Zonification and Pricing in Carsharing: Formulations and exact solutions
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Combinatorial Optimization
Solving the Partial Inverse Knapsack Problem
In this paper, we investigate the partial inverse knapsack problem, a bilevel optimization problem in which the follower solves a classical 0/1-knapsack problem with item profit values comprised of a fixed part and a modification determined by the leader. Specifically, the leader problem seeks a minimal change to given item profits such that there is … Read more
Extending the reflect flow formulation to variable-sized one-dimensional cutting and skiving stock problems
Flow formulations have been widely studied for the one-dimensional cutting stock problem and several of its extensions. Among these, the so-called reflect model has shown the best empirical performance when solved directly with a general-purpose integer linear programming solver due to its reduced number of variables and constraints. However, existing adaptations of reflect for the … Read more
The Minimization of the Weighted Completion Time Variance in a Single Machine: A Specialized Cutting-Plane Approach
This study addresses the problem of minimizing the weighted completion time variance (WCTV) in single-machine scheduling. Unlike the unweighted version, which has been extensively studied, the weighted variant introduces unique challenges due to the absence of theoretical properties that could guide the design of efficient algorithms. We propose a mathematical programming framework based on a … Read more
Recoverable Robust Cardinality Constrained Maximization with Commitment of a Submodular Function
We consider a game-theoretic variant of maximizing a monotone increasing, submodular function under a cardinality constraint. Initially, a solution to this classical problem is determined. Subsequently, a predetermined number of elements from the ground set, not necessarily contained in the initial solution, are deleted, potentially reducing the solution’s cardinality. If any deleted elements were part … Read more
On the Structure of the Inverse-Feasible Region of a Multiobjective Integer Program
Many optimization problems are made more challenging due to multiple, conflicting criteria. The subjective nature of balancing these criteria motivates techniques for inverse optimization. This study establishes foundations for an exact representation of the inverse feasible region of a multiobjective integer program. We provide the first insights into its exact structure, as well as two … Read more
Implied Integrality in Mixed-Integer Optimization
Implied-integer detection is a well-known presolving technique that is used by many Mixed-Integer Linear Programming solvers. Informally, a variable is said to be implied integer if its integrality is enforced implicitly by integrality of other variables and the constraints of a problem. In this work we formalize the definition of implied integrality by taking a … Read more
Strength of the Upper Bounds for the Edge-Weighted Maximum Clique Problem
We theoretically and computationally compare the strength of the two main upper bounds from the literature on the optimal value of the Edge-Weighted Maximum Clique Problem (EWMCP). We provide a set of instances for which the ratio between either of the two upper bounds and the optimal value of