Bicriteria optimisation of the makespan and mean flowtime on two identical parallel machines

This paper proposes an efficient algorithm to solve optimally the bicriteria problem of minimising the weighted sum of makespan and mean flowtime on two identical parallel machines. The proposed algorithm allows the decision-maker to minimise makespan and flowtime simultaneously according to his or her relative preference as reflected through the weights placed on makespan and flowtime. Our computational results show that the proposed algorithm can solve optimally problem instances with a large number of jobs in a reasonably small amount of CPU time.     

Rare event simulation for a slotted time M/G/s model

This paper develops a rare-event simulation algorithm for a discrete-time version of the M/G/s loss system and a related Markov-modulated variant of the same loss model. The algorithm is shown to be efficient in the many-server asymptotic regime in which the number of servers and the arrival rate increase to infinity in fixed proportion. A key idea is to study the system as a measure-valued Markov chain and to steer the system to the rare event through a randomization of the time horizon over which the rare event is induced.     

A new model for the asymmetric vehicle routing problem with simultaneous pickup and deliveries

The asymmetric vehicle routing problem with simultaneous pickup and deliveries is considered. This paper develops four new classes of valid inequalities for the problem. We generalize the idea of a no-good cut. Together, these help us solve 45-node randomly generated problem instances more efficiently. We report results on a set of benchmark instances in literature. In this set, we are able to show an order of magnitude improvement in computational times over currently published results in literature.     

A multi-objective evolutionary optimization approach for an integrated location-inventory distribution network problem under vendor-managed inventory systems

This paper develops a λ mean-hybrid entropy model to deal with portfolio selection problem with both random uncertainty and fuzzy uncertainty. Solving this model provides the investor a tradeoff frontier between security return and risk. We model the security return as a triangular fuzzy random variable, where the investor’s individual preference is reflected by the pessimistic-optimistic parameter λ. We measure the security risk using the hybrid entropy in this model. Algorithm is developed to solve this bi-objective portfolio selection model. Beside, a numerical example is also presented to illustrate this approach.     

Multi-objective optimization for a closed-loop network design problem using an improved genetic algorithm

This paper develops a multi-objective Mixed Integer Programming model for a closed-loop network design problem. In addition to the overall costs, the model optimizes overall carbon emissions and the responsiveness of the network. An improved genetic algorithm based on the framework of NSGA II is developed to solve the problem and obtain Pareto-optimal solutions. An example with 95 cities in China is presented to illustrate the approach. Through randomly generated examples with different sizes; the computational performance of the proposed algorithm is also compared with former genetic algorithms in the literature employing the weight-sum technique as a fitness evaluation strategy. Computational results indicate that the proposed algorithm can obtain superior Pareto-optimal solutions.     

An efficient algorithm to solve connectivity problem on trapezoid graphs

The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs withn vertices andm edges takesO(K(G)mn ^1.5) time, whereK(G) is the vertex connectivity ofG. In this paper, an efficient algorithm is designed to solve vertex connectivity problem, which takesO(n ²) time andO(n) space for a trapezoid graph.     

A branch and bound algorithm for the two-stage assembly scheduling problem

This paper develops a branch and bound algorithm for the two-stage assembly scheduling problem. In this problem, there are m machines at the first stage, each of which produces a component of a job. When all m components are available, a single assembly machine at the second stage completes the job. The objective is to schedule the jobs on the machines so that the maximum completion time, or makespan, is minimized. A lower bound based on solving an artificial two-machine flow shop problem is derived. Also, several dominance theorems are established and incorporated into the branch and bound algorithm. Computational experience with the algorithm is reported for problems with up to 8000 jobs and 10 first-stage machines.     

Algorithms for Large-scale Travelling Salesman Problems

The paper describes a new algorithm to produce r-optimal tours for the travelling salesman problem. This algorithm is faster than the original r-optimal method, and computation times increase much less rapidly with problem size. The new algorithm makes it possible to solve large-scale travelling salesman problems and examples are given for problems varying in size from 100 to 500 cities. The paper also discusses r-optimality in terms of multistage 2-optimality.     

A note on solving large p-median problems

In a previous paper we presented a tree search algorithm for the p-median problem, the problem of locating p facilities (medians) on a network, which was based upon La grangean relaxation and subgradient optimisation. That algorithm solved (optimally) problems with an arbitrary number of medians and having up to 200 vertices.In this note we show that it is possible to enhance that algorithm to solve (optimally) problems having up to 900 vertices using the Cray-1S computer.     

A unitary Hessenberg QR-based algorithm via semiseparable matrices

In this paper, we present a novel method for solving the unitary Hessenberg eigenvalue problem. In the first phase, an algorithm is designed to transform the unitary matrix into a diagonal-plus-semiseparable form. Then we rely on our earlier adaptation of the QR algorithm to solve the dpss eigenvalue problem in a fast and robust way. Exploiting the structure of the problem enables us to yield a quadratic time using a linear memory space. Nonetheless the algorithm remains robust and converges as fast as the customary QR algorithm. Numerical experiments confirm the effectiveness and the robustness of our approach.     

