Abstract Consider two principles for social evaluation. The first, “laissez-faire”, says that mean-preserving redistribution away from laissez-faire incomes should be regarded as a worsening. This principle captures key aspect of libertarian political philosophy. second, weak Pareto, states an increase in the disposable income each individual improvement. We show combination implies total ought...

In this paper, we propose to integrate particle swarm optimization algorithm into cultural algorithms frame to develop a more efficient cultural particle swarm algorithms (CPSA) for constrained multi-objective optimization problem. In our CPSA, the population space of cultural algorithms consists of n+1 subswarms which are used to search for the n single-objective optimums and an additional mul...

Multi-objective optimisation problems normally have not one but a set of solutions, which are called Pareto-optimal solutions or non-dominated solutions. Once a Pareto-optimal set has been obtained, the decision-maker faces the challenge of analysing a potentially large set of solutions. Selecting one solution over others can be quite a challenging task because the Pareto set can contain an unm...

The Pareto set of a multiobjective optimization problem consists of the solutions for which one or more objectives can not be improved without deteriorating one or more other objectives. We consider problems with linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large...