Verbal ordinal classification with multicriteria decision aiding

Professionals in neuropsychology usually perform diagnoses of patients’ behaviour in a verbal rather than in a numerical form. This fact generates interest in decision support systems that process verbal data. It also motivates us to develop methods for the classification of such data. In this paper, we describe ways of aiding classification of a discrete set of objects, evaluated on set of criteria that may have verbal estimations, into ordered decision classes. In some situations, there is no explicit additional information available, while in others it is possible to order the criteria lexicographically. We consider both of these cases. The proposed Dichotomic Classification (DC) method is based on the principles of Verbal Decision Analysis (VDA). Verbal Decision Analysis methods are especially helpful when verbal data, in criteria values, are to be handled. When compared to the previously developed Verbal Decision Analysis classification methods, Dichotomic Classification method performs better on the same data sets and is able to cope with larger sizes of the object sets to be classified. We present an interactive classification procedure, estimate the effectiveness and computational complexity of the new method and compare it to one of the previously developed Verbal Decision Analysis methods. The developed and studied methods are implemented in the framework of a decision support system, and the results of testing on artificial sets of data are reported.     

NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point

Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers’ hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates the previous one. Although only the last solution will be Pareto optimal, the decision maker never looses sight of the Pareto optimal set, and the search is oriented so that (s)he progressively focusses on the preferred part of the Pareto optimal set. Each new solution is obtained by minimizing an achievement scalarizing function including preferences about desired improvements in objective function values. NAUTILUS is specially suitable for avoiding undesired anchoring effects, for example in negotiation support problems, or just as a means of finding an initial Pareto optimal solution for any interactive procedure. An illustrative example demonstrates how this new method iterates.     

An enantioselective synthesis of the C(33)-C(37) fragment of Amphotericin B

An enantioselective synthesis of the C(33)-C(37) tripropionate fragment of Amphotericin B has been developed in only 6 steps.     

Oxidation of crocein orange G by lignin peroxidase isoenzymes

The ligninolytic enzyme system ofPhanerochaete chrysosporiun is able to decolorize several recalcitrant dyes. Three lignin peroxidase isoenzymes, LiP 3.85, LiP 4.15, and LiP 4.65, were purified by preparative isoelectric focusing from the carbon-limited culture medium ofP. chrysosporium. Based on amino terminal sequences, the purified isoenzymes correspond to the isoenzymes H8, H6, and H2, respectively, from theN-limited culture. The purified isoenzymes were used for decolorization of an azo dye, Crocein Orange G (COG). According to the kinetic data obtained, the oxidation of COG by lignin peroxidase appeared to follow Michaelis-Menten kinetics. Kinetic parameters for each isoenzyme were determined. The inactivating effect of ascending H₂O₂ concentrations on COG oxidation is shown to be exponential within the used concentration range. The best degree of decolorization of 100 μM COG was obtained when the H₂O₂ concentration was 150 μM. This was also the lowest H₂O₂ concentration for maximal decolorization of 100 μM COG, regardless of the amount of lignin peroxidase used in the reaction.     

A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes

In this paper, we develop a version of the bundle method to solve unconstrained difference of convex (DC) programming problems. It is assumed that a DC representation of the objective function is available. Our main idea is to utilize subgradients of both the first and second components in the DC representation. This subgradient information is gathered from some neighborhood of the current iteration point and it is used to build separately an approximation for each component in the DC representation. By combining these approximations we obtain a new nonconvex cutting plane model of the original objective function, which takes into account explicitly both the convex and the concave behavior of the objective function. We design the proximal bundle method for DC programming based on this new approach and prove the convergence of the method to an \(\varepsilon \)-critical point. The algorithm is tested using some academic test problems and the preliminary numerical results have shown the good performance of the new bundle method. An interesting fact is that the new algorithm finds nearly always the global solution in our test problems.     

On cone characterizations of weak, proper and Pareto optimality in multiobjective optimization

Efficient, weakly and properly Pareto optimal solutions of multiobjective optimization problems can be characterized with the help of different cones. Here, contingent, tangent and normal cones as well as cones of feasible directions are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.