This document details the rationales behind assessing the performance of numerical blackbox optimizers on multi-objective problems within the COCO platform and in particular on the biobjective test suite bbob-biobj. The evaluation is based on a hypervolume of all nondominated solutions in the archive of candidate solutions and measures the runtime until the hypervolume value succeeds prescribed...

The effective distribution of relief plays a critical role for rescue operations in post disaster. This paper constructs a multi-objective location-routing model for relief distribution problem. Nondominated sorting differential evolution algorithm is introduced to solve the model. Case studies expound the application of the model and algorithm in practice.

We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case, integrability conditions are needed as nonexistence may arise even if the value function is nite.

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...

In this study, a nondominated-solution-based multi-objective greedy method is proposed and applied to sensor selection problem based on the multiple indices of optimal design experiments. The simultaneously considers set functions applies idea Pareto ranking for sets. Specifically, new index iteratively added nondominated solutions sets, are evaluated selected from examined solutions, next sets...

An approach for searching unsupported integer solutions of the bicriteria network flow problem is suggested. Some of the integer points in the triangles, defined by two neighbouring extreme nondominated points, are investigated by appropriately defined problems for a flow with one side constraint and for minimal cost flow.