求解可分离连续凸二次背包问题的直接算法

经典算法一般采用迭代过程求解连续凸二次背包问题,研究了求解可分离连续凸二次背包问题的直接算法。分析了可分离连续凸二次背包问题的结构特性,通过两个命题和两个定理研究了可分离连续凸二次背包问题的解的特性,提出了一种快速的求解该问题的直接算法。该算法能快速有效地求解可分离连续凸二次背包问题的最优解,算法的时间复杂度和空间复杂度都是O(n),都比经典算法节约很多。     

两阶段资金投入条件下多项目组合中基于项目启动水平的资金分配问题研究

对两阶段资金投入条件下多项目组合中基于项目启动水平的资金分配问题进行了研究.由于已启动项目的资金不能按预算全额投入,因此文中引入了项目启动水平的概念,低于最低启动水平则项目不能启动.假设每个项目的净收益值与资金投入值可表示为与启动水平有关的线性函数,据此对两阶段投资过程分别建立了数学模型,分析认为它们分别属于0/1背包问题和连续背包问题,且都为NP难题.在建立了相关定理及定义的基础上,基于连续松弛条件下的价值密度贪婪准则,分别应用分枝定界算法、动态规划算法得到了该问题的资金分配最优策略.     

Quantum-inspired ant algorithm for knapsack problems

The knapsack problem is a well-known combinatorial optimization problem which has been proved to be NP-hard. This paper proposes a new algorithm called quantum-inspired ant algorithm (QAA) to solve the knapsack problem. QAA takes the advantage of the principles in quantum computing, such as qubit, quantum gate, and quantum superposition of states, to get more probabilistic-based status with small colonies. By updating the pheromone in the ant algorithm and rotating the quantum gate, the algorithm can finally reach the optimal solution. The detailed steps to use QAA are presented, and by solving series of test cases of classical knapsack problems, the effectiveness and generality of the new algorithm are validated.     

Intermediate carriers for UAV swarms: problem of fleet composition

This article introduces a fleet composition algorithm for a fleet of intermediate carriers,which should deliver a swarm of miniature unmanned aerial vehicles(mini-UAVs) to a mission area.The algorithm is based on the sequential solution of several knapsack problems with various constraints.The algorithm allows both to form an initial set of required types of intermediate carriers, and to generate a fleet of intermediate carriers.The formation of a fleet of intermediate carriers to solve a suppression of enemy air defense(SEAD) problem is presented to illustrate the proposed algorithm.     

Multiple optimal solutions to a sort of nonlinear optimization problem

The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.     

A LAGRANGIAN RELAXATION APPROACH FOR SUPPLY CHAIN PLANNING WITH ORDER／SETUP COSTS AND CAPACITY CONSTRAINTS

A heuristic approach is developed for supply chain planning modeled as multi-item multi-levelcapacitated lot sizing problems. The heuristic combines Lagrangian relaxation(LR) with local search.Different from existing LR approaches that relax capacity constraints and/or inventory balanceconstraints, our approach only relaxes the technical constraints that each 0-1 setup variable must takevalue 1 if its corresponding continuous variable is positive. The relaxed problem is approximatelysolved by using the simplex algorithm for linear programming, while Lagrange multipliers are updatedby using a surrogate subgradient method that ensures the convergence of the dual problem in case ofthe approximate resolution of the relaxed problem. At each iteration, a feasible solution of the originalproblem is constructed from the solution of the relaxed problem. The feasible solution is furtherimproved by a local search that changes the values of two setup variables at each time. By taking theadvantages of a special stru     

利用改进的二进制狼群算法求解多维背包问题

(1. Materiel Engineering College, Armed Police Force Engineering University, Xi’an 710086, China; 2. Materiel Management and Safety Engineering College, Air Force Engineering University,  Xi’an 710051, China;3. Air Traffic Control and Navigation College, Air Force  Engineering University, Xi’an 710051, China)     

A QUANTIFIER-ELIMINATION BASED HEURISTIC FOR AUTOMATICALLY GENERATING INDUCTIVE ASSERTIONS FOR PROGRAMS

A method using quantifier-elimination is proposed for automatically generating programinvariants/inductive assertions.Given a program,inductive assertions,hypothesized as parameterizedformulas in a theory,are associated with program locations.Parameters in inductive assertions arediscovered by generating constraints on parameters by ensuring that an inductive assertion is indeedpreserved by all execution paths leading to the associated location of the program.The method can beused to discover loop invariants-properties of variables that remain invariant at the entry of a loop.Theparameterized formula can be successively refined by considering execution paths one by one;heuristicscan be developed for determining the order in which the paths are considered.Initialization of programvariables as well as the precondition and postcondition,if available,can also be used to further refinethe hypothesized invariant.The method does not depend on the availability of the precondition andpostcondition of a program.Constraints on parameters generated in this way are solved for possiblevalues of parameters.If no solution is possible,this means that an invariant of the hypothesizedform is not likely to exist for the loop under the assumptions/approximations made to generate theassociated verification condition.Otherwise,if the parametric constraints are solvable,then undercertain conditions on methods for generating these constraints,the strongest possible invariant of thehypothesized form can be generated from most general solutions of the parametric constraints.Theapproach is illustrated using the logical languages of conjunction of polynomial equations as well asPresburger arithmetic for expressing assertions.     

基于状态转移的组合优化方法

NP问题的解空间太大导致利用现有技术求解十分困难。针对这一问题．提出基于状态转移的组合优化方法。结合0／1背包问题的求解。阐明这种方法求解问题的过程。实验结果表明这种方法是有效的。     

Safety-Critical Optimal Control for Autonomous Systems

This paper presents an overview of the state of the art for safety-critical optimal control of autonomous systems. Optimal control methods are well studied, but become computationally infeasible for real-time applications when there are multiple hard safety constraints involved. To guarantee such safety constraints, it has been shown that optimizing quadratic costs while stabilizing affine control systems to desired(sets of) states subject to state and control constraints can be reduced to a sequence of Quadratic Programs(QPs) by using Control Barrier Functions(CBFs) and Control Lyapunov Functions(CLFs). The CBF method is computationally efficient, and can easily guarantee the satisfaction of nonlinear constraints for nonlinear systems, but its wide applicability still faces several challenges. First, safety is hard to guarantee for systems with high relative degree, and the above mentioned QPs can easily be infeasible if tight or time-varying control bounds are involved. The resulting solution is also sub-optimal due to its myopic solving approach. Finally, this method works conditioned on the system dynamics being accurately identified. The authors discuss recent solutions to these issues and then present a framework that combines Optimal Control with CBFs, hence termed OCBF, to obtain near-optimal solutions while guaranteeing safety constraints even in the presence of noisy dynamics. An application of the OCBF approach is included for autonomous vehicles in traffic networks.     

随机急诊需求下基于分支定价算法的手术计划研究

手术计划是优化医疗资源配置的重要组成部分,涉及众多的不确定性,是目前医疗管理领域研究的热点和难点问题.本文聚焦于考虑急诊病人随机手术时长需求的择期病人手术计划问题研究,在各个手术室具有异质性的情况下,优化手术室的超时成本和闲置成本,并为一个计划周期内的择期手术进行手术室和手术日期的分配.建立了一个0-1整数规划模型,针对问题情境和手术计划特有的约束条件提出了满足问题特性的分支定界和列生成相结合的精确型分支定价求解算法.其中在分支定界算法上,通过对比选择适合问题特性的节点选择策略,并且提出了分步分支策略加快搜索过程.为加快列生成算法的求解,通过数值积分和等价转换将带有不确定性的子问题转变为一个0-1背包问题的变形,然后设计动态规划算法进行求解.数值实验表明,根据问题特性设计的分支定价算法可有效求解具有不同实例规模下的手术计划问题,和CPLEX相比,大规模情形下能够在可接受的计算时间内得到问题最优解.     

Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient

<正> This paper applies bilinear immersed finite elements (IFEs) in the interior penalty discontinuousGalerkin (DG) methods for solving a second order elliptic equation with discontinuous coefficient.A discontinuous bilinear IFE space is constructed and applied to both the symmetric and nonsymmetricinterior penalty DG formulations.The new methods can solve an interface problem on a Cartesianmesh independent of the interface with local refinement at any locations needed even if the interfacehas a nontrivial geometry.Numerical examples are provided to show features of these methods.     

单机订单接受与加工调度问题的拉格朗日松弛算法

针对不同类型订单加工切换时机器需要准备时间的实际生产情况,研究了单机订单接受与加工调度优化决策问题,旨在最大化企业净收益。鉴于研究问题的强NP难属性,设计了基于拉格朗日松弛理论的启发式算法。首先,该算法通过加入相邻订单相异性约束以提高松弛解质量;其次,应用动态规划递推公式求解拉格朗日松弛问题;最后,利用问题的优化性质并基于贪婪规则构造原问题可行解。不同规模问题的实验结果表明,该算法能在合理计算时间内得到满意的近优解。     

Sequencing deliveries to minimize inventory holding cost with dominant upstream supply chain partner

This paper studies a two stage supply chain with a dominant upstream partner. Manufacturer is the dominant partner and operates in a Just-in-Time environment. Production is done in a single manufacturing line capable of producing two products without stopping the production for switching from one product to the other. The manufacturer imposes constraints on the distributor by adhering to his favorable production schedule which minimizes his manufacturing cost. Distributor on the other hand caters to retailers' orders without incurring any shortages and is responsible for managing the inventory of finished goods. Adhering to manufacturer's schedule may lead to high inventory carrying costs for the distributor. Distributor's problem, which is to find an optimal distribution sequence which minimizes the distributor's inventory cost under the constraint imposed by the manufacturer is proved NP-Hard by Manoj et al. (2008). Therefore, solving large size problems require efficient heuristics. We develop algorithms for the distribution problem by exploiting its structural properties. We propose two heuristics and use their solutions in the initial population of a genetic algorithm to arrive at solutions with an average deviation of less than 3.5% from the optimal solution for practical size problems.     

