Virtual interpolation of discrete multi-objective programming solutions with probabilistic operation

This work presents a novel framework to address the long term operation of a class of multi-objective programming problems. The proposed approach considers a stochastic operation and evaluates the long term average operating costs/profits. To illustrate the approach, a two-phase method is proposed which solves a prescribed number of K monoobjective problems to identify a set of K points in the Paretooptimal region. In the second phase, one searches for a set of non-dominated probability distributions that define the probability that the system operates at each point selected in the first phase, at any given operation period. Each probability distribution generates a vector of average long-term objectives and one solves for the Pareto-optimal set with respect to the average objectives. The proposed approach can generate virtual operating points with average objectives that need not have a feasible solution with an equal vector of objectives. A few numerical examples are presented to illustrate the proposed method

The political form of the constitution: the separation of powers, rights and representative democracy

According to article 16 of the French Declaration of the Rights of Man and of the Citizen of 1789, 'A society where rights are not secured or the separation of powers established has no constitution at all'. Together with representative government, which to a large extent was assimilated to the second, these two principles have defined constitutionalism. In recent years. however, the first has come to predominate. This article suggests an alternative story. I shall argue that both historically and substantively liberal rights-based constitutionalism must be located within a more republican conception of the constitution as a system of politics.’ I begin by analysing the main features and problems of the doctrine of the separation of powers, and its relationship to rights and the rule of law. I then survey the historical development of the theory. I note how it was first combined with organic theories of mixed government and the balancing of powers within the body politic, and then transformed by the view of political societies as a popular construct and incorporated within representative democracy