The multiple-choice multi-period knapsack problem sits in the interface of multiple choice programming and knapsack problems. Previous studies of this problem had attempted to find its optimal solution through the branch-and-bound procedure using special-ordered-sets. In this paper, we propose another solution approach based on the dynamic programming to locate its optimal solution through the ...

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0– 1 problems. Furthermore, its tractability is highlighted. Then, an op...

This paper presents a layered encoding cascade evolutionary approach to solve a 0/1 knapsack optimization problem. A layered encoding structure is proposed and developed based on the schema theorem and the concepts of cascade correlation and multi-population evolutionary algorithms. Genetic algorithm (GA) and particle swarm optimization (PSO) are combined with the proposed layered encoding stru...

Multi-fuzzy set theory is an extension of fuzzy set theory, L-fuzzy set theory and Atanassov intuitionistic fuzzy set theory. In this paper we study the relation between Atanassov intuitionistic fuzzy and the proposed extension called Multi-fuzzy. Also we present the notion of Multi-fuzzy mappings and Atanassov Intuitionistic Fuzzy Sets Generating Maps. Mathematics Subject Classification: MSC: ...

supplier selection is one of the most important activities of purchasing departments. this importance is increased even more by new strategies in a supply chain, because of the key role suppliers perform in terms of quality, costs and services which affect the outcome in the buyer’s company. supplier selection is a multiple criteria decision making problem in which the objectives are not equall...

We assume that a flat space E with translation space V is given and we put n := dimE = dimV. Let B be a norming cell of V (see Vol.I, Sect.51). A concept of volume for the space E should have the following property: If the norming cell B has volume 1, then a cell in E modelled on B of a given scale s ∈ P I has volume s. (Recall that such a cell is a set of the form q + sB, with q ∈ E .) Intuiti...

Λ(A)(f) = (−1)A(u)(delp(f)) + (−1) A(u)(delq(f)). (11.5) It is clear from (11.4) and the definition (11.2) that delp(f) = del(p+1)(f). Hence the two terms on the right side of (11.5) cancel and we have Λ(A)(f) = 0. Since the non-injective f ∈ Vk+1 with adjacent repeated terms was arbitrary, it follows from Prop.9 of Sect.11 that Λ(A) is skew. In View of the Lemma, we may regard (11.3) as the de...