New coordination scheme for multi-robot systems based on state space models

A new coordination scheme for multi-robot systems is proposed.A state space model of the multi robot system is defined and constructed in which the system's initial and goal states are included along with the task definition and the system's internal and external constraints.Task accomplishment is considered a transition of the system state in its state space(SS)under the system's constraints.Therefore,if there exists a connectable path within reachable area of the SS from the initial state to the goal state,the task is realizable.The optimal strategy for the task realization under constraints is investigated and reached by searching for the optimal state transition trajectory of the robot system in the SS.Moreover,if there is no connectable path,which means the task cannot be performed successfully,the task could be transformed to be realizable by making the initial state and the goal state connectable and finding a path connecting them in the system's SS.This might be done via adjusting the system's configuration and/or task constraints.Experiments of multi-robot formation control with obstacles in the environment are conducted and simulation results show the validity of the proposed method.     

New coordination scheme for multi-robot systems based onstate space models

A new coordination scheme for multi-robot systems is proposed. A state space model of the multi- robot system is defined and constructed in which the system＇s initial and goal states are included along with the task definition and the system＇s internal and external constraints. Task accomplishment is considered a transition of the system state in its state space （SS） under the system＇s constraints. Therefore, if there exists a connectable path within reachable area of the SS from the initial state to the goal state, the task is realizable. The optimal strategy for the task realization under constraints is investigated and reached by searching for the optimal state transition trajectory of the robot system in the SS. Moreover, if there is no connectable path, which means the task cannot be performed Successfully, the task could be transformed to be realizable by making the initial state and the goal state connectable and finding a path connecting them in the system＇s SS. This might be done via adjusting the system＇s configuration and/or task constraints. Experiments of multi-robot formation control with obstacles in the environment are conducted and simulation results show the validity of the proposed method.     

装卸一体化车辆路径问题的遗传算法研究

针对装卸混合的车辆路径问题这一类典型的NP难题,采用四位数的遗传编码,并对解的可行性进行验证,降低对交叉算子和变异算子的要求,有效提高解的质量.最后对二十个客户点的装卸混合的问题作了数值试验,结果表明遗传算法作为一种有效的随机型全局搜索算法,体现出群体智能的分布型、鲁棒性和快速性的特点.     

SENSITIVITY ANALYSIS OF THE KNAPSACK PROBLEM： TIGHTER LOWER AND UPPER BOUND LIMITS

In this paper, we study the sensitivity of the optimum of the knapsack problem to the perturbation of the profit of a subset of items. We propose a polynomial heuristic in order to establish both lower and upper bound limits of the sensitivity interval. The aim is to stabilize any given optimal solution obtained by applying any exact algorithm. We then evaluate the effectiveness of the proposed solution procedure on an example and a set of randomly generated problem instances.     

基于Branch ＆Bound方法MIQP问题的求解及应用

研究基于Branch＆Bound(B＆B)方法的混合整数二次规划(Mixed Integer Quadratic Programming，MQP)问题的求解，以及在一类混杂系统优化控制中的应用。B＆B算法求解MIQP问题的过程，可视为对于一个二叉树的搜索。影响B＆B算法寻优效率的两个主要方面是：分支变量的选择规则，以及树搜索策略。通过设定控制变量QPmax，用以限制寻优过程求解QP问题的最大数目，可以在较短的时间内获得MIQP问题的满足整数约束条件次优解。利用MATLAB编制MIQP问题的求解程序，并在混杂系统优化控制中的应用，做了仿真计算。     

分布式环境下多任务调度问题的分析与求解

将约束条件归纳为任务约束、链路约束和资源约束,在允许任务复制的情况下,建立了问题的约束与目标的完整数学模型;提出了一种基于任务复制的模拟人类社会中关系演化过程的簇调度算法IREA,包括前沿调度、动态分簇和分离图三个子算法.IREA采用全新的优先级规则,定义了关系数、依赖度、归并度等表示簇的优先级.通过对两个经典算例的计算,发现IREA能求出比算例所在文献算法所得解更优的解;对MJD算例,还得到了一个不同于原文献所给理论最优格局的一个新的最优格局.