Related papers: The Robust Bilevel Selection Problem
We study a robust extensible bin packing problem with budgeted uncertainty, under a budgeted uncertainty model where item sizes are defined to lie in the intersection of a box with a one-norm ball. We propose a scenario generation algorithm…
Hierarchical decision problems are often modeled as bilevel programs in which a leader commits to a policy and a follower responds optimally. When the follower's optimal response is nonunique, or when only near-optimal follower behavior can…
The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…
Stochastic bilevel optimization generalizes the classic stochastic optimization from the minimization of a single objective to the minimization of an objective function that depends the solution of another optimization problem. Recently,…
Motivated by the increasing attention to overall social benefits in networked multi-agent systems, this paper investigates an optimization problem building on noncooperative games under high-level regulation, which can be formulated in a…
Design under uncertainty is a challenging problem, as a systems performance can be highly sensitive to variations in input parameters and model uncertainty. A conventional approach to addressing such problems is robust optimization, which…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
Motivated by emerging applications in wireless sensor networks and large-scale data processing, we consider distributed optimization over directed networks where the agents communicate their information locally to their neighbors to…
We first show a simple but striking result in bilevel optimization: unconstrained $C^\infty$ smooth bilevel programming is as hard as general extended-real-valued lower semicontinuous minimization. We then proceed to a worst-case analysis…
A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where…
In this paper we begin by discussing the simple bilevel programming problem (SBP) and its extension the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their…
In this paper, we introduce a family of sequential decision-making problems, collectively termed the Keychain Problem, that involve exploring a set of actions to maximize expected payoff when only a subset of actions are available in each…
The balance between convergence and diversity is a key issue of evolutionary multi-objective optimization. The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of…
We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not…
We formulate selecting the best optimizing system (SBOS) problems and provide solutions for those problems. In an SBOS problem, a finite number of systems are contenders. Inside each system, a continuous decision variable affects the…
Stackelberg games are a classic example of bilevel optimization problems, which are often encountered in game theory and economics. These are complex problems with a hierarchical structure, where one optimization task is nested within the…
We primarily consider bilevel programs where the lower level is a convex quadratic minimization problem under integer constraints. We show that it is $\Sigma_2^p$-hard to decide if the optimal objective for the leader is lesser than a given…