27619841
Dynamic programming algorithms for the conditional covering problem on path and extended star graphs
The Conditional Covering Problem (CCP) is a facility location problem on a graph, where the set of nodes represents demand points and potential facility locations. The key aspect of the CCP is that each facility covers all nodes within a given facility-specific coverage radius, except for the node at which it is located. The objective of this problem is to minimize the sum of the facility location costs required to cover all demand points. We first discuss the worst-case complexity of the CCP by examining literature related to the total domination problem, which is a special case of the CCP. Next, we examine the special case of path graphs and provide an O(n2) algorithm for its solution. Finally, we leverage information obtained from this procedure to derive an optimal algorithm for “extended star” graphs (multiple paths having one node in common), without increasing the worst-case complexity of the algorithm. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(4), 177–185 2005
44866557
A Multiple-Criterion Model for Machine Scheduling
We consider a scheduling problem involving a single processor being utilized by two or more customers. Traditionally, such scenarios are modeled by assuming that each customer has the same criterion. In practice, this assumption may not hold. Instead of using a single criterion, we examine the implications of minimizing an aggregate scheduling objective function in which jobs belonging to different customers are evaluated based on their individual criteria. We examine three basic scheduling criteria: minimizing makespan, minimizing maximum lateness, and minimizing total weighted completion time. Although determining a minimum-cost schedule according to any one of these criteria is polynomially solvable, we demonstrate that when minimizing a mix of these criteria, the problem becomes NP-hard.
37305588
A dynamic programming algorithm for the conditional covering problem on tree graphs
In a previous article, we presented algorithms for solving the Conditional Covering Problem (CCP) on path and extended star graphs. The CCP on these graphs can be solved in O(n2) time, where n is the number of nodes in the graph. In this article, we propose a new dynamic programming procedure to solve the CCP on tree graphs. This recursion works from the leaf nodes of the tree up to the root node, using notions of protected and unprotected costs as done for the CCP path algorithm in our previous work. We introduce new preliminary routines and data structures to merge information from subpaths and subtrees, resulting in an O(n4) algorithm to optimally solve the problem. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(4), 186–197 2005
41948538
Enhanced Model Representations for an Intra-Ring Synchronous Optical Network Design Problem Allowing Demand Splitting
In this paper, we consider a network design problem arising in the context of deploying synchronous optical networks (SONET) using a unidirectional path switched ring architecture, a standard of transmission using optical fiber technology. Given several rings of this type, the problem is to find an assignment of nodes to possibly multiple rings, and to determine what portion of demand traffic between node pairs spanned by each ring should be allocated to that ring. The constraints require that the demand traffic between each node pair should be satisfiable given the ring capacities, and that no more than a specified maximum number of nodes should be assigned to each ring. The objective function is to minimize the total number of node-to-ring assignments, and hence, the capital investment in add-drop multiplexer equipments. We formulate the problem as a mixed-integer programming model, and propose several alternative modeling techniques designed to improve the mathematical representation of this problem. We then develop various classes of valid inequalities for the problem along with suitable separation procedures for tightening the representation of the model, and accordingly, prescribe an algorithmic approach that coordinates tailored routines with a commercial solver (CPLEX). We also propose a heuristic procedure which enhances the solvability of the problem and provides bounds within 5--13% of the optimal solution. Promising computational results are presented that exhibit the viability of the overall approach and that lend insights into various modeling and algorithmic constructs.
18781640
An Analysis of the Alias Method for Discrete Random-Variate Generation
This paper introduces and studies an optimization problem related to the alias method for discrete random-variate generation. The alias method is an efficient method to generate random variates from a discrete probability distribution. The efficiency of the alias method can be improved by designing the alias table such that the expected number of computations that must be performed per value generated is minimized. The problem of optimizing the construction of the alias table is proven to be strongly NP-hard, even if either of two variations of the alias method relaxing the alias-table-generation restrictions are used. Integer-programming formulations describing these three optimization problems are presented, and insights regarding necessary optimality criteria and relationships among their optimal solutions are discussed.
10698762
Exact and heuristic algorithms for solving the generalized minimum filter placement problem
We consider a problem of placing route-based filters in a communication network to limit the number of forged address attacks to a prescribed level. Nodes in the network communicate by exchanging packets along arcs, and the originating node embeds the origin and destination addresses within each packet that it sends. In the absence of a validation mechanism, one node can send packets to another node using a forged origin address to launch an attack against that node. Route-based filters can be established at various nodes on the communication network to protect against these attacks. A route-based filter examines each packet arriving at a node, and determines whether or not the origin address could be legitimate, based on the arc on which the packet arrives, the routing information, and possibly the destination. The problem we consider seeks to find a minimum cardinality subset of nodes to filter so that the prescribed level of security is achieved. We formulate a mixed-integer programming model for the problem and derive valid inequalities for this model by identifying polynomially-solvable subgraphs of the communication network. We also present three heuristics for solving the filter placement problem and evaluate their performance against the optimal solution provided by the mixed-integer programming model.
