多下层分式双层规划问题的改进遗传算法

针对一类具有多个线性下层问题的分式双层规划, 提出一种基于新编码方式的遗传算法。 首先,利用对偶理论,将问题化为单层非线性规划;接着,利用下层对偶问题的可行基编码,针对任意编码个体,解出对偶变量值,使得单层规划变为线性分式规划;最后,求解产生的线性分式规划,其目标值作为个体的适应度值。 这种编码方式及适应度的计算有效提高了遗传算法的效率。 通过对4个算例的计算,验证了算法的有效性。     

A fuzzy bi-criteria transportation problem

In this paper, a fuzzy bi-criteria transportation problem is studied. Here, the model concentrates on two criteria: total delivery time and total profit of transportation. The delivery times on links are fuzzy intervals with increasing linear membership functions, whereas the total delivery time on the network is a fuzzy interval with a decreasing linear membership function. On the other hand, the transporting profits on links are fuzzy intervals with decreasing linear membership functions and the total profit of transportation is a fuzzy number with an increasing linear membership function. Supplies and demands are deterministic numbers. A nonlinear programming model considers the problem using the max–min criterion suggested by Bellman and Zadeh. We show that the problem can be simplified into two bi-level programming problems, which are solved very conveniently. A proposed efficient algorithm based on parametric linear programming solves the bi-level problems. To explain the algorithm two illustrative examples are provided, systematically.     

基于双层规划的高超声速飞行器预警资源分配方法

针对高超声速飞行器预警系统中资源难以合理利用的问题,提出一种基于双层规划的预警资源分配方法.首先,建立高超声速飞行器运动状态的马尔可夫模型,提出威胁评估的方法;其次,基于隐马尔可夫模型和卡尔曼滤波,提出双层规划的高超声速飞行器预警资源分配模型,下层规划以单位资源损耗下信息增益为目标函数,上层规划以风险的降低为目标函数;...     

求解一类特殊的双层规划问题的遗传算法

主要研究上层函数及其约束函数不要求具有凸性和可微性,下层是关于下层决策变量是凸二次规划的双层规划模型,通过Karush-Kuhn-Tucher 条件转化为一个单层规划,利用下层是正定二次规划,将下层的决策变量表示为关于 Lagrangian乘子的表达式,从而降低了搜索空间的维数,设计了遗传算法,并通过数值实验表明该遗传算非常有效。     

双层规划的改进混合布谷鸟搜索量子行为粒子群优化算法

为解决粒子群优化（PSO）算法求解双层规划问题时易陷入局部最优解的问题,提出了一种基于模拟退火（SA）Metropolis准则的改进混合布谷鸟搜索量子行为粒子群优化（ICSQPSO）算法。首先,该混合算法引入SA算法中的Metropolis准则,在求解过程中既能接受好解也能以一定的概率接受坏解,增强全局寻优能力;接着,为布谷鸟搜索算法设计一种改进动态步长Lévy飞行,以保持粒子群在优化过程中较高的多样性,保证搜索广度;最后,利用布谷鸟搜索算法中的偏好随机游走机制帮助粒子跳出局部最优解。通过对13个涵盖非线性规划、分式规划、多个下层规划的双层规划实例的数值实验,结果表明：ICSQPSO算法所得12个双层规划的目标函数最优值显著优于对比算法,只有1例的结果稍差,并且有半数实例的结果优于对比算法50%。由此可见,ICSQPSO算法对双层规划的寻优能力明显优于对比算法。     

求解双层规划优化问题的层次风驱动优化算法

针对双层规划的求解问题, 提出一种层次风驱动优化算法. 初始化上层优化变量后, 首先对下层规划进行求解, 满足约束条件的同时, 更新下层规划中的空气质点速度和位置; 然后, 利用风驱动优化算法对上层规划问题进行求解; 最后, 在优化解集合中, 选择上下层规划目标值次序之和最小的解作为最终优化解. 实验结果表明, 所提出的层次风驱动算法是一种有效的求解双层规划问题的方法.

