A characterization of nonemptiness and boundedness of the solution set for set-valued vector equilibrium problems via scalarization and stability results

International audienceAttitude is a key concept in social psychology. The paper presents a novel agent-based model to simulate attitude formation by combining a rational and an emotional components based on cognitive, psychological and social theories. Individuals of the artificial population perceive actions taken by actors such as government or brands, they form an attitude toward them and also communicate the events through a social network. The model outputs are first studied through a functional analysis in which some unique macroscopic behaviors have emerged such as the impact of social groups, the resistance of the population toward disinformation campaigns or the social pressure. We then applied our model on a real world scenario depicting the effort of French Forces in their stabilization operations in Kapisa (Afghanistan) between 2010 and 2012. We calibrated the model parameters based on this scenario and the results of opinion polls that were conducted in the area during the same period about the sentiment of the population toward the Forces. Our model was able to reproduce polls results with a global error under 3%. Based on these results, we show the different dynamics tendencies that emerged among the population by applying a non-supervised classification algorithm

Connectedness of Solution Sets for Weak Vector Variational Inequalities on Unbounded Closed Convex Sets

We study the connectedness of solution set for set-valued weak vector variational inequality in unbounded closed convex subsets of finite dimensional spaces, when the mapping involved is scalar C-pseudomonotone. Moreover, the path connectedness of solution set for set-valued weak vector variational inequality is established, when the mapping involved is strictly scalar C-pseudomonotone. The results presented in this paper generalize some known results by Cheng (2001), Lee et al. (1998), and Lee and Bu (2005)

Robust Solutions to Uncertain Multiobjective Programs

Decision making in the presence of uncertainty and multiple conflicting objec-tives is a real-life issue, especially in the fields of engineering, public policy making, business management, and many others. The conflicting goals may originate from the variety of ways to assess a system’s performance such as cost, safety, and affordability, while uncertainty may result from inaccurate or unknown data, limited knowledge, or future changes in the environment. To address optimization problems that incor-porate these two aspects, we focus on the integration of robust and multiobjective optimization. Although the uncertainty may present itself in many different ways due to a diversity of sources, we address the situation of objective-wise uncertainty only in the coefficients of the objective functions, which is drawn from a finite set of scenarios. Among the numerous concepts of robust solutions that have been proposed and de-veloped, we concentrate on a strict concept referred to as highly robust efficiency in which a feasible solution is highly robust efficient provided that it is efficient with respect to every realization of the uncertain data. The main focus of our study is uncertain multiobjective linear programs (UMOLPs), however, nonlinear problems are discussed as well. In the course of our study, we develop properties of the highly robust efficient set, provide its characterization using the cone of improving directions associated with the UMOLP, derive several bound sets on the highly robust efficient set, and present a robust counterpart for a class of UMOLPs. As various results rely on the polar and strict polar of the cone of improving directions, as well as the acuteness of this cone, we derive properties and closed-form representations of the (strict) polar and also propose methods to verify the property of acuteness. Moreover, we undertake the computation of highly robust efficient solutions. We provide methods for checking whether or not the highly robust efficient set is empty, computing highly robust efficient points, and determining whether a given solution of interest is highly robust efficient. An application in the area of bank management is included

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios