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.

     

A global optimization algorithm for solving the bi-level linear fractional programming problem

In this paper, we obtain the solution to bi-level linear fractional programming problem (BLFP) by means of an optimization algorithm based on the duality gap of the lower level problem. In our algorithm, the bi-level linear fractional programming problem is transformed into an equivalent single level programming problem by forcing the dual gap of the lower level problem to zero. Then, by obtaining all vertices of a polyhedron, the single level programming problem can be converted into a series of linear fractional programming problems. Finally, the performance of the proposed algorithm is tested on a set of examples taken from the literature.     

A Relaxation Approach for Estimating Origin–Destination Trip Tables

The problem of estimating origin-destination travel demands from partial observations of traffic conditions has often been formulated as a network design problem (NDP) with a bi-level structure. The upper level problem in such a formulation minimizes a distance metric between measured and estimated traffic conditions, and the lower level enforces user-equilibrium traffic conditions in the network. Since bi-level problems are usually challenging to solve numerically, especially for large-scale networks, we proposed, in an earlier effort (Nie et al., Transp Res, 39B:497–518, 2005), a decoupling scheme that transforms the O–D estimation problem into a single-level optimization problem. In this paper, a novel formulation is proposed to relax the user equilibrium conditions while taking users’ route choice behavior into account. This relaxation approach allows the development of efficient solution procedures that can handle large-scale problems, and makes the integration of other inputs, such as path travel times and historical O–Ds rather straightforward. An algorithm based on column generation is devised to solve the relaxed formulation and its convergence is proved. Using a benchmark example, we compare the estimation results obtained from bi-level, decoupled and relaxed formulations, and conduct various sensitivity analysis. A large example is also provided to illustrate the efficiency of the relaxation method.     

Optimization–Simulation Model for Planning Supply Transport to Large Infrastructure Public Works Located in Congested Urban Areas

This article proposes an optimization–simulation model for planning the transport of supplies to large public infrastructure works located in congested urban areas. The purpose is to minimize their impact on the environment and on private transportation users on the local road network. To achieve this goal, the authors propose and solve an optimization problem for minimizing the total system cost made up of operating costs for various alternatives for taking supplies to the worksite and the costs supported by private vehicle users as a result of increased congestion due to the movement of heavy goods vehicles transporting material to the worksite. The proposed optimization problem is a bi-level Math Program model. The upper level defines the total cost of the system, which is minimized taking into account environmental constraints on atmospheric and noise pollution. The lower level defines the optimization problem representing the private transportation user behavior, assuming they choose the route that minimizes their total individual journey costs. Given the special characteristics of the problem, a heuristic algorithm is proposed for finding optimum solutions. Both the model developed and the specific solution algorithm are applied to the real case of building a new port at Laredo (Northern Spain). A series of interesting conclusions are obtained from the corresponding sensitivity analysis.     

Constrained optimal control of switched systems based on modified BFGS algorithm and filled function method

In this paper, we consider an optimal control problem of switched systems with a continuous-time inequality constraint. Because of the complexity of this constraint, it is difficult to solve this problem by standard optimization techniques. To overcome this difficulty, the problem is divided into a bi-level optimization problem involving a combination of a continuous-time optimal control problem and a discrete optimization problem. Then, a modified Broyden-Fletcher-Goldfarb-Shanno algorithm and a discrete filled function method is first proposed to solve this bi-level optimization problem. Finally, a numerical example is presented to illustrate the efficiency of our method.     

考虑备灾的双层规划应急资源调度选址—路径优化模型与算法

备灾措施可以为救灾做准备,为确保灾后应急物资可以及时高效地到达灾区,提出了考虑备灾的双层规划应急资源调度选址—路径优化模型,上层规划以供应站建设和运营总成本最低为目标,而下层规划以配送路径成本最小化为目标.设计了一种改进的双层樽海鞘遗传算法求解该问题,结合迭代划分的概念更新领导者位置,采用自然指数惯性权值策略修正控制因子,利用混沌映射更新追随者位置,采用田口分析方法获取参数合理取值.最后,通过使用双层樽海鞘遗传算法与遗传粒子群混合算法、粒子群优化算法、免疫优化算法对OR-Library中的LRP(location-routing problem,LRP)数据集进行求解和对比分析,验证了所提模型和算法的可行性和有效性.     

