Preference inference based on Pareto models

In this paper, we consider Preference Inference based on a generalised form of Pareto order. Preference Inference aims at reasoning over an incomplete specification of user preferences. We focus on two problems. The Preference Deduction Problem (PDP) asks if another preference statement can be deduced (with certainty) from a set of given preference statements. The Preference Consistency Problem (PCP) asks if a set of given preference statements is consistent, i.e., the statements are not contradicting each other. Here, preference statements are direct comparisons between alternatives (strict and non-strict). It is assumed that a set of evaluation functions is known by which all alternatives can be rated. We consider Pareto models which induce order relations on the set of alternatives in a Pareto manner, i.e., one alternative is preferred to another only if it is preferred on every component of the model. We describe characterisations for deduction and consistency based on an analysis of the set of evaluation functions, and present algorithmic solutions and complexity results for PDP and PCP, based on Pareto models in general and for a special case. Furthermore, a comparison shows that the inference based on Pareto models is less cautious than some other types of well-known preference model.

Characterizing Paretian Preferences

A characterization of a property of binary relations is of type M if it can be stated in terms of ordered M-tuples of alternatives. A characterization of finite type provides an easy test of whether preferences over a large set of alternatives possesses the property characterized. Unfortunately, there is no characterization of finite type for Pareto representability in R..2. A partial result along the same lines is obtained for Pareto representability in R..k, k .. 2.

Finite Characterizations and Paretian Preferences

A characterization of a property of binary relations is of finite type if it is stated in terms of ordered T-tuples of alternatives for some positive integer T. A characterization of finite type can be used to determine in polynomial time whether a binary relation over a finite set has the property characterized. Unfortunately, Pareto representability in R2 has no characterization of finite type (Knoblauch, 2002). This result is generalized below Rl, l larger than 2. The method of proof is applied to other properties of binary relations.

Continuous Paretian Preferences

Two forms of continuity are defined for Pareto representations of preferences. They are designated continuity and coordinate continuity. Characterizations are given of those Pareto representable preferences that are continuously representable and, in dimension two, of those that are coordinate-continuously representable.

An investigation of higher-order multi-objective optimisation for 3D aerodynamic shape design

We investigate the performance of different variants of a suitably tailored Tabu Search optimisation algorithm on a higher-order design problem. We consider four objective func- tions to describe the performance of a compressor stator row, subject to a number of equality and inequality constraints. The same design problem has been previously in- vestigated through single-, bi- and three-objective optimisation studies. However, in this study we explore the capabilities of enhanced variants of our Multi-objective Tabu Search (MOTS) optimisation algorithm in the context of detailed 3D aerodynamic shape design. It is shown that with these enhancements to the local search of the MOTS algorithm we can achieve a rapid exploration of complicated design spaces, but there is a trade-off be- tween speed and the quality of the trade-off surface found. Rapidly explored design spaces reveal the extremes of the objective functions, but the compromise optimum areas are not very well explored. However, there are ways to adapt the behaviour of the optimiser and maintain both a very efficient rate of progress towards the global optimum Pareto front and a healthy number of design configurations lying on the trade-off surface and exploring the compromise optimum regions. These compromise solutions almost always represent the best qualitative balance between the objectives under consideration. Such enhancements to the effectiveness of design space exploration make engineering design optimisation with multiple objectives and robustness criteria ever more practicable and attractive for modern advanced engineering design. Finally, new research questions are addressed that highlight the trade-offs between intelligence in optimisation algorithms and acquisition of qualita- tive information through computational engineering design processes that reveal patterns and relations between design parameters and objective functions, but also speed versus optimum quality. © 2012 AIAA.

Reasoning with sorted-pareto dominance and other qualitative and partially ordered preferences in soft constraints

In decision making problems where we need to choose a particular decision or alternative from a set of possible choices, we often have some preferences which determine if we prefer one decision over another. When these preferences give us an ordering on the decisions that is complete, then it is easy to choose the best or one of the best decisions. However it often occurs that the preferences relation is partially ordered, and we have no best decision. In this thesis, we look at what happens when we have such a partial order over a set of decisions, in particular when we have multiple orderings on a set of decisions, and we present a framework for qualitative decision making. We look at the different natural notions of optimal decision that occur in this framework, which gives us different optimality classes, and we examine the relationships between these classes. We then look in particular at a qualitative preference relation called Sorted-Pareto Dominance, which is an extension of Pareto Dominance, and we give a semantics for this relation as one that is compatible with any order-preserving mapping of an ordinal preference scale to a numerical one. We apply Sorted-Pareto dominance to a Soft Constraints setting, where we solve problems in which the soft constraints associate qualitative preferences to decisions in a decision problem. We also examine the Sorted-Pareto dominance relation in the context of our qualitative decision making framework, looking at the relevant optimality classes for the Sorted-Pareto case, which gives us classes of decisions that are necessarily optimal, and optimal for some choice of mapping of an ordinal scale to a quantitative one. We provide some empirical analysis of Sorted-Pareto constraints problems and examine the optimality classes that result.

Ranking of microRNA target prediction scores by Pareto front analysis

Over the past ten years, a variety of microRNA target prediction methods has been developed, and many of the methods are constantly improved and adapted to recent insights into miRNA-mRNA interactions. In a typical scenario, different methods return different rankings of putative targets, even if the ranking is reduced to selected mRNAs that are related to a specific disease or cell type. For the experimental validation it is then difficult to decide in which order to process the predicted miRNA-mRNA bindings, since each validation is a laborious task and therefore only a limited number of mRNAs can be analysed. We propose a new ranking scheme that combines ranked predictions from several methods and - unlike standard thresholding methods - utilises the concept of Pareto fronts as defined in multi-objective optimisation. In the present study, we attempt a proof of concept by applying the new ranking scheme to hsa-miR-21, hsa-miR-125b, and hsa-miR-373 and prediction scores supplied by PITA and RNAhybrid. The scores are interpreted as a two-objective optimisation problem, and the elements of the Pareto front are ranked by the STarMir score with a subsequent re-calculation of the Pareto front after removal of the top-ranked mRNA from the basic set of prediction scores. The method is evaluated on validated targets of the three miRNA, and the ranking is compared to scores from DIANA-microT and TargetScan. We observed that the new ranking method performs well and consistent, and the first validated targets are elements of Pareto fronts at a relatively early stage of the recurrent procedure. which encourages further research towards a higher-dimensional analysis of Pareto fronts. (C) 2010 Elsevier Ltd. All rights reserved.

Increase of the Delivered Power Probability in Distribution Networks using Pareto DC Programming

A methodology to increase the probability of delivering power to any load point through the identification of new investments in distribution network components is proposed in this paper. The method minimizes the investment cost as well as the cost of energy not supplied in the network. A DC optimization model based on mixed integer non-linear programming is developed considering the Pareto front technique in order to identify the adequate investments in distribution networks components which allow increasing the probability of delivering power for any customer in the distribution system at the minimum possible cost for the system operator, while minimizing the energy not supplied cost. Thus, a multi-objective problem is formulated. To illustrate the application of the proposed methodology, the paper includes a case study which considers a 180 bus distribution network

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Analog circuit synthesis performing fast Pareto frontier exploration and analysis through 3D graphs

This paper presents a technique for performing analog design synthesis at circuit level providing feedback to the designer through the exploration of the Pareto frontier. A modified simulated annealing which is able to perform crossover with past anchor points when a local minimum is found which is used as the optimization algorithm on the initial synthesis procedure. After all specifications are met, the algorithm searches for the extreme points of the Pareto frontier in order to obtain a non-exhaustive exploration of the Pareto front. Finally, multi-objective particle swarm optimization is used to spread the results and to find a more accurate frontier. Piecewise linear functions are used as single-objective cost functions to produce a smooth and equal convergence of all measurements to the desired specifications during the composition of the aggregate objective function. To verify the presented technique two circuits were designed, which are: a Miller amplifier with 96 dB Voltage gain, 15.48 MHz unity gain frequency, slew rate of 19.2 V/mu s with a current supply of 385.15 mu A, and a complementary folded cascode with 104.25 dB Voltage gain, 18.15 MHz of unity gain frequency and a slew rate of 13.370 MV/mu s. These circuits were synthesized using a 0.35 mu m technology. The results show that the method provides a fast approach for good solutions using the modified SA and further good Pareto front exploration through its connection to the particle swarm optimization algorithm.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.