorithms, especially in the context of combinatorial optimization. In this paper a new local search method is proposed that utilizes the knowledge concerning promising search directions. The proposed method can be used as a general framework and combined with many methods of iterating over a neighbourhood of an initial solution as well as various decomposition approaches. In the experiments the proposed local search method was used with an EA and tested on 2-, 3- and 4-objective versions of two well-known combinatorial optimization problems: the travelling salesman problem (TSP) and the quadratic assignment problem (QAP). For comparison two well-known local search methods, one based on Pareto dominance and the other based on decomposition, were used with the same EA. The results show that the EA coupled with the directional local search yields better results than the same EA coupled with any of the two reference methods on both the TSP and QAP problems.     

信息筛选多任务优化自组织迁移算法

针对现有自组织迁移算法(SOMA)只能求解单个优化问题及其隐并行性未能被充分挖掘的缺陷,提出信息筛选多任务优化自组织迁移算法(SOMAMIF)实现同一时刻处理多个优化问题.首先,构造多任务统一搜索空间,并根据任务个数设置相应的子种群;然后,对各子种群当前最优适应值进行判断,当任务连续若干代停滞进化时则产生信息交互需...     

Maple code of gamma algorithm for global optimization of uncertain functions over compact robust sets

Problems with uncertainties are ubiquitous in many areas of science and technology. Due to imprecision of measurements (Heisenberg’s relation), such problems are normal in nuclear physics. Due to fluidity of media, ships at sea and planes in the air have to deal with instability of the currents they move in. Yields in agriculture depend on the whims of weather. Due to the lack of information in economy and finance, problems with uncertainties (stock prices, marketing problems, inflation, unemployment) are commonplace. In such situations, it is necessary to make a choice of better parameters that produce finite intervals of possible values of a given uncertain function at each point of the parameter space. The gamma algorithm [E.A. Galperin, Global optimization in problems with uncertainties, Journal of Nonlinear Analysis 47 (2001) 941–952; E.A. Galperin, Global optimization in problems with uncertainties. The gamma algorithm. Computer and Mathematics with Applications 44 (2002) 853–862] presents a method to make that choice. A new variant of the gamma algorithm based on the beta algorithm is presented for global optimization of uncertain functions over compact robust sets in . The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [0,1]ⁿ for all problems. On this basis, a MAPLE code of modular structure is developed for full global optimization of functions of n variables. The code does not create ill-conditioned situations. Graphics are included, and the solution set can be visualized in plane projections and sections. The code is ready for engineering applications. The results of numerical experiments are presented, with graphs, to illustrate the use of the code.     

求解多目标优化问题的分级变异量子进化算法

分析量子进化算法和免疫算子的特点,提出一种分级变异的量子进化算法,用于求解多目标优化问题,算法主要基于两个策略:首先,利用快速非受控排序和密度距离计算种群抗原-抗体的亲和度;然后,基于亲和度排序将个体进行分级,最优分级中的个体作为算法中的最优个体,大部分实施量子旋转更新和免疫操作,而剩余分级中的个体实施免疫交叉操作以获得新的个体补充种群,求解多目标0/1背包问题的实验结果表明了该算法的有效性.     

A new solution for topology optimization problems with multiple loads:The guide-weight method

The guide-weight method is introduced to solve two kinds of topology optimization problems with multiple loads in this paper.The guide-weight method and its Lagrange multipliers' solution methods are presented first,and the Lagrange multipliers' soution method of problems with multiple constraints is improved by the dual method.Then the iterative formulas of the guide-weight method for topology optimization problems of minimum compliance and minimum weight are derived and coresponding numerical examples are...     

BSTBGA: A hybrid genetic algorithm for constrained multi-objective optimization problems

Most of the existing multi-objective genetic algorithms were developed for unconstrained problems, even though most real-world problems are constrained. Based on the boundary simulation method and trie-tree data structure, this paper proposes a hybrid genetic algorithm to solve constrained multi-objective optimization problems (CMOPs). To validate our approach, a series of constrained multi-objective optimization problems are examined, and we compare the test results with those of the well-known NSGA-II algorithm, which is representative of the state of the art in this area. The numerical experiments indicate that the proposed method can clearly simulate the Pareto front for the problems under consideration.