Design is a multi-objective decision-making process considering manufacturing, cost, aesthetics, usability among many other product attributes. The set of optimal solutions, the Pareto set, indicates the tradeoffs between objectives. Decision-makers generally select their own optima from the Pareto set based on personal preferences or other judgements. However, uncertainties from manufacturing ...

We propose a multi-objective machine learning approach guaranteed to find the Pareto optimal set of hybrid classification models consisting of comprehensible and incomprehensible submodels. The algorithm run-times are below 1 s for typical applications despite the exponential worst-case time complexity. The user chooses the model with the best comprehensibilityaccuracy trade-off from the Pareto...

another, so that it is not possible to improve on any of the objective functions without deteriorating at least one of the other objective functions. This is known as the concept of Pareto optimality (Rao, 1991). In multiobjective optimization, as opposed to single-objective optimization, there may not exist an unambigous optimal solution (global minimum or global maximum). Characteristic of th...

A novel multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) framework is proposed to utilize a minimal number of training samples efficiently for sequential model updates. All the sample points are enforced to be feasible, and to provide coverage of sparsely explored sparse design regions using a new optimization subproblem. The MO-ASMO method only evaluates high-fidelity fu...

The main goal of this work is to design a team of agents that can accomplish consensus over a common value for the agents’ output using cooperative game theory approach. A semi-decentralized optimal control strategy that was recently introduced by the authors is utilized that is based on minimization of individual cost using local information. Cooperative game theory is then used to ensure team...

Real world production planning is involved in optimizing different objectives while considering a spectrum of parameters, decision variables, and constraints of the corresponding cases. This comes from the fact that production managers desire to utilize from an ideal production plan by considering a number of objectives over a set of technological constraints. This paper presents a new multi-ob...

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

We consider the problem of approximating the Pareto set of convex multicriteria optimization problems by a discrete set of points and their convex combinations. Finding the scalarization parameters that maximize the improvement in bound on the approximation error when generating a single Pareto optimal solution is a nonconvex optimization problem. This problem is solvable by enumerative techniq...

This paper introduces a deterministic method for capturing the Pareto front in multi-objective real parameter optimization problems. It is an effort to deal with multi-objective optimization problems that were until now confronted only by stochastic algorithms, specifically evolutionary algorithms. The method is based on a theoretical result that proves the equivalence of non-dominated points t...

A kind of unrelated parallel machines scheduling problem is discussed. The memberships of fuzzy due dates denote the grades of satisfaction with respect to completion times with jobs. Objectives of scheduling are to maximize the minimum grade of satisfaction while makespan is minimized in the meantime. Two kind of genetic algorithms are employed to search optimal solution set of the problem. Bo...