The spherical search algorithm for bound-constrained global optimization problems

In this paper, a new optimization algorithm called Spherical Search (SS) is proposed to solve the bound-constrained non-linear global optimization problems. The main operations of SS are the calculation of spherical boundary and generation of new trial solution on the surface of the spherical boundary. These operations are mathematically modeled with some more basic level operators: Initialization of solution, greedy selection and parameter adaptation, and are employed on the 30 black-box bound constrained global optimization problems. This study also analyzes the applicability of the proposed algorithm on a set of real-life optimization problems. Meanwhile, to show the robustness and proficiency of SS, the obtained results of the proposed algorithm are compared with the results of other well-known optimization algorithms and their advanced variants: Particle Swarm Optimization (PSO), Differential Evolution (DE), and Covariance Matrix Adapted Evolution Strategy (CMA-ES). The comparative analysis reveals that the performance of SS is quite competitive with respect to the other peer algorithms.     

Biasing Bayesian Optimization Algorithm using Case Based Reasoning

Studies show that application of the prior knowledge in biasing the Estimation of Distribution Algorithms (EDAs), such as Bayesian Optimization Algorithm (BOA), increases the efficiency of these algorithms significantly. One of the main advantages of the EDAs over other optimization algorithms is that the former provides a trail of probabilistic models of candidate solutions with increasing quality. Some recent studies have applied these probabilistic models, obtained from previously solved problems in biasing the BOA algorithm, to solve the future problems. In this paper, in order to improve the previous works and reduce their disadvantages, a method based on Case Based Reasoning (CBR) is proposed for biasing the BOA algorithm. Herein, after running BOA for solving optimization problems, each problem, the corresponding solution, as well as the last Bayesian network obtained from the BOA algorithm, will be stored as an entry in the case-base. Upon introducing a new problem, similar problems from the case-base are retrieved and the last Bayesian networks of these solved problems are combined according to the degree of their similarity with the new problem; hence, a compound Bayesian network is constructed. The compound Bayesian network is sampled and the initial population for the BOA algorithm is generated. This network will be applied efficiently for biasing future probabilistic models during the runs of BOA for the new problem. The proposed method is tested on three well-known combinatorial benchmark problems. Experimental results show significant improvements in algorithm execution time and quality of solutions, compared to previous methods.     

面向离散优化问题的量子协同演化算法

为解决现有离散优化算法在有限时间内容易出现过早收敛或难以收敛的问题,提出了面向离散优化问题的量子协同演化算法。该算法通过种群初始化策略构建分布均匀的初始种群,并改进粒子群和单点优化算法成为具有不同搜索能力的协同演化策略,进而利用量子旋转门根据种群个体的进化情况自适应地选择合适的演化策略,最后利用精英保持策略避免种群的退化。在标准离散问题和背包问题的测试环境中,各算法的平均收敛精度和实际收敛情况均表明,已提出的算法能够在有限时间内,收敛到精度较高的解,可用于求解具有时效要求的离散优化问题。     

改进的细菌觅食优化算法求解0-1背包问题

细菌觅食优化算法作为一种新兴的智能优化算法,一般用来解决连续域的问题。为了解决离散域问题,提出了一种改进的细菌觅食优化算法。采用线性递减的思想和随机的游动长度代替固定步长和随机游动方向,改进了趋向性操作方案,并将其应用于解决0-1背包问题。将改进的细菌觅食优化算法与遗传算法、离散粒子群优化算法及基本的离散化细菌觅食优化算法分别在小规模和大规模的0-1背包问题上进行了仿真比较,表明了改进的细菌觅食优化算法能取得较好的效果,寻优能力强。     

A Stochastic Optimization Model to Reduce Expected Post-Disaster Response Time Through Pre-Disaster Investment Decisions

