AMUO
Advances in Multiobjective Optimization

Invited Session

Time Slot: Tuesday Afternoon

Room: AUD_B

Chair: Pierluigi Mansueto

Multi-objective simulation-based optimization using a machine learning-based mathematical programming model

Time: 16:30

Marco Boresta (Sapienza Università di Roma / IASI-CNR), Giovannelli Tommaso, Lucidi Stefano, Roma Massimo

We present a novel approach to solving a multi-objective simulation-based optimization problem that employs Artificial Neural Networks (ANN) to approximate the objective function whose values are obtained by running a simulation model.This method involves replacing such objective function with a metamodel with the structure of a Multilayer Perceptron, allowing the use of gradient-based methods to solve the optimization problem. The Pareto Frontier is then generated by solving a series of single-objective problems, with the objective function obtained as a weighted combination of the different conflicting objectives.We test this approach on a real problem for the Emergency Department (ED) of a large Italian hospital which is significantly affected by the phenomenon of overcrowding: the ED of Policlinico Umberto I in Rome, Italy, one of the largest EDs in Europe. We compare its performance to that of a globally convergent Derivative-Free (DF) method on the same data and with the same budget of function evaluations. The results are encouraging, demonstrating that the ANN approach has several advantages over the DF approach, such as a significant reduction in computation time, the generation of a Pareto Frontier with more distinct, better distributed points, and higher robustness to changes in the problem statement.

A derivative-free approach to mixed integer constrained multiobjective nonsmooth optimization

Time: 16:50

Giampaolo Liuzzi (DIAG – Sapienza), Giovannelli Tommaso, Lucidi Stefano, Rinaldi Francesco

In this work, we consider multiobjective optimization problems with both boundconstraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. Furthermore, we consider the case where a subset of the variables can only take integer values. We propose a new linesearch-based solution method and show that it converges to a set of stationary points for the problem. For what concerns the continuous variables, we employ a strategy for the estimation of the Pareto frontier recently proposed in the literature and which takes advantage of dense seuqnces of search directions. The subset of variables that must assume dicrete values are dealt with using primitive directions appropriately modified to take into account the presence of more than one objective functions. Numerical results obtained with the proposed method on a set of test problems and comparison with other solution methods show the viability and efficiency of the proposed approach.

A new approach to solve multi-objective mixed-integer convex optimization problems

Time: 17:10

Gabriele Eichfelder (Technische Universität Ilmenau), Leo Warnow

We propose a new numerical method for solving multi-objective mixed-integer convex optimization problems. The algorithm determines a covering of the whole set of nondominated solutions which is the image set of efficient solutions, also known as Pareto frontier. It works mainly in the image space and can thus handle larger numbers of variables.In multi-objective mixed-integer convex optimization multiple convex objective functions need to be optimized simultaneously while some of the variables are only allowed to take integer values. We present an approach to compute an enclosure of the nondominated set of such optimization problems by calculating lower and upper bound sets. For obtaining this covering, we decompose the multi-objective mixed-integer convex optimization problem into several multi-objective continuous convex optimization problems, which we refer to as patches. Then, we iteratively compute and improve enclosures of the nondominated sets of those patches to finally combine them to obtain an enclosure of the nondominated set of the multi-objective mixed-integer convex optimization problem with a certain width as quality guarantee. Additionally, we introduce a mechanism to reduce the number of patches that need to be considered in total by using linear relaxations.

A Quasi-Newton Approach for Large Scale Multi-Objective Optimization

Time: 17:30

Pierluigi Mansueto (University of Florence), Lapucci Matteo

We propose a Limited Memory Quasi-Newton method for large scale unconstrained multi-objective optimization. The algorithm approximates the combinations of the objective functions Hessians through positive definite matrices, whose formula is similar to the one of the L-BFGS method for scalar optimization. By means of a Wolfe line search, our method is well defined even for non-convex optimization problems. We compare the performance of the proposed algorithm with other state-of-the-art Newton and Quasi-Newton approaches, showing its effectiveness and strengths with respect to the competitors.