     

Optimal decision making in multi-product dual sourcing procurement with demand forecast updating

In this paper, we will investigate a buyer's decision making problem in procuring multiple products, each treated as a newsvendor, from two markets. The contract market has a long lead time, a fixed wholesale price and resource constraints. While the spot market has an instant lead time and a highly volatile price. The purchasing decision at the spot market can be made near the beginning of the selling season to take the advantage of the most recent demand forecast. The buyer needs to determine the purchasing quantity for each product at the two markets to maximize the expected profit by trading off between the resource availability, demand uncertainty and price variability. The procurement decision making is modeled as a bi-level programming problem under both a single resource constraint and under multiple resource constraints. We show that this bi-level programming problem can be formulated as a single-level concave programming problem. We then develop a sequential algorithm which solves for a linear approximation of the concave programming problem in each iteration. This algorithm can be used to solve a real world problem with up to thousands of kinds of products, and is found to be highly efficient and effective.     

Optimizing Frequencies in a Transit Network: a Nonlinear Bi-level Programming Approach

We consider the problem of optimizing the frequencies of transit lines in an urban transportation network. The problem is formulated first as a nonlinear nonconvex mixed integer programming problem and then it is converted into a bi-level Min–Min nonconvex optimization problem. This problem is solved by a projected (sub)gradient algorithm, where a (sub)gradient is obtained at each iteration by solving the lower level problem. Computational results obtained with this algorithm are presented for the transit networks of the cities of Stockholm, Sweden, Winnipeg, Man., Canada and Portland, OR, U.S.A.     

城市快速路网匝道与污染控制双层多目标规划模型

基于环境容量和交通容量,建立了一个双层多目标规划模型描述城市快速道路网的污染控制与匝道控制,并考虑了用户的路径选择行为．设计了基于改进遗传算法的启发式求解算法。该算法借助不可微精确罚函数将约束问题转化为单个无约束问题来解决,采用混合杂交和间歇变异提高算法的搜索能力．最后。通过算例说明该模型及算法的有效性．     

灰色二层多目标线性规划问题及其解法

针对二层多目标线性规划问题,结合灰色系统的特性,提出了一般灰色二层多目标线性规划问题,并给出了模型的相关定义和定理.针对漂移型灰色二层多目标线性规划问题,提出一种具有全局收敛性质的求解算法.首先通过线性加权模理想点法把多目标转化为单目标;然后当可行域为非空紧集时,利用库恩塔克条件把双层转化为单层,再利用粒子群算法搜索单目标单层线性规划即可得到原问题的解;最后通过算例表明了该算法的有效性.     

A new co-evolutionary decomposition-based algorithm for bi-level combinatorial optimization

Bi-Level Optimization Problems (BLOPs) are a class of challenging problems with two levels of optimization tasks. The main goal is to optimize the upper level problem which has another optimization problem as a constraint. The latter is called the lower level problem. In this way, the evaluation of each upper level solution requires finding an (near) optimal solution to the corresponding lower level problem, which is computationally very expensive. Many real world applications are bi-level by nature, ranging from logistics to software engineering. Further, proposed bi-level approaches have been restricted to solve linear BLOPs. This fact has attracted the evolutionary computation community to tackle such complex problems and many interesting works have recently been proposed. Unfortunately, most of these works are restricted to the continuous case. Motivated by this observation, we propose in this paper a new Co-evolutionary Decomposition Algorithm inspired from Chemical Reaction Optimization algorithm, called E-CODBA (Energy-based CODBA), to solve combinatorial bi-level problems. Our algorithm is based on our previous works within this research area. The main idea behind E-CODBA is to exploit co-evolution, decomposition, and energy laws to come up with good solution(s) within an acceptable execution time. The statistical analysis of the experimental results on the Bi-level Multi-Depot Vehicle Routing Problem (Bi-MDVRP) show the out-performance of our E-CODBA against four recently proposed works in terms of effectiveness and efficiency.     