This paper seeks to enhance network survivability under a disaster and reduce the expected post-disaster response time for transportation networks through pre-disaster investment decisions. The planning focuses on determining the links of the network to strengthen through investment under two types of uncertainties: the disaster characteristics, and the surviving network under each disaster. A bi-level stochastic optimization model is proposed for this problem, in which link investment decisions are made at the upper level to enhance the network survivability subject to a budget constraint such that the expected post-disaster response time is minimized at the lower level. A two-stage heuristic algorithm is proposed to obtain effective solutions efficiently. The numerical experiments indicate that the proposed heuristic algorithm converges to a fixed point representing a feasible solution, within an acceptable tolerance level, of the bi-level stochastic optimization model which is an effective solution under disasters of moderate severity. Parametric and sensitivity analyses reinforce the need for a holistic approach that integrates multiple relevant considerations to determine the link investment decisions.     

基于改进的PSO算法求解电力公司最优报价策略

电力公司报价策略是一个双层优化问题,其中上层的ISO是保证社会公共效益最大化而制定的市场清除价模型,确定参与发电的电力公司,下层是基于发电公司利润最大的模型。采用启发式算法求解简单易行,最优解具有全局性,且与初始点选择无关。运用改进后的粒子群优化算法（PSO）求解电力公司利润最大的优化问题,并与确定性方法的计算结果进行了比较。在IEEE30节点6机系统验证了该方法的有效性。     

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;...     

基于多任务强化学习的堆垛机调度与库位推荐

堆垛机调度是物流仓储自动化中的重要任务,任务中的出入库效率、货物存放等情况影响仓储系统的整体效益。传统调度方法在面对较大规模调度问题时,因处理大状态空间从而导致性能受限和收益降低。与此同时,库位优化与调度运行联系密切,但现有多数工作在处理调度问题时未能考虑到库位优化问题。为解决仓储中堆垛机调度问题,提出一种基于深度强化学习算法的近端策略优化调度方法。将调度问题视为序列决策问题,通过智能体与环境的持续交互进行自我学习,以在不断变化的环境中优化调度。针对调度中伴生的库位优化问题,提出一种基于多任务学习的调度、库位推荐联合算法,并基于调度网络构建适用于库位推荐的Actor网络,通过与Critic网络进行交互反馈,促进整体的联动和训练,从而提升整体效益。实验结果表明,与原算法模型相比,该调度方法的累计回报值指标平均提升了33.6%,所提的多任务学习的联合算法能有效地应对堆垛机调度和库位优化的应用场景,可为该类多任务问题提供可行的解决方案。     

A bi-level evolutionary optimization approach for integrated production and transportation scheduling

This paper investigates an integrated production and transportation scheduling (IPTS) problem which is formulated as a bi-level mixed integer nonlinear program. This problem considers distinct realistic features widely existing in make-to-order supply chains, namely unrelated parallel-machine production environment and product batch-based delivery. An evolution-strategy-based bi-level evolutionary optimization approach is developed to handle the IPTS problem by integrating a memetic algorithm and heuristic rules. The efficiency and effectiveness of the proposed approach is evaluated by numerical experiments based on industrial data and industrial-size problems. Experimental results demonstrate that the proposed approach can effectively solve the problem investigated.     

An orthogonal opposition-based-learning Yin–Yang-pair optimization algorithm for engineering optimization

