存在整数约束的分布式驱动变体飞行器控制分配

针对一类含有整数控制约束的分布式驱动变体飞行器在线控制分配问题,提出了一种基于布谷鸟搜索算法的求解策略.首先,考虑到指令分配误差以及作动器的损耗,将飞行器在线作动器控制分配问题表示为一类整数规划问题.然后,设计改进的布谷鸟搜索算法求解作动器的控制指令,采用Tent混沌映射初始化种群、自适应的步长控制量等措施提高算法的搜索效率.最后,将提出的控制分配方法应用于一类新型操纵面飞行器,仿真结果验证了该方法的有效性.     

一种求解整数规划与混合整数规划非线性罚函数方法

证明了任何一个变量有界的整数规划问题（IP）和混合整数规划问题（MIP）都可以转化为一个等价的非整数（或连续化）规划问题（NIP），并给出一个用非线性精确罚函数法来求解该等价NIP的方法，从而达到求解IP或MIP的目的，数值实验表明了算法的可行性。该方法可广泛用于各应用领域里IP和MIP的求解，特别是为非线性IP和MIP问题提供了一条通用 的求解途径，对解决许多实际优化问题具有重要意义。     

On the use of mixed‐integer linear programming for predictive control with avoidance constraints

This technical note concerns the predictive control of discrete‐time linear models subject to state, input and avoidance polyhedral constraints. Owing to the presence of avoidance constraints, the optimization associated with the predictive control law is non‐convex, even though the constraints themselves are convex. The inclusion of the avoidance constraints in the predictive control law is achieved by the use of a modified version of a mixed‐integer programming approach previously derived in the literature. The proposed modification consists of adding constraints to ensure that linear segments of the system trajectories between consecutive sampling times do not cross existing obstacles. This avoids the significant extra computation that would be incurred if the sampling time was reduced to prevent these crossings. Simulation results show that the inclusion of these additional constraints successfully prevents obstacle collisions that would otherwise occur. Copyright © 2008 John Wiley & Sons, Ltd.     

Maximal matching polytope in trees

Given a weighted simple graph, the minimum weighted maximal matching (MWMM) problem is the problem of finding a maximal matching of minimum weight. The MWMM problem is NP-hard in general, but is polynomial-time solvable in some special classes of graphs. For instance, it has been shown that the MWMM problem can be solved in linear time in trees when all the edge weights are equal to one. In this paper, we show that the convex hull of the incidence vectors of maximal matchings (the maximal matching polytope) in trees is given by the polytope described by the linear programming relaxation of a recently proposed integer programming formulation. This establishes the polynomial-time solvability of the MWMM problem in weighted trees. The question of whether or not the MWMM problem can be solved in linear time in weighted trees is open.     

Feasibility check for the distance geometry problem: an application to molecular conformations

The distance geometry problem (DGP) consists in finding an embedding in a metric space of a given weighted undirected graph such that for each edge in the graph, the corresponding distance in the embedding belongs to a given distance interval. We discuss the relationship between the existence of a graph embedding in a Euclidean space and the existence of a graph embedding in a lattice. Different approaches, including two integer programming (IP) models and a constraint programming (CP) approach, are presented to test the feasibility of the DGP. The two IP models are improved with the inclusion of valid inequalities, and the CP approach is improved using an algorithm to perform a domain reduction. The main motivation for this work is to derive new pruning devices within branch‐and‐prune algorithms for instances occurring in real applications related to determination of molecular conformations, which is a particular case of the DGP. A computational study based on a set of small‐sized instances from molecular conformations is reported. This study compares the running times of the different approaches to check feasibility.     

Analysis of integer programming formulations of clustering problems

Five different integer programming formulations of the clustering problem are discussed. Three new heuristic algorithms for solving these problems are presented. Some of the existing algorithms are generalized. The relevance of integer programming and combinatorial theory to cluster analysis is discussed. Many other applicable algorithms are listed.     

面向图相似性搜索的高效图编辑距离算法

在图相似性搜索问题中,图编辑距离是较为普遍的度量方法,其计算性能很大程度上决定了图相似性搜索算法的性能。针对传统图编辑距离算法中存在的因大量冗余映射和较大搜索空间导致的性能低下问题,提出了一种改进的图编辑距离算法。该算法首先对图中顶点进行等价划分,以此计算映射编码来判断等价映射;然后定义映射完整性更新等价映射优先级,选出主映射参与扩展;其次,设计高效的启发式函数,提出基于映射编码的下界计算方法,快速得到最优映射。最后,将改进的图编辑距离算法扩展应用于图相似性搜索。在不同数据集上的实验结果表明,该算法具有更好的搜索性能,在搜索空间上最大可降低49%,速度提升了约29%。     