Detecting and Preventing Routing Problems in the Planning Process of CCSS #7 Networks

Common Channel Signalling System #7 (CCSS#7) has become nowadays widely used by most of the operators which are strongly dependant on its performance. This paper develops next issues. First, usual problems with routing in CCSS#7 networks that can not be solved by the protocol are described, and a checking algorithm based on modified dynamic programming techniques is proposed. And secondly, the problem of updating routing tables of nodes and several alternatives to solve it, are presented and compared. Two kind of solutions to solve this second problem are proposed and tested. Conclusions are presented.     

Capacitated Network Design using Bin-Packing

In this paper, we consider the Capacitated Network Design (CND) problem. We investigate the relationship between CND and the Bin-Packing problem. This is exploited for identifying new classes of valid inequalities for the CND problem and developing a branch-and-cut algorithm to solve it efficiently.     

Issues in the implementation of the DSD algorithm for the traffic assignment problem

In this paper we consider the practical implementation of the disaggregated simplicial decomposition (DSD) algorithm for the traffic assignment problem. It is a column generation method that at each step has to solve a huge number of quadratic knapsack problems (QKP). We propose a Newton-like method to solve the QKP when the quadratic functional is convex but not necessarily strictly. Our O(n) algorithm does not improve the complexity of the current methods but extends them to a more general case and is better suited for reoptimization and so a good option for the DSD algorithm. It also allows the solution of many QKP’s simultaneously in a vectorial or parallel way.     

New models for shortest path problem with fuzzy arc lengths

This paper considers the shortest path problem with fuzzy arc lengths. According to different decision criteria, the concepts of expected shortest path, α-shortest path and the most shortest path in fuzzy environment are originally proposed, and three types of models are formulated. In order to solve these models, a hybrid intelligent algorithm integrating simulation and genetic algorithm is provided and some numerous examples are given to illustrate its effectiveness.     

Fast approximate solution of large scale sparse linear systems

In this paper we apply the Fast Approximate Inversion Algorithm of Frederickson to solve a large scale sparse linear system arising from the triangular finite element solution to the second order elliptic problems. The main advantage of this algorithm is that the rate of convergence is independent of n for equations in the class considered. Several approximate inversion techniques for the algorithm are proposed and numerical results for these techniques are also provided.     

The finite criss-cross method for hyperbolic programming

In this paper the finite criss-cross method is generalized to solve hyperbolic (fractional linear) programming problems. Just as in the case of linear or quadratic programming the criss-cross method can be initialized with any, not necessarily feasible basic solution. It is known that if the feasible region of the problem is unbounded then some of the known algorithms fail to solve the problem. Our criss-cross algorithm does not have such drawback. Finiteness of the procedure is proved under the usual mild assumptions. Some small numerical examples illustrate the main features of the algorithm and show that our method generates different iterates than other earlier published methods.     

A Birnbaum-importance based genetic local search algorithm for component assignment problems

This paper considers the component assignment problem (CAP) of finding the optimal assignment of n available components to n positions in a system such that the system reliability is maximized. To solve the CAP, an important type of problems in reliability, we propose a Birnbaum-importance based genetic local search (BIGLS) algorithm in which a local search using the Birnbaum importance is embedded into the genetic algorithm. This paper presents comprehensive numerical tests to compare the performance of the BIGLS with a general genetic algorithm and a Birnbaum-importance based two-stage heuristic. The testing results show that the BIGLS is robust (with respect to its random operations) and effective, and outperforms two benchmark methods in terms of solution quality. It demonstrates the effectiveness of embedding the Birnbaum importance in the local search under the genetic evolutionary mechanism.     

A new penalty function algorithm for convex quadratic programming

In this paper, we develop an exterior point algorithm for convex quadratic programming using a penalty function approach. Each iteration in the algorithm consists of a single Newton step followed by a reduction in the value of the penalty parameter. The points generated by the algorithm follow an exterior path that we define. Convergence of the algorithm is established. The proposed algorithm was motivated by the work of Al-Sultan and Murty on nearest point problems, a special quadratic program. A preliminary implementation of the algorithm produced encouraging results. In particular, the algorithm requires a small and almost constant number of iterations to solve the small to medium size problems tested.     

An analog of Schensted's algorithm for Shifted Young Tableaux

Schensted [Canad. J. Math. 13 (1961)] constructed an algorithm giving a bijective correspondence between permutations and pairs of Young Tableaux. The author develops an analogous algorithm relating permutations and triples consisting of two Shifted Tableaux and a set. Various properties of this algorithm are also examined.     

A bicriteria flowshop scheduling with a learning effect

In many situations, a worker’s ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the learning effect. In this paper the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes a weighted sum of total completion time and makespan. Total completion time and makespan are widely used performance measures in scheduling literature. To solve this scheduling problem, an integer programming model with n² + 6n variables and 7n constraints where n is the number of jobs is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, the problem with up to 30 jobs can be solved. A heuristic algorithm and a tabu search based heuristic algorithm are presented to solve large size problems. Experimental results show that the proposed heuristic methods can solve this problem with up to 300 jobs rapidly. According to the best of our knowledge, no work exists on the bicriteria flowshop with a learning effect.