A computational algorithm for pole assignment of linear multiinput systems

An efficient computational algorithm for pole assignment of linear multiinput systems is proposed. A preliminary stage of the algorithm is a reduction of the system matrices into orthogonal canonical form. The gain matrix elements are then found by orthogonal transformation of the closed-loop system matrix into upper quasi-triangular form whose diagonal blocks correspond to the desired poles. The algorithm is numerically stable, the computed gain matrix being exact for a system with slightly perturbed matrices. It works equally well with real and complex, distinct, and multiple poles and is applicable to ill-conditioned and high-order problems.     

A new algorithm for an eigenvalue assignment problem from singularcontrol theory

In this paper, a new numerical algorithm for an eigenvalue assignment problem, which arises from a singular system control, is developed. The algorithm is based on orthogonal row/column compressions which can be implemented in a numerically reliable way     

An effective subgradient algorithm for the generalized assignment problem

A modified subgradient algorithm is presented for the generalized assignment problem, which, like the classical assignment problem, is concerned with the minimum cost assignment of agents to jobs. The generalized assignment problem, however, permits differences in job performance efficiencies among agents and thereby allows the possibility that each agent may be assigned more than a single job, as long as each job is ultimately assigned and the total resources available to every agent are not exceeded. A two stage heuristic algorithm using a modified subgradient approach and branch and bound is developed for solving the problem. By computing step sizes precisely and using the dual as a bound, the algorithm is shown to be particularly effective and easy to program and implement. A numerical example is presented to illustrate the model and method, and computational experience is cited for problems containing up to 12,000 0–1 variables.     

An algorithm for minimizing the norm of state feedback controllers in eigenvalue assignment

Minimization of the norm of parametric feedback controllers which assign desired eigenvalues to the closed-loop system is achieved by implementation of vector companion forms described in an earlier paper. The simple algorithm which emerges gives insight into the mechanism by which parametric eigenvalue assignment is affected. A couple of numerical examples are presented to illustrate advantages of this algorithm which easily computes the controller gain matrix with minimum norm.     

An improved differential evolution algorithm for the task assignment problem

An improved differential evolution algorithm (IDE) is proposed to solve task assignment problem. The IDE is an improved version of differential evolution algorithm (DE), and it modifies two important parameters of DE algorithm: scale factor and crossover rate. Specially, scale factor is adaptively adjusted According to the objective function values of all candidate solutions, and crossover rate is dynamically adjusted with the increasement of iterations. The adaptive scale factor and dynamical crossover rate are combined to increase the diversity of candidate solutions, and to enhance the exploration capacity of solution space of the proposed algorithm. In addition, a usual penalty function method is adopted to trade-off the objective and the constraints. Experimental results demonstrate that the optimal solutions obtained by the IDE algorithm are all better than those obtained by the other two DE algorithms on solving some task assignment problems.     

An algorithm for computing state feedback in multiinput linear systems

A new algorithm is proposed in this note to compute the state feedback for arbitrary pole placement in multiinput linear systems. The algorithm has good numerical behavior. It also allows the user to adjust the eigenstructure of the resulting feedback system and, therefore, improve the condition of the problem and computation.     

A simple solution to the optimal eigenvalue assignment problem

The problem of the optimal eigenvalue assignment for multi-input linear systems is considered. It is proven that for an n-order system with m independent inputs, the problem is split into the following two sequential stages. Initially, the n-m eigenvalues are assigned using an (n-m)-order system. This assignment is not constrained to satisfy optimality criteria. Next, an m-order system is used to assign the remaining m eigenvalues in such a way that linear quadratic optimal criteria are simultaneously satisfied. Therefore, the original n-order optimal eigenvalue assignment problem is reduced to an m-order optimal assignment problem. Moreover, the structure of the equivalent m-order system permits further simplifications which lead to solutions obtained by inspection     

An algorithm for computing the restriction scaffold assignment problem in computational biology

Let S and T be two finite sets of points on the real line with |S|+|T|=n and |S|>|T|. The restriction scaffold assignment problem in computational biology assigns each point of S to a point of T such that the sum of all the assignment costs is minimized, with the constraint that every element of T must be assigned at least one element of S. The cost of assigning an element si of S to an element tj of T is |si−tj|, i.e., the distance between si and tj. In 2003 Ben-Dor, Karp, Schwikowski and Shamir [J. Comput. Biol. 10 (2) (2003) 385] published an O(nlogn) time algorithm for this problem. Here we provide a counterexample to their algorithm and present a new algorithm that runs in O(n²) time, improving the best previous complexity of O(n³).     

