Using evolutionary algorithms and simulation for the optimization of manufacturing systems

This paper is concerned with an optimization method for manufacturing systems. This method can be applied to optimize problems with any type of variables (variables from a real set, e.g., conveyor speed; an integer set, e.g., size of buffer; or any general set, e.g., dispatching rules). It is based on the association of an evolutionary algorithm and a simulation model. Extensions of Michalewicz's evolutionary operators and algorithm are proposed to tackle manufacturing system problems. The particular case of stochastic models is discussed. This method is applied to an example: the configuration of a workshop producing plastic yoghurt pots. The criterion to optimize is the cost of the workshop and the three variables are the size of a silo, the size of a warehouse and a choice between two manufacturing methods. The application has been realized by connecting an evolutionary algorithm programmed in C and a simulation language.     

VON-FOERSTER'S CONJECTURE—TRIVIAL MACHINES AND ALIENATION IN SYSTEMS

In this paper, we demonstrate how the proper modelling of general systems allows us to address the question of how the actions of many independent but inter-connected agents contribute to a global behaviour. In particular, we apply the techniques of information theory to probabilistic automata to formalize and prove what has come to be known as the ?Von-Foerster conjecture”.

In the first part of this paper we describe Von-Foerster's conjecture in its historical context. In the second part we restate it using formal definitions and we prove it.     

ON FUZZY INTERPOLATION*

Abstract

This note intends to discuss several connections between interpolative reasoning and fuzzy sets and the role played by the extension principle in this connection. It is first recalled how gradual rules can encode linear or non-linear interpolation between precisely known points and can exactly reconstruct any single-input monotonic real function when the membership functions of the fuzzy sets involved in the rules are suitably chosen. Then linear interpolation between fuzzy points is investigated. The interest of gradual rules as opposed to other approximation schemes is singled out.     

Using multi-agent architecture in FMS for dynamic scheduling

The proposed scheduling strategy is based on a multi-agent architecture. Each agent of this architecture is dedicated to a work centre (i.e. a set of resources of the manufacturing system); it selects locally and dynamically the most suitable dispatching rules. Depending on local and global considerations, a new selection is carried out each time a predefined event occurs (for example, a machine becomes available, or a machine breaks down). The selection depends on: (1) primary and secondary performance objectives, (2) the operating conditions, and (3) an analysis of the system state, which aims to detect particular symptoms from the values of certain system variables. We explain how the scheduling strategy is shared out between agents, how each agent performs a local dynamic scheduling by selecting an adequate dispatching rule, and how agents can coordinate their actions to perform a global dynamic scheduling of the manufacturing system. Each agent can be implemented through object-oriented formalisms. The selection method is improved through the optimization of the numerical thresholds used in the detection of symptoms. This approach is compared with the use of SPT, SIX, MOD, CEXSPT and CR/SPT on a jobshop problem, already used in other research works. The results indicate significant improvements.     

FUZZY LABELS,IMPRECISION AND CONTEXTUAL DEPENDENCY Comments on Milan Zelený's “Cognitive Equilibrium: a Knowledge-based Theory of Fuzziness and Fuzzy Sets”

Formal concept analysis is a method of exploratory data analysis that aims at the extraction of natural clusters from object-attribute data tables. The clusters, called formal concepts, are naturally interpreted as human-perceived concepts in a traditional sense and can be partially ordered by a subconcept-superconcept hierarchy. The hierarchical structure of formal concepts (so-called concept lattice) represents a structured information obtained automatically from the input data table. The present paper focuses on the analysis of input data with a predefined hierarchy on attributes thus extending the basic approach of formal concept analysis. The motivation of the present approach derives from the fact that very often, people (consciously or unconsciously) attach various importance to attributes which is then reflected in the conceptual classification based on these attributes. We define the notion of a formal concept respecting the attribute hierarchy. Formal concepts which do not respect the hierarchy are considered not relevant. Elimination of the non-relevant concepts leads to a reduced set of extracted concepts making the discovered structure of hidden concepts more comprehensible. We present basic formal results on our approach as well as illustrating examples.     

A SET-THEORETIC VIEW OF BELIEF FUNCTIONS Logical operations and approximations by fuzzy sets†

A body of evidence in the sense of Shafer can be viewed as an extension of a probability measure, but as a generalized set as well. In this paper we adopt the second point of view and study the algebraic structure of bodies of evidence on a set, based on extended set union, intersection and complementation. Several notions of inclusion are exhibited and compared to each other. Inclusion is used to compare a body of evidence to the product of its projections. Lastly, approximations of a body of evidence under the form of fuzzy sets are derived, in order to squeeze plausibility values between two grades of possibility. Through all the paper, it is pointed out that a body of evidence can account for conjunctive as well as a disjunctive information, i.e. the focal elements can be viewed either as sets of actual values or as restrictions on the (unique) value of a variable.     

Interdiffusion Coefficients in SiO2-K2O Melts

Chemical diffusion coefficients for Si were measured in potassium silicate compositions containing from 64 to 85 wt% SiO₂; unidirectional diffusion couples were heated for 0.1 to 720 h at 600° to 1400°C. The diffusion coefficients, which were calculated by the Boltzmann-Matano method, are described for a silicate containing 70 wt% SiO₂ by:
The diffusion coefficients decreased with increasing O₂ pressure. Below 800°C, the coefficients decreased with increasing SiO₂ concentration; above 800°C, their dependence on SiO₂ concentration was too weak to detect by the methods used. On the basis of a simple structural model for the glass, it was possible, from a phenomenological analysis of the diffusion, to establish a relation between the oxygen self-diffusion coefficient and the chemical diffusion coefficient for a given composition.     

ENERGY PAY-BACK TIME OF PHOTOVOLTAIC MODULES

The energy invested in photovoltaic modules has been investigated on the basis of currently operating commercial production lines in France. The analysis was made for two types of solar cells, polycrystalline silicon and amorphous silicon. The energy which was calculated in this way was compared with the energy produced by these modules under operating conditions in various European climates. An average energy pay-back time of 1.2 years for amorphous silicon modules and 2.1 years for crystalline silicon modules was found. It can be anticipated that these energy pay-back times will decrease in the future.     

ROUGH FUZZY SETS AND FUZZY ROUGH SETS*

The notion of a rough set introduced by Pawlak has often been compared to that of a fuzzy set, sometimes with a view to prove that one is more general, or, more useful than the other. In this paper we argue that both notions aim to different purposes. Seen this way, it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems. First, one may think of deriving the upper and lower approximations of a fuzzy set, when a reference scale is coarsened by means of an equivalence relation. We then come close to Caianiello's C-calculus. Shafer's concept of coarsened belief functions also belongs to the same line of thought. Another idea is to turn the equivalence relation into a fuzzy similarity relation, for the modeling of coarseness, as already proposed by Farinas del Cerro and Prade. Instead of using a similarity relation, we can start with fuzzy granules which make a fuzzy partition of the reference scale. The main contribution of the paper is to clarify the difference between fuzzy sets and rough sets, and unify several independent works which deal with similar ideas in different settings or notations.