The parameters optimisation design for variable speed control momentum gyroscopes

Control momentum gyroscopes (CMGs) have many advantages over other actuators for the attitude control of a spacecraft. Compared with the single-gimbal control moment gyroscopes (SGCMGs), the mass and power of the flywheel of variable-speed control moment gyroscopes (VSCMGs) are greatly increased. In this paper, a new solving strategy of singularity problem is proposed, which concludes the exchangeable momentum and steering law, and the parameters of VSCMGs are designed based on the constraint of singular problem. The configuration characteristics of VSCMGs with the constraint of upper and lower bounds of the flywheel regulation speed are revealed. The steering characteristics of weighted pseudo-inverse with null motion (WPINM) are analysed, then the flywheel torque requirement of WPINM is evaluated based on the geometry theory. At last, the parameter design problem of VSCMGs is cast as multi-objectives and bi-level programming problem. The bi-level programming is transformed into a single-level programming problem by using of the Karush–Kuhn–Tucker condition. Finally, the intelligent algorithm of particle swarm optimisation is presented to solve the nonlinear multi-objective problem.     

基于Pareto支配的双目标优化求解非线性双层规划问题

双层规划问题是一类具有双层递阶结构的系统优化问题。采用Pareto支配的双目标优化策略求解非线性双层规划问题。利用K-T条件把双层规划问题等价转化单层规划问题,进而结合约束部分建立可行性度量目标形成双目标规划问题。在基本的差分进化算法框架中融入非负的最小二乘曲线拟合判断候选解的可行性,构造基于动态概率的Pareto支配选择策略挑选下一代个体,解决种群容易陷入局部最优的缺陷。15个标准函数的测试结果对比显示,该算法在求解非线性双层规划问题中具有较好的全局寻优能力、较低的计算复杂度、较强的稳定性和适用性,可以获得全局最优解。     

Interactive balance space approach for solving multi-level multi-objective programming problems

This paper studies a multi-level multi-objective decision-making (ML-MODM) problems with linear or non-linear constraints. The objective functions at each level are non-linear functions, which are to be maximized or minimized.This paper presents a three-level multi-objective decision-making (TL-MODM) model and an interactive algorithm for solving such a model. The algorithm simplifies three-level multi-objective decision-making problems by transforming them into separate multi-objective decision making problems at each level, thereby avoiding the difficulty associated with non-convex mathematical programming. Our algorithm is an extension of the work of Shi and Xia [X. Shi, H. Xia, Interactive bi-level multi-objective decision making, Journal of the Operational Research Society 48 (1997) 943-949], which dealt with interactive bi-level multi-objective decision-making problems, with some modifications in assigning satisfactoriness to each objective function in all the levels of the TL-MODM problem. Also, we solve each separate multi-objective decision making problem of the TL-MODM problem by the balance space approach.A new formula is introduced to interconnect the satisfactoriness and the proportions of deviation needed to reflect the relative importance of each objective function. Thus, we have the proportions of deviation including satisfactoriness.In addition, we present new definitions for the satisfactoriness and the preferred solution in view of singular-level multi-objective decision making problems that corresponds to the η-optimal solution of the balance space approach. Also, new definitions for the feasible solution and the preferred solution (η-optimal point) of the TL-MODM problem are presented. An illustrative numerical example is given to demonstrate the algorithm.     

高速公路网入口流量控制的双层规划模型及算法

建立双层规划模型用于解决高速公路网的入口流量控制问题。提出了一种结合遗传算法和Aloplex算法的新算法——GAA算法来求解双层规划问题。实验结果表示，GAA算法在求解双层规划问题上优于遗传算法；分车型测算得出进入路网的流量使上层目标函数值更小（相对于单车型情况），并且使路网利用程度得到进一步的提高。     

Study on continuous network design problem using simulated annealing and genetic algorithm

In general, a continuous network design problem (CNDP) is formulated as a bi-level program. The objective function at the upper level is defined as the total travel time on the network, plus total investment costs of link capacity expansions. The lower level problem is formulated as a certain traffic assignment model. It is well known that such bi-level program is non-convex and non-differentiable and algorithms for finding global optimal solutions are preferable to be used in solving it. Simulated annealing (SA) and genetic algorithm (GA) are two global methods and can then be used to determine the optimal solution of CNDP. Since application of SA and GA on continuous network design on real transportation network requires solving traffic assignment model many times at each iteration of the algorithm, computation time needed is tremendous. It is important to compare the efficacy of the two methods and choose the more efficient one as reference method in practice. In this paper, the continuous network design problem has been studied using SA and GA on a simulated network. The lower level program is formulated as user equilibrium traffic assignment model and Frank–Wolf method is used to solve it. It is found that when demand is large, SA is more efficient than GA in solving CNDP, and much more computational effort is needed for GA to achieve the same optimal solution as SA. However, when demand is light, GA can reach a more optimal solution at the expense of more computation time. It is also found that increasing the iteration number at each temperature in SA does not necessarily improve solution. The finding in this example is different from [Karoonsoontawong, A., & Waller, S. T. (2006). Dynamic continuous network design problem – Linear bilevel programming and metaheuristic approaches. Network Modeling 2006 Transportation Research Record (1964) (pp. 104–117)]. The reason might be the bi-level model in this example is nonlinear while the bi-level model in their study is linear.     

A monotonic projective algorithm for fractional linear programming

We demonstrate that Karmarkar's projective algorithm is fundamentally an algorithm for fractional linear programming on the simplex. Convergence for the latter problem is established assuming only an initial lower bound on the optimal objective value. We also show that the algorithm can be easily modified so as to assure monotonicity of the true objective values, while retaining all global convergence properties. Finally, we show how the monotonic algorithm can be used to obtain an initial lower bound when none is otherwise available.     

A monotonic projective algorithm for fractional linear programming

We demonstrate that Karmarkar's projective algorithm is fundamentally an algorithm for fractional linear programming on the simplex. Convergence for the latter problem is established assuming only an initial lower bound on the optimal objective value. We also show that the algorithm can be easily modified so as to assure monotonicity of the true objective values, while retaining all global convergence properties. Finally, we show how the monotonic algorithm can be used to obtain an initial lower bound when none is otherwise available.     

Bi-level programming modeling and hierarchical hybrid algorithm for antimissile dynamic firepower allocation problem with uncertain environment

Aiming at the shortcomings of antimissile dynamic firepower allocation (ADFA) researches under uncertain environment, the fuzzy chance-constrained bi-level programming model with complex constraints is proposed by introducing the uncertain programming theory. Firstly, maximization cost-effectiveness ratio and earliest interception time as the upper and the lower objective functions of the model, respectively, are used. In order to close to the battlefield environment, the model constraint includes interception time window, effective damage lower bound and intercept strategy, etc. Secondly, a particle coding scheme and repairing scheme are given with hierarchical structure for multi-constrained bi-level ADFA problem. Furthermore, the improved variable neighborhood PSO algorithm with convergence criterions and the PSO algorithm with doubt and repulsion factor (PSO-DR) are effectively combined. On these bases, the hierarchical hybrid fuzzy particle swarm optimization algorithm is presented with fuzzy simulation technique. Finally, the results of comparison show the proposed algorithm has stronger global searching ability and faster convergence speed, which can effectively solve large-scale ADFA problem and adapt to the requirements of real-time decision.     

Robust ℋ2 filtering for LTI systems with linear fractional representation

This article introduces a new approach to ?₂ robust filtering design for continuous and discrete-time LTI systems subjected to linear fractional parameter uncertainty representation. The novelty consists on the determination of a performance certificate in terms of the gap between lower and upper bounds of a minimax programming problem which defines the optimal robust filter and the associated equilibrium cost. The calculations are performed through convex programming methods, applying slack variables, known as multipliers, to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty. The theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load.