15346455
An Adaptive Poly-Parental Recombination Strategy
A genetic recombination framework is presented within which both the unit of inheritance of genetic material from a parent, and the number of parents involved in the creation of a new individual are potentially learnt through the evolution of competing subpopulations representing different strategies.
2766632
On Appropriate Adaptation Levels for the Learning of Gene Linkage
A number of algorithms have been proposed aimed at tackling the problem of learning “Gene Linkage” within the context of genetic optimisation, that is to say, the problem of learning which groups of co-adapted genes should be inherited together during the recombination process. These may be seen within a wider context as a search for appropriate relations which delineate the search space and “guide” heuristic optimisation, or, alternatively, as a part of a comprehensive body of work into Adaptive Evolutionary Algorithms.In this paper, we consider the learning of Gene Linkage as an emergent property of adaptive recombination operators. This is in contrast to the behaviour observed with fixed recombination strategies in which there is no correspondence between the sets of genes which are inherited together between generations, other than that caused by distributional bias. A discrete mathematical model of Gene Linkage is introduced, and the common families of recombination operators, along with some well known linkage-learning algorithms, are modelled within this framework. This model naturally leads to the specification of a recombination operator that explicitly operates on sets of linked genes.Variants of that algorithm, are then used to examine one of the important concepts from the study of adaptivity in Evolutionary Algorithms, namely that of the level (population, individual, or component) at which learning takes place. This is an aspect of adaptation which has received considerable attention when applied to mutation operators, but which has been paid little attention in the context of adaptive recombination operators and linkage learning. It is shown that even with the problem restricted to learning adjacent linkage, the population based variants are not capable of correctly identifying building blocks. This is in contrast to component level adaptation which outperforms conventional operators whose bias is ideal for the problems considered.
17816721
Triangle Guarding
We consider the problem of triangle guarding ( -guarding) a simple, 2D polygon Q. A polygon Q is -guarded if every point q of Q is contained in the convex hull of some three guards that can all see q. This rather odd condition approximates a desire, for example, to see all sides of q or to locate (via triangulation) q from at least two angularly well-separated views. If we restrict the guards to lie in Q and Q has a transparent boundary then the vertices of the convex hull of Q (CH (Q)) form the minimum set of -guards. We examine two other variations of the problem. In the first, the guards may be placed within a transparent border surrounding Q. For this variation, we describe a polynomial time algorithm, related to the classic algorithm for finding min-link separators, that finds a minimum set of -guards. In the second, we consider the case where Q’s boundary is opaque and show that, as in the traditional art gallery problem, finding a minimum set of vertex -guards is NP-hard. Transparent Fences Given simple polygons P and Q with Q contained in P , where |Q|+ |P | = n, what is the minimum number and placement of guards in P needed to -guard Q, assuming that both Q and P have transparent boundaries? Our algorithm for this problem is inspired by an algorithm for finding min-link separators between two convex polygons, one contained in the other [1]. The following basic lemmas motivate using this approach. Define legal regions to be regions of the outer polygon P , that are not contained in the interior of CH (Q) (Figure 1).
14227060
Visualization of design knowledge component relationships to facilitate reuse
Within the software development process, reuse at the requirements level has become an increasingly more compelling notion. Following a human-centric approach, this work focuses on both requirements and design solution reuse using a design knowledge repository. In recent years, many improvements have been made to increase reuse through design knowledge repositories, but retrieval of knowledge in the context of design activities continues to be a formidable challenge. We propose a new system, called CERVi, to browse a repository through visualization by exploiting relationships between units of knowledge (in our case, claims). These relationships are key to finding the most appropriate reusable knowledge based on design conditions. Testing shows that CERVi enhances the design knowledge selection process and helps users proceed through structured design decision making. Our approach would be most useful to those interested in unlocking the potential of design knowledge reuse.
17502763
Alignment Of Protein Structures With A Memetic Evolutionary Algorithm
CATEGORY: Real-World Applications 
 
Structural comparison of proteins is a core problem in modern biomedical research. Identifying structural similarities is essential for the assessment of the relationship between structure and function in proteins, and structural comparison techniques play a key role in applications like rational drug design. In this paper we consider a technique for protein structure comparison known as the maximum contact map overlap problem. In this problem, the similarity between two protein structures is computed by aligning the proteins to maximize the number of shared contacts in their corresponding contact maps. 
 
We present a new approach to this problem that uses a Multimeme evolutionary algorithm. The best solution found by our algorithm provides a lower bound on the value of the optimal structural alignment between the proteins. We have evaluated the Multimeme algorithm on a range of benchmark problems and compared with previous heuristics. We apply a linear programming method, which provides an upper bound, to assess the accuracy of our solutions. Our experiments show that the Multimeme evolutionary algorithm represents a significant improvement on the current state of the art in metaheuristics for this problem.