The purpose of this note– inspired by and using a number of properties from Barbara and Jackson [2] – is to characterize the Pareto dominance relation. The set-up and interpretation is completely analogous to [2]. In particular, situations are considered where different actions are to be compared on the basis of their consequences, which are described by vectors of real numbers. Ranking actions...

PURPOSE To introduce a method to simultaneously explore a collection of Pareto surfaces. The method will allow radiotherapy treatment planners to interactively explore treatment plans for different beam angle configurations as well as different treatment modalities. METHODS The authors assume a convex optimization setting and represent the Pareto surface for each modality or given beam set by...

We describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in R, and are typically only partially ordered. These can still be solved by a variable elimination algorithm, leading to a set of maximal values of expected utility. If the Pareto ordering is used this set can often be prohibitively large. We consider approximate representations of ...

We consider one type of stability (quasistability) of a vector combinatorial problem of finding the Pareto set. Under quasistability we understand a discrete analogue of lower semicontinuity by Hausdorff of the many-valued mapping, which defines the Pareto choice function. A vector problem on a system of subsets of a finite set (trajectorial problem) with non-linear partial criteria is in focus...

Commercial plant breeders improve economically important traits by selectively mating individuals from a given breeding population. Potential pairings are evaluated before the growing season using Monte Carlo simulation, and a mating design is created to allocate a fixed breeding budget across the parent pairs to achieve desired population outcomes. We introduce a novel objective function for t...

Many real-world optimization problems involve multiple conflicting objectives and the use of evolutionary algorithms to solve the problems has attracted much attention recently. This paper investigates the application of multi-objective optimization technique for the design of a Thyristor Controlled Series Compensator (TCSC)-based controller to enhance the performance of a power system. The des...

In general, Multi-objective Evolutionary Algorithms do not guarantee find solutions in the Pareto-optimal set. We propose a new approach for solving decomposable deceptive multi-objective problems that can find all solutions of the Pareto-optimal set. Basically, the proposed approach starts by decomposing the problem into subproblems and, then, combining the found solutions. The resultant appro...

1 Abstract Pareto optimal designs are the best designs that can be produced for a given problem formulation for a given set of criteria when the criteria are not combined in any way. If the goal is to improve the performance in those criteria then it is possible to manipulate the problem formulation to achieve an improvement. The approach adopted is to encode the formulation in a genetic algori...

Although there are many versions of evolutionary algorithms that are tailored to multi–criteria optimization, theoretical results are apparently not yet available. Here, it is shown that results known from the theory of evolutionary algorithms in case of single criterion optimization do not carry over to the multi–criterion case. At first, three different step size rules are investigated numeri...

Standard single-objective methods such as value iteration are not applicable to multi-objective Markov decision processes (MOMDPs) because they depend on a maximization, which is not defined if the rewards are multi-dimensional. As a result, special multi-objective algorithms are needed to find a set of policies that contains all optimal trade-offs between objectives, i.e. a set of Pareto optim...