Integrating integer programming and probabilistic deduction graphs for probabilistic reasoning

Optimal solutions of several variants of the probabilistic reasoning problem were found by a new technique that integrates integer programming and probabilistic deduction graphs (PDG). PDGs are extended from deduction graphs of the and-type via normal deduction graphs. The foregoing variants to be solved can involve multiple hypotheses and multiple evidences where the former is given and the latter is unknown and being found or vice versa. The relationship among these hypotheses and evidences with possible intermediaries is represented by a causal graph. The proposed method can handle a large causal graph of any type and find an optimal solution by invoking a linear integer programming package. In addition, formulating the reasoning problem to fit integer programming takes a polynomial time. H.-L. Li was visiting the Department of Computer Sciences, University of North Texas in 1988–1989. He is with the Institute of Information Management, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.     

Polyhedral Flows in Hybrid Automata

A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete updates with differential constraints for capturing continuous flows. Formal verification of hybrid automata relies on symbolic fixpoint computation procedures that manipulate sets of states. These procedures can be implemented using boolean combinations of linear constraints over system variables, equivalently, using polyhedra, for the subclass of linear hybrid automata. In a linear hybrid automaton, the flow at each control mode is given by a rate polytope that constrains the allowed values of the first derivatives. The key property of such a flow is that, given a state-set described by a polyhedron, the set of states that can be reached as time elapses, is also a polyhedron. We call such a flow a polyhedral flow. In this paper, we study if we can generalize the syntax of linear hybrid automata for describing flows without sacrificing the polyhedral property. In particular, we consider flows described by origin-dependent rate polytopes, in which the allowed rates depend, not only on the current control mode, but also on the specific state at which the mode was entered. We identify necessary and sufficient conditions for a class of flows described by origin-dependent rate polytopes to be polyhedral. We also propose and study additional classes of flows: strongly polyhedral flows, in which the set of states that can be reached up to a given time starting from a polyhedron is guaranteed to be a polyhedron, and polyhedrally sliced flows, in which the set of states that can be reached at a given time starting from a polyhedron is guaranteed to be a polyhedron. Finally, we discuss an application of the above classes of flows to approximate exponential behaviours.     

Parametric tabu-search for mixed integer programs

A parametric form of tabu-search is proposed for solving mixed integer programming (MIP) problems that creates and solves a series of linear programming (LP) problems embodying branching inequalities as weighted terms in the objective function. The approach extends and modifies a parametric branch and bound procedure of Glover [Parametic branch and bound. OMEGA, The International Journal of Management Science 1978;6:1–9], replacing its tree search memory by the adaptive memory framework of tabu-search and introducing new associated strategies that are more flexible than the mechanisms of branch and bound.     

Approximation schemes for deal splitting and covering integer programs with multiplicity constraints

We consider the problem of splitting an order for R goods, R≥1, among a set of sellers, each having bounded amounts of the goods, so as to minimize the total cost of the deal. In deal splitting with packages (DSP), the sellers offer packages containing combinations of the goods; in deal splitting with price tables (DST), the buyer can generate such combinations using price tables. Our problems, which often occur in online reverse auctions, generalize covering integer programs with multiplicity constraints (CIP), where we must fill up an R-dimensional bin by selecting (with a bounded number of repetitions) from a set of R-dimensional items, such that the overall cost is minimized. Thus, both DSP and DST are NP-hard, already for a single good, and hard to approximate for arbitrary number of goods.In this paper we focus on finding efficient approximations for DSP and DST instances where the number of goods is some fixed constant. In particular, we develop polynomial time approximation schemes (PTAS) for several subclasses of instances of practical interest. Our results include a PTAS for CIP in fixed dimension, and a more efficient (combinatorial) scheme for CIP_∞, where the multiplicity constraints are omitted. Our approximation scheme for CIP_∞ is based on a non-trivial application of the fast scheme for the fractional covering problem, proposed by Fleischer [L. Fleischer, A fast approximation scheme for fractional covering problems with variable upper bounds, in: Proc. of the 15th ACM-SIAM Symposium on Discrete Algorithm, 2004, pp. 994-1003].     

Spherical cuts for integer programming problems

We introduce a new family of valid inequalities for general linear integer programming problems, based on the distance of the relaxed solution to the closest integral point. We show that these are valid cuts, establish some relations with Balas' intersection cuts, and show that a straightforward cutting plane algorithm derived from either spherical or intersection cuts will in general only converge if a suitable Gomory‐type strengthening is put in place.     

求解整数线性规划问题的定界阻止算法的改进*

在现有求解整数线性规划问题的定界阻止算法的基础上提出了一种改进。该算法通过目标函数超平面截线性规划松弛问题的有效约束锥而形成一个单纯形;然后,引入一串平行片来切割该单纯形产生更低维的凸多面体;最后,在片上的这些凸多面体上执行阻止搜寻程序。由于单纯形和片上凸多面体的极顶点可以直接通过公式计算,且变量在片上凸多面体上的取值区间更窄,改进的定界阻止算法既方便又高效,这得到了一些经典算例和随机产生的算例的验证。     

Sequential integer programming methods for stress constrained topology optimization

This paper deals with topology optimization of load carrying structures defined on a discretized design domain where binary design variables are used to indicate material or void in the various finite elements. The main contribution is the development of two iterative methods which are guaranteed to find a local optimum with respect to a 1-neighbourhood. Each new iteration point is obtained as the optimal solution to an integer linear programming problem which is an approximation of the original problem at the previous iteration point. The proposed methods are quite general and can be applied to a variety of topology optimization problems defined by 0-1 design variables. Most of the presented numerical examples are devoted to problems involving stresses which can be handled in a natural way since the design variables are kept binary in the subproblems.     

求解整数线性规划的一种高效隐数搜寻

提出了一种求解整数线性规划的新的隐数算法。首先,该算法引入了一组线性变换,将线性松弛问题的最优非基变量变换到一组新变量,使新变量有更小的取值范围。然后,在目标函数超平面上对非基变量和新变量进行隐数计算,从而大大提高了隐数搜寻的效率。     

Task allocation and trajectory planning for multiple agents in the presence of obstacle and connectivity constraints with mixed‐integer linear programming

This article addresses the problem of maneuvering multiple agents that must visit a number of target sets, while enforcing connectivity constraints and avoiding obstacle as well as interagent collisions. The tool to cope with the problem is a formulation of model predictive control including binary decision variables. In this regard, two mixed‐integer linear programming formulations are presented, considering a trade‐off between optimality and scalability between them. Simulation results are also shown to illustrate the main features of the proposed approaches.     

偶发实时系统可调度性分析问题的整数规划方法

偶发实时任务最早截止期优先（earliest deadline first,简称EDF）可调度分析是实时系统领域经典的NP困难问题.现有的伪多项式时间判定算法（pseudo-polynomail time decision algorithm,简称PTDA）均局限于利用率U严格小于1的同步任务系统.对于U≤1的同步系统或更加困难的异步系统,现有PTDA则不再适用.针对以上问题,为同步和异步两类实时系统建立了统一的整数规划模型,其规模并不依赖于利用率U的取值.基于多面体理论证明了模型维数和极大诱导不等式,进而提出了同/异步系统上EDF可调度性分析问题统一的多项式时间线性松弛求解方法.实验结果表明,该方法能够获得较紧的问题解下界,在异步和同步系统中,线性松弛解与最优解之间的平均百分界差gap分别为0.78%和1.27%.另外,随机生成了大量同步和异步系统的算例,用于该算法和传统算法进行性能比较.对于同步算例,实验结果表明,在U>0.99时,该算法能够对70%的算例给出判定结果,算法性能与QPA算法相比有指数级提升.对于异步算例,实验结果表明,该算法能够对近96%的算例给出可调度性判定.与传统算法相比,该方法将不能判定可调度性的算例比例平均降低了29.27%.对于剩余的4%的算例,该算法将可调度上界的值平均降低了近10⁴倍.     

Binary integer programming formulations for scheduling in market-driven foundries

This paper describes the development and solution of binary integer formulations for production scheduling problems in market-driven foundries. This industrial sector is comprised of small and mid-sized companies with little or no automation, working with diversified production, involving several different metal alloy specifications in small tailor-made product lots. The characteristics and constraints involved in a typical production environment at these industries challenge the formulation of mathematical programming models that can be computationally solved when considering real applications. However, despite the interest on the part of these industries in counting on effective methods for production scheduling, there are few studies available on the subject. The computational tests prove the robustness and feasibility of proposed models in situations analogous to those found in production scheduling at the analyzed industrial sector.     

整数规划的量子行为蝙蝠算法

蝙蝠算法是一种新型群体智能算法,传统的蝙蝠算法在解决整数规划问题时容易陷入局部最优并出现早熟收敛现象,为了解决这些弊端,提出了一种基于势阱的具有量子行为的蝙蝠算法。论述了算法的优化原理和实现方式,并通过仿真实验,与粒子群算法和量子行为粒子群算法进行性能对比。实验结果表明,量子行为蝙蝠算法不仅能够有效地解决整数规划问题,而且比其他算法具有更好的性能。