We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy 2 the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems (containing many important widely studied problems such as shortest paths, spanning tree, matching and many others), we can compute in polynomial time an 2-Pareto set ...

This paper presents a Multi-objective Evolutionary Algorithm (MOEA) to derive a set of optimal operation policies for a multipurpose reservoir system. One of the main goals in multiobjective optimization is to find a set of well distributed optimal solutions along the Pareto front. Classical optimization methods often fail in attaining a good Pareto front. To overcome the drawbacks faced by the...

For a set T of n points in a metric space (X, d), a point y ∈ X is dominated by a point x ∈ X if d(x, t) ≤ d(y, t) for all t ∈ T and there exists t ∈ T such that d(x, t) < d(y, t). The set of nondominated points of X is called the Pareto envelope of T. H. Kuhn (1973) established that in Euclidean spaces, the Pareto envelopes and the convex hulls coincide. Chalmet et al. (1981) characterized the...

where x is an n-dimensional vector of variables, A is an m × n matrix, b is the RHS vector and the vectors ci (i = 1, ...,m) represent the coefficients of the objective functions (criteria). Let’s denote yi = fi(x), i = 1, ...,m, and let y = (y1, ..., ym) be a vector in the criteria space. The set Y ⊂ Rm composed by all possible criterion vectors y = f(x) when x ∈ X, is known as Feasible Criter...

This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality ǫ. The core of the algorithm is a new selection criterion based on a hypothetical multilevel grid on the objective space. It is shown that, when using this criterion for accepting new search points, the sequence of solution ...

Our goal in this work is to develop analytical tools to support the definition of balanced and compatible sets of vehicle specifications in the early stages of vehicle development. In this paper, we discuss the development and application of a Technical Feasibility Model (TFM) that may be used in preliminary design to assess the technical feasibility and optimality of specified combinations of ...

In multi-objective optimization the hypervolume indicator is a measure for the size of the space within a reference set that is dominated by a set of μ points. It is a common performance indicator for judging the quality of Pareto front approximations. As it does not require a-priori knowledge of the Pareto front it can also be used in a straightforward manner for guiding the search for finite ...

We introduce an unconstrained multicriteria optimization problem and discuss its relation to various well-known scalar robust optimization problems with a finite uncertainty set. Specifically, we show that a unique solution of a robust optimization problem is Pareto optimal for the unconstrained optimization problem. Furthermore, it is demonstrated that the set of weakly Pareto optimal solution...

| Many, if not most, optimization problems have multiple objectives. Historically , multiple objectives have been combined ad hoc to form a scalar objective function , usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The genetic algorithm (GA), however, is readily modiied to deal with multiple objectives by incorporating ...

A Multi-objective optimization procedure has been developed to determine some kinetic parameters of free radical polymerization of vinyl acetate based on genetic algorithm. For this purpose, mathematical modeling of free radical polymerization of vinyl acetate is carried out first and then selected kinetic parameters are optimized by minimizing objective functions defined from comparing exp...