Yin–Yang-pair Optimization (YYPO) is a recently developed philosophy-inspired meta-heuristic algorithm, which works with two main points for exploitation and exploration, respectively, and then generates more points via splitting to search the global optimum. However, it suffers from low quality of candidate solutions in its exploration process owing to the lack of elitism. Inspired by this, a new modified algorithm named orthogonal opposition-based-learning Yin–Yang-pair Optimization (OOYO) is proposed to enhance the performance of YYPO. First, the OOYO retains the normalization operation in YYPO and starts with a single point to exploit. A set of opposite points is designed by a method of opposition-based learning with split points generated from the current optimum for exploration. Then, the points, i.e., candidate solutions, are constructed by the randomly selected split point and opposite points through the idea of orthogonal experiment design to make full use of information from the space. The proposed OOYO does not add additional time complexity and eliminates a user-defined parameter in YYPO, which facilitates parameter adjustment. The novel orthogonal opposition-based learning strategy can provide inspirations for the improvement of other optimization algorithms. Extensive test functions containing a classic test suite of 23 standard benchmark functions and 2 test suites of Swarm Intelligence Symposium 2005 and Congress on Evolutionary Computation 2020 from Institute of Electrical and Electronics Engineers are employed to evaluate the proposed algorithm. Non-parametric statistical results demonstrate that OOYO outperforms YYPO and furnishes strong competitiveness compared with other state-of-the-art algorithms. In addition, we apply OOYO to solve four well-known constrained engineering problems and a practical problem of parameters optimization in a rainstorm intensity model.

     

基于多目标蝗虫优化算法的移动机器人路径规划

在静态多障碍物环境下的移动机器人路径规划问题中，粒子群算法存在容易产生早熟收敛和局部寻优能力较差等缺点，导致机器人路径规划精度低。为此，提出一种多目标蝗虫优化算法（MOGOA）来解决这一问题。根据移动机器人路径规划要求将路径长度、平滑度和安全性作为路径优化的目标，建立相应的多目标优化问题的数学模型。在种群的搜索过程中，引入曲线自适应策略以提高算法收敛速度，并使用Pareto最优准则来解决三个目标之间的共存问题。实验结果表明：所提出的算法在解决上述问题中寻找到的路径更短，表现出更好的收敛性。该算法与多目标粒子群（MOPSO）算法相比路径长度减少了约2.01%，搜索到最小路径的迭代次数减少了约19.34%。     

双局部粒子群算法解决环境经济调度问题

提出一种基于双局部最优的多目标粒子群优化算法,与可行解为优的约束处理方法相结合,来求解决非线性带约束的多目标电力系统环境经济调度问题。该算法针对传统多目标粒子群算法多样性低的局限性,通过对搜索空间的分割归类来增加帕累托最优解的多样性;并采用一种新的双局部最优来引导粒子的搜索,从而增强了算法的全局搜索能力。算法加入了可行解为优的约束处理方法对IEEE30节点六发电机电力系统环境经济负荷分配模型分别在几个不同复杂性问题的情况进行仿真测试,并与文献中的其他算法进行了比较。结果表明,改进的算法能够在保持帕累托最优解多样性的同时具有良好的收敛性能,更有效地解决电力系统环境经济调度问题。     

区域低碳物流运输网络双层优化研究

区域低碳物流网络优化是建立低碳物流系统的重要环节。引入低碳理念,考虑政府低碳线路规划与货主之间的博弈,上层区域物流网络的优化以碳排放、成本、时间最少化,下层货流运用改进的Logit路径选择分配,建立了基于低碳理念的区域物流运输网络双层优化模型。根据模型求解的复杂性,运用网络变形和遗传算法给出求解优化模型的方法和步骤。算例仿真计算结果表明,该模型与算法在区域物流运输网络低碳优化组合中是准确且可行的,有益于低碳物流网络构建。     

Optimization of reinforced concrete frames subjected to historical time-history loadings using DMPSO algorithm

In this paper, the seismic design of reinforced concrete (RC) frames subjected to time-history loadings was formulated as an optimization problem. Because finding the optimum design is relatively difficult and time-consuming for structural dynamics problems, an innovative algorithm combining multi-criterion decision-making (DM) and Particle Swarm Optimization (PSO), called DMPSO, was presented for accelerating convergence toward the optimum solution. The effectiveness of the proposed algorithm was illustrated in some benchmark reinforced concrete optimization problems. The main goal was to minimize the cost or weight of structures subjected to time-history loadings while satisfying all design requirements imposed by building design codes. The results confirmed the ability of the proposed algorithm to find the optimal solutions for structural optimization problems subjected to time-history loadings.