求解频率指派问题的Multi-Quadric算法

为有效解决频率指派问题,提出了一种解决该问题的曲面拟合Multi-Quadric算法,算法将随机指派方案及其对应的干扰值作为多元散乱数据采样点,以此为基础进行多元散乱数据拟合,通过对拟合曲面极小值的寻找从而完成对频率指派问题的优化。优化结果可直接应用于实际工程,也可作为其它优化算法的初始解。算法在电台数量规模较大的应用中体现出良好的性能,算法结果作为蚁群、遗传算法的初始解,后继算法收敛速度明显提高。     

An orthogonal systolic design for the assignment problem

A systolic array for the solution of the assignment problem is presented. The algorithm requires O(n²) time on an orthogonally connected array of (n + 2) * (n + 2) cells consisting of simple adders and control logic. The design is area efficient and incorporates the new concept of a Systolic Control Ring (SCR) to generate the necessary systolic wavefronts in any orientation within the design, while special cells are positioned only on the periphery of the design. The design was simulated and tested by an OCCAM program.     

Genetic algorithm for the personnel assignment problem with multiple objectives

The assignment problem is a well-known graph optimization problem defined on weighted-bipartite graphs. The objective of the standard assignment problem is to maximize the summation of the weights of the matched edges of the bipartite graph. In the standard assignment problem, any node in one partition can be matched with any node in the other partition without any restriction. In this paper, variations of the standard assignment problem are defined with matching constraints by introducing structures in the partitions of the bipartite graph, and by defining constraints on these structures. According to the first constraint, the matching between the two partitions should respect the hierarchical-ordering constraints defined by forest and level graph structures produced by using the nodes of the two partitions respectively. In order to define the second constraint, the nodes of the partitions of the bipartite graph are distributed into mutually exclusive sets. The set-restriction constraint enforces the rule that in one of the partitions all the elements of each set should be matched with the elements of a set in the other partition. Even with one of these constraints the assignment problem becomes an NP-hard problem. Therefore, the extended assignment problem with both the hierarchical-ordering and set-restriction constraints becomes an NP-hard multi-objective optimization problem with three conflicting objectives; namely, minimizing the numbers of hierarchical-ordering and set-restriction violations, and maximizing the summation of the weights of the edges of the matching. Genetic algorithms are proven to be very successful for NP-hard multi-objective optimization problems. In this paper, we also propose genetic algorithm solutions for different versions of the assignment problem with multiple objectives based on hierarchical and set constraints, and we empirically show the performance of these solutions.     

An ANTS heuristic for the frequency assignment problem

The problem considered in this paper consists in assigning frequencies to radio links between base stations and mobile transmitters in order to minimize the global interference over a given region. This problem is NP-hard and few results have been reported on techniques for solving it to optimality. We have applied to this problem an ANTS metaheuristic, that is, an approach following the ant colony optimization paradigm. Computational results, obtained on a number of standard problem instances, testify the effectiveness of the proposed approach.     

Backbone analysis and algorithm design for the quadratic assignment problem

As the hot line in NP-hard problems research in recent years, backbone analysis is crucial for phase transition, hardness, and algorithm design. Whereas theoretical analysis of backbone and its applications in algorithm design are still at a begin- ning state yet, this paper took the quadratic assignment problem （QAP） as a case study and proved by theoretical analysis that it is NP-hard to find the backbone, i.e., no algorithm exists to obtain the backbone of a QAP in polynomial time. Results of this paper showed that it is reasonable to acquire approximate backbone by inter- section of local optimal solutions. Furthermore, with the method of constructing biased instances, this paper proposed a new meta-heuristic -- biased instance based approximate backbone （BI-AB）, whose basic idea is as follows： firstly, construct a new biased instance for every QAP instance （the optimal solution of the new instance is also optimal for the original one）; secondly, the approximate backbone is obtained by intersection of multiple local optimal solutions computed by some existing algorithm; finally, search for the optimal solutions in the reduced space by fixing the approximate backbone. Work of the paper enhanced the research area of theoretical analysis of backbone. The meta-heuristic proposed in this paper provided a new way for general algorithm design of NP-hard problems as well.     

