Real time task scheduling allowing fuzzy due dates

The paper deals with periodical task scheduling. The tasks are described by fuzzy due dates and fuzzy execution times. The goal of scheduling is to find an optimal assignment of priorities such that the satisfaction associated with due dates and execution times be minimized. The paper shows how the rules associated with task priorities improve the optimal assignment search.     

Recovering Beam Search: Enhancing the Beam Search Approach for Combinatorial Optimization Problems

A hybrid heuristic method for combinatorial optimization problems is proposed that combines different classical techniques such as tree search procedures, bounding schemes and local search. The proposed method enhances the classic beam search approach by applying to each partial solution corresponding to a node selected by the beam, a further test that checks whether the current partial solution is dominated by another partial solution at the same level of the search tree. If this is the case, the latter solution becomes the new current partial solution. This step allows to partially recover from previous wrong decisions of the beam search procedure and can be seen as a local search step on the partial solution. We present here the application to two well known combinatorial optimization problems: the two-machine total completion time flow shop scheduling problem and the uncapacitated p-median location problem. In both cases the method strongly improves the performances with respect to the basic beam search approach and is competitive with the state of the art heuristics.     

Three-dimensional coronary artery MR imaging using prospective real-time respiratory navigator and linear phase shift processing: comparison with conventional coronary angiography.

Respiratory gating with navigator echo is a recent technique to detect diaphragm position in 3D magnetic resonance (MR) coronary angiography. The purpose of our study was to image proximal coronary arteries and to detect significant stenoses in patients with coronary artery diseases and to compare with contrast enhanced angiography results. Twenty patients with coronary artery diseases who were referred for conventional angiography underwent magnetic resonance angiography (MRA). Three-dimensional gradient echo volumes were acquired using cardiac and respiratory gating and fat suppression. Using reformatted oblique planes and maximum intensity projection technique, visualization coronary segments and detection of significant coronary stenoses were made. Eighty-three coronary segments were analyzed. The sensitivity and specificity were 65% and 93%, respectively. The corresponding positive and negative predictive values were 69% and 91%. This study shows the ability to image correctly coronary arteries and to identify proximal stenoses, but image quality need to be improved for an efficiency detection of coronary artery stenoses in clinical practice.     

EVE-OPT: a hybrid algorithm for the capacitated vehicle routing problem

This paper presents EVE-OPT, a Hybrid Algorithm based on Genetic Algorithms and Taboo Search for solving the Capacitated Vehicle Routing Problem. Several hybrid algorithms have been proposed in recent years for solving this problem. Despite good results, they usually make use of highly problem-dependent neighbourhoods and complex genetic operators. This makes their application to real instances difficult, as a number of additional constraints need to be considered. The algorithm described here hybridizes two very simple heuristics and introduces a new genetic operator, the Chain Mutation, as well as a new mutation scheme. We also apply a procedure, the k-chain-moves, able to increase the neighbourhood size, thereby improving the quality of the solution with negligible computational effort. Despite its simplicity, EVE-OPT is able to achieve the same results as very complex state-of-the art algorithms.     

A new decomposition approach for the single machine total tardiness scheduling problem

This paper deals with the single machine total tardiness problem. From Emmons’ basic dominance conditions a new partition theorem is derived which generalises Lawler’s decomposition rule and leads to a new double decomposition procedure. This procedure is embedded into a branch and bound method which applies a new lower bound based on due dates reassignment. The branch and bound method is tested on problems with size up to 150 jobs.     

Minimising makespan in the two-machine flow-shop with release times

This paper considers the two-machine flow-shop problem with the objective of minimising the makespan subject to different release times. In view of the strongly NP-hard nature of this problem, five lower bounds and two new dominance criteria are proposed together with a decomposition procedure that reduces the problem size by setting jobs at the beginning of the sequence. Several branch and bound procedures are described by applying different lower bounds and branching schemes. A detailed computational campaign has been performed on different kinds of instances testing problems with size up to 200 jobs.     

Stochastic single machine scheduling problem as a multi-stage dynamic random decision process

In this work, we study a stochastic single machine scheduling problem in which the features of learning effect on processing times, sequence-dependent setup times, and machine configuration selection are considered simultaneously. More precisely, the machine works under a set of configurations and requires stochastic sequence-dependent setup times to switch from one configuration to another. Also, the stochastic processing time of a job is a function of its position and the machine configuration. The objective is to find the sequence of jobs and choose a configuration to process each job to minimize the makespan. We first show that the proposed problem can be formulated through two-stage and multi-stage Stochastic Programming models, which are challenging from the computational point of view. Then, by looking at the problem as a multi-stage dynamic random decision process, a new deterministic approximation-based formulation is developed. The method first derives a mixed-integer non-linear model based on the concept of accessibility to all possible and available alternatives at each stage of the decision-making process. Then, to efficiently solve the problem, a new accessibility measure is defined to convert the model into the search of a shortest path throughout the stages. Extensive computational experiments are carried out on various sets of instances. We discuss and compare the results found by the resolution of plain stochastic models with those obtained by the deterministic approximation approach. Our approximation shows excellent performances both in terms of solution accuracy and computational time.

     

Computing the asymptotic worst-case of bin packing lower bounds

This paper addresses the issue of computing the asymptotic worst-case of lower bounds for the Bin Packing Problem. We introduce a general result that allows to bound the asymptotic worst-case performance of any lower bound for the problem and to derive for the first time the asymptotic worst-case of the well-known bound L₃ by Martello and Toth. We also show that the general result allows to easily derive the asymptotic worst-case of several lower bounds proposed in the literature.     

The Multi-Handler Knapsack Problem under Uncertainty

The Multi-Handler Knapsack Problem under Uncertainty is a new stochastic knapsack problem where, given a set of items, characterized by volume and random profit, and a set of potential handlers, we want to find a subset of items which maximizes the expected total profit. The item profit is given by the sum of a deterministic profit plus a stochastic profit due to the random handling costs of the handlers. On the contrary of other stochastic problems in the literature, the probability distribution of the stochastic profit is unknown. By using the asymptotic theory of extreme values, a deterministic approximation for the stochastic problem is derived. The accuracy of such a deterministic approximation is tested against the two-stage with fixed recourse formulation of the problem. Very promising results are obtained on a large set of instances in negligible computing time.     

The multi-stage dynamic stochastic decision process with unknown distribution of the random utilities

We consider a decision maker who performs a stochastic decision process over a multiple number of stages, where the choice alternatives are characterized b