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The training of a Multi-Layer Perceptron (MLP) classifier is considered as a Combinatorial Optimization task and solved using the Reactive Tabu Search (RTS) method. RTS needs only forward passes (no derivatives) and does not require high precision network parameters. TOTEM, a special-purpose VLSI chip, was developed to take advantage of the limited memory and processing requirements of RTS: the final system effects a very close match between hardware and training algorithm. The RTS algorithm and the design of TOTEM are discussed, together with the operational characteristics of the VLSI chip and some preliminary training and generalization tests on triggering tasks.

We propose a dynamical model for reaching consensus in group decision making based on the interplay between a gradual diffusion mechanism and an individual aversion to opinion changing We illustrate our model in the one dimensional case, when each decison maker chooses between only .two alternatives. KeywordsGroup decision making, fuzzy preference relations, consensus optimization, opinion changing aversion, dynamic models. Decison makers and preferencematrices Our starting point is a set of individual fuzzy preference relations. Let (k = 1, . . ..m} be an index set for a group of decision makers and A = {ai,i = 1, . . . . n} a set of decisional alternatives. Each decison maker builds its individual fuzzy preference relation rk : A x A -[0, l] actor-ding to the following semantics: if T-Z denotes rkk(u,,aj), then T-I: = 1 when ai is definitely preferred over oj and rf;; = 0 when aj "Petmission to copy without fee ail or part of this material is gantcd provided that the copies are not made or distributed for direct c~ahl advantage. the ACM copyright notice and the title of the publication and its date appear, and notice is givea that copying is by permission Of the ~~sociaacm for computing ~~hitwy.TO copy otherwise. or 10 rcpubld. requires a fee m&or specific petmission." 8 1995 ACM 0-89791-658-l 95 OC02 3.50 493 is definitely preferred over Q+ When the two alternatives ai and aj are indifferent T& = 0.5. Consistently, the matrix elements $ associated with the fuzzy preferences are required to satisfy the following constraints: r$ +T;~ = 1 and r/j = 0.5. The simplest example of group decision process corresponds to the case in which each decision maker is given a choice between only two, alternatives: i,j = 1,2. Accordingly, the preference matrix T$ of the decision maker k has only one independent element, say r&. If we denote it by rk, we can write the preference matrix elements as Tf2 = Tk , T;l = 1 -Tk , Tfl = T& = 0.5We shall refer to this single degree of freedom case in order to illustrate our dynamic model of consensus. 2.Dissensus between two decision makers Given the fuzzy preferences T$ one can construct a measure of dissensus V(k, k') E [O, 1) ,

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