An iterative genetic algorithm for the assembly line worker assignment and balancing problem of type-II

In this study, we consider the assembly line worker assignment and balancing problem of type-II (ALWABP-2). ALWABP-2 arises when task times differ depending on operator skills and concerns with the assignment of tasks and operators to stations in order to minimize the cycle time. We developed an iterative genetic algorithm (IGA) to solve this problem. In the IGA, three search approaches are adopted in order to obtain search diversity and efficiency: modified bisection search, genetic algorithm and iterated local search. When designing the IGA, all the parameters such as construction heuristics, genetic operators and local search operators are adapted specifically to the ALWABP-2. The performance of the proposed IGA is compared with heuristic and metaheuristic approaches on benchmark problem instances. Experimental results show that the proposed IGA is very effective and robust for a large set of benchmark problems.     

A negative dual rectangle cancellation algorithm for the linear assignment problem

In this paper, we consider three alternative primal models and their corresponding alternative dual models for the linear assignment problem. We then define the concept of Negative Dual Rectangle (NDR) and suggest an algorithm that solves two of these dual problems by repeatedly finding and cancelling NDRs until it yields an optimal solution to the assignment problem. The algorithm is simple, flexible, efficient, and unified. We also introduce the notion of partial zero cover as an interpretation of an NDR. We then introduce some heuristic methods for finding NDRs. We also state and prove a lemma to establish the optimal use of an NDR. Furthermore, we show that on a new class of benchmark instances that is introduced in this paper the running time of our algorithm is highly superior to a well-known pure shortest path algorithm.     

A column generation and branch-and-cut algorithm for the channel assignment problem

We present an exact algorithm for solving the channel assignment problem in cellular telephony networks. This problem consists of assigning sets of channels to the network cells in such a way that the channel demand is satisfied, while avoiding co-channel interference and adjacent channel interference and respecting the channel spacing constraint for each antenna. In a previous article [Jaumard B, Marcotte O, Meyer C, Vovor T. Comparison of column generation models for channel assignment in cellular networks. Discrete Applied Mathematics 2002; 118:299–322], we formulated this problem as a covering problem in two different ways and compared these two formulations and another formulation both from a theoretical and computational point of view (by solving their linear relaxations). In the present article we focus on the best set covering formulation, where the subsets are sets of cells that can be assigned the same channel, and we actually solve two versions of the integer program. In the first version, we seek to minimize the unmet demand, while in the second, we seek to minimize the overall interference while assigning the required number of channels to each cell. In either version, the integer program is solved by an algorithm combining the column generation technique and a branch-and-cut scheme. Finally, we present the solutions produced by these algorithms for some instances of European networks and real-life instances supplied by the Bell Mobilité company.     

A hybrid Hopfield network-genetic algorithm approach for the terminal assignment problem

This paper presents a hybrid Hopfield network-genetic algorithm (GA) approach to tackle the terminal assignment (TA) problem. TA involves determining minimum cost links to form a communications network, by connecting a given set of terminals to a given collection of concentrators. Some previous approaches provide very good results if the cost associated with assigning a single terminal to a given concentrator is known. However, there are situations in which the cost of a single assignment is not known in advance, and only the cost associated with feasible solutions can be calculated. In these situations, previous algorithms for TA based on greedy heuristics are no longer valid, or fail to get feasible solutions. Our approach involves a Hopfield neural network (HNN) which manages the problem's constraints, whereas a GA searches for high quality solutions with the minimum possible cost. We show that our algorithm is able to achieve feasible solutions to the TA in instances where the cost of a single assignment in not known in advance, improving the results obtained by previous approaches. We also show the applicability of our approach to other problems related to the TA.     

An algorithm for the selection problem

A refinement to a well-known selection algorithm is described. The refinement results in a useful improvement in the performance of the original algorithm, particularly when the selection index is small relative to the median.