Chance-constrained programming with fuzzy stochastic coefficients

International audienceWe consider fuzzy stochastic programming problems with a crisp objective function and linear constraints whose coefficients are fuzzy random variables, in particular of type L-R. To solve this type of problems, we formulate deterministic counterparts of chance-constrained programming with fuzzy stochastic coefficients, by combining constraints on probability of satisfying constraints, as well as their possibility and necessity. We discuss the possible indices for comparing fuzzy quantities by putting together interval orders and statistical preference. We study the convexity of the set of feasible solutions under various assumptions. We also consider the case where fuzzy intervals are viewed as consonant random intervals. The particular cases of type L-R fuzzy Gaussian and discrete random variables are detailed

Hamiltonicity in Partly claw-free graphs


Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such that n such that δ(G) ≥ (n-2)/3, then G is Hamiltonian. We generalize these results by considering the graphs satisfying the following property: for every vertex v ∈ A, there exist exactly two vertices x and y of V\A such that N(v) ⊆ N[x] ∪ N[y]. We extend some other known results on claw-free graphs to this new class of graphs

An Algorithm For Solving Multiple Objective Integer Linear Programming Problem

In the present paper a complete procedure for solving Multiple Objective Integer Linear Programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one

Makespan minimization for two-stage hybrid Flow shop with dedicated machines and additional constraints

International audienc

New Algorithm Permitting the Construction of an Effective Spanning Tree

In this paper, we have done a rapid and very simple algorithm that resolves the multiple objective combinatorial optimization problem. This, by determining a basic optimal solution, which is a strong spanning tree constructed, according to a well-chosen criterion. Consequently, our algorithm uses notions of Bellman’s algorithm to determine the best path of the network, and Ford Fulkerson’s algorithm to maximise the flow value. The Simplex Network Method that permits to reach the optimality conditions manipulates the two algorithms. In short, the interest of our work is the optimization of many criteria taking into account the strong spanning tree, which represents the central angular stone of the network. To illustrate that, we propose to optimize a bi-objective distribution problem

Tangent circle graphs and 'orders'

Consider a horizontal line in the plane and let γ (A) be a collection of n circles, possibly of different sizes all tangent to the line on the same side. We define the tangent circle graph associated to γ (A) as the intersection graph of the circles. We also define an irreflexive and asymmetric binary relation P on A; the pair (a, b) representing two circles of γ (A) is in P iff the circle associated to a lies to the right of the circle associated to b and does not intersect it. This defines a new nontransitive preference structure that generalizes the semi-order structure. We study its properties and relationships with other well-known order structures, provide a numerical representation and establish a sufficient condition implying that P is transitive. The tangent circle preference structure offers a geometric interpretation of a model of preference relations defined by means of a numerical representation with multiplicative threshold; this representation has appeared in several recently published papers. © 2006 Elsevier B.V. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe