Three-linking in Eulerian digraphs
The effective scheduling of operations in batch plants has a great potential for high economic returns, in which the formulation and an optimal solution algorithm are the main issues of study. Petri nets have proven to be a promising technique for solving many difficult problems associated with the modelling, formal analysis, design and coordination control of discrete-event systems. One of the major advantages of using a Petri-net model is that the same model can be used for the analysis of behavioural...
Fuzzy algebra is a special type of algebraic structure in which classical addition and multiplication are replaced by maximum and minimum (denoted and , respectively). The eigenproblem is the search for a vector (an eigenvector) and a constant (an eigenvalue) such that , where is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation with given matrices and unknown constant and vector . Generalized eigenvectors have interesting...
Minimizing shutterings assembling time on construction sites can yield significant savings in labor costs and crane moves. It requires solving a pairing problem that optimizes the ability for the crane to move chains of shutterings as a whole when they can be later reused together to frame another wall of the site. In this paper, we show that this problem is NP-hard in the strong sense as well as both its multiflow and ordering aspects. We also introduce a linear relaxation that computes reasonably...
In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure y+ onto a measure y- with the same mass. This approach is realistic for simple good distribution networks (water, electric power,. ..) but it is no more realistic when we want to specify who goes where, like in the mailing problem or the optimal urban traffic network problem. In this paper, we present a new framework generalizing the former approathes...
For a multidimensional control problem involving controls , we construct a dual problem in which the variables ν to be paired with u are taken from the measure space rca (Ω,) instead of . For this purpose, we add to a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.
In this paper we deal with the preemptive asymmetric stacker crane problem in a heuristic way. We first present some theoretical results which allow us to turn this problem into a specific tree design problem. We next derive from this new representation an integer linear programming model together with simple and efficient greedy and local search heuristics. We conclude by presenting experimental results which aim at both testing the efficiency of our heuristic and evaluating the impact of the...
In this paper we deal with the preemptive asymmetric stacker crane problem in a heuristic way. We first present some theoretical results which allow us to turn this problem into a specific tree design problem. We next derive from this new representation an integer linear programming model together with simple and efficient greedy and local search heuristics. We conclude by presenting experimental results which aim at both testing the efficiency of our heuristic and evaluating the impact of the...