In this paper we present a genetic algorithm-based heuristic for non-unicost set covering problems. We propose several modifications to the basic genetic procedures including a new fitness-based crossover operator (fusion), a variable mutation rate and a heuristic feasibility operator tailored specifically for the set covering problem. The performance of our algorithm was evaluated on a large set of randomly generated problems. Computational results showed that the genetic algorithm-based heuristic is capable of producing high-quality solutions. Keywords: genetic algorithms; set covering; optimisation. 1 Introduction The set covering problem (SCP) is the problem of covering the rows of a m-row, n- column, zero-one matrix (a ij ) by a subset of the columns at minimal cost. Defining x j = 1 if column j (with cost c j ? 0) is in the solution and x j = 0 otherwise, the SCP is Minimise n X j=1 c j x j (1) Subject to n X j=1 a ij x j 1, i = 1; : : : ; m (2) x j 2 f0; 1g, j = 1; ...

In this dissertation we report on our efforts to develop a parallel genetic algorithm and apply it to the solution of the set partitioning problem--a difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. We developed a distributed steady-state genetic algorithm in conjunction with a specialized local search heuristic for solving the set partitioning problem. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steady-state genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty real-world set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, high-quality integer feasible solutions were found for problems with 36,699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints.

We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows and 1,000,000 columns, arising from crew scheduling in the Italian Railway Company, Ferrovie dello Stato SpA. In 1994 Ferrovie dello Stato SpA, jointly with the Italian Operational Research Society, organized a competition, called FASTER, intended to promote the development of algorithms capable of producing good solutions for these instances, since the classical approaches meet with considerable difficulties in tackling them. The main characteristics of the algorithm we propose are (1) a dynamic pricing scheme for the variables, akin to that used for solving large-scale LP's, to be coupled with subgradient optimization and greedy algorithms, and (2) the systematic use of column fixing to obtain improved solutions. Moreover, we propose a number of improvements on the standard way o...

This paper surveys much of the classical and current work in the area of path problems on digraphs. After a search of more than sixty five papers that reference Warshall's algorithm, we have concluded that our work on threshold transitive closure has probably not appeared in the literature. This work does not fit easily into any of the previous axiomatic treatments of Warshall's algorithm, and it may be possible to axiomize our work to solve AND/OR path problems, thereby generalizing much of the previous work. 96

Abstract—As the community strives towards autonomous multirobot systems, there is a need for these systems to autonomously form coalitions to complete assigned missions. Numerous coalition formation algorithms have been proposed in the software agent literature. Algorithms exist that form agent coalitions in both super additive and non-super additive environments. The algorithmic techniques vary from negotiation-based protocols in multi-agent system (MAS) environments to those based on computation in distributed problem solving (DPS) environments. Coalition formation behaviors have also been discussed in relation to game theory. Despite the plethora of MAS coalition formation literature, to the best of our knowledge none of the proposed algorithms have been demonstrated with an actual multi-robot system. There exists a discrepancy between the multi-agent algorithms and their applicability to the multi-robot domain. This paper aims to bridge that discrepancy by unearthing the issues that arise while attempting to tailor these algorithms to the multi-robot domain. A well-known multi-agent coalition formation algorithm has been studied in order to identify the necessary modifications to facilitate its application to the multi-robot domain. This paper reports multi-robot coalition formation results based upon simulation and actual robot experiments. A multi-agent coalition formation algorithm has been demonstrated on an actual robot system. Index Terms—Coalition formation, coalition imbalance, task allocation.

This paper discusses the development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steady-state genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of forty real-world problems. It found the optimal solution for half the problems, and good solutions for nine others. The results were compared to those obtained with branch-and-cut and branchand -bound algorithms. The branch-and-cut algorithm was significantly more successful than the hybrid algorithm, and the branch-and-bound algorithm slightly better. 1 Introduction Genetic algorithms (GAs) are search algorithms that were developed by John Holland [17]. They are based on an analogy with natural selection and population genetics. One common application of GAs is for finding approximate solutions to difficult optimization problems. In this paper we describe the application of a hybrid GA (a genetic algorithm combined with a local s...

High transmission speeds, increased burstiness of traffic, and statistical multiplexing of traffic render traditional approaches to network management and control ineffective. This thesis develops insight into the operation and performance of high-speed networks by developing tractable models and approximations. The insight gained is utilized to propose ways of enhancing the efficiency of network resources and facilitating ease of network management and control. Dynamic routing algorithms for routing Virtual Circuits (VCs) in Asynchronous Transfer Mode (ATM) must take into account their heterogeneous bandwidth characteristics and quality of service requirements. We classify ATM networks according to the network characteristics which have the greatest bearing on the performance of dynamic routing algorithms and discuss appropriate routing algorithms for each cla...

A new combinatorial approach for modelling and reconstructing sibling relationships in a single generation of individuals without parental information is proposed in this paper. Simple genetic constraints on the full-sibling groups, imposed by the Mendelian inheritance rules, are employed to investigate data from codominant DNA markers. To extract the minimum number of biologically consistent sibling groups, the proposed combinatorial approach is employed to formulate this minimization problem as a set covering problem, which is a well-known NP-hard combinatorial optimization problem. We conducted a simulation study of a relaxed version of the proposed algorithm to demonstrate that our combinatorial approach is reasonably accurate and the exact version of the sibling relationship construction algorithm should be pursued. In addition, the results of this study suggest that the proposed algorithm will pave our way to a new approach in computational population genetics as it does not require any a priori knowledge about allele frequency, population size, mating system or family size distributions to reconstruct sibling relationships.

The set covering problem (SCP) calls for a minimum cost family of subsets from n given subsets, which together covers the entire ground set. In this paper, we propose a local search algorithm for SCP, which has the following three features. (1) The use of 3-flip neighborhood, which is the set of solutions obtainable from the current solution by exchanging at most three subsets. As the size of 3-flip neighborhood is O(n ), the neighborhood search becomes expensive if implemented naively. To overcome this, we propose an e#cient implementation that reduces the number of candidates in the neighborhood without sacrificing the solution quality. (2) We allow the search to visit infeasible region, and incorporate the strategic oscillation technique. (3) The size reduction of the problem by using the information from the Lagrangian relaxation is incorporated, which turned out to be e#ective in solving very large instances. According to computational comparisons on benchmark instances with other existing heuristic algorithms for SCP, our algorithm performs quite e#ectively for various types of problems, especially for very large-scale instances.

This paper presents the design and implementation of an air-crew assignment system for producing and refining a solution to this problem based on the Artificial Intelligence principles and techniques of abductive reasoning as captured by the framework of Abductive Logic Programming (ALP). The system offers a high-level of flexibility in addressing both the tasks of crew scheduling and rescheduling. It can be used to generate a valid and good quality initial solution and then to help the human operators adjust and refine further this solution in order to meet extra requirements of the problem. These additional needs can arise either due to new foreseen requirements that the company wants to have or experiment with for a particular period in time or due to unexpected events that have occurred while the solution (crew-roster) is in operation. Our work shows the ability and flexibility of abduction, and more specifically of ALP, in tackling problems of this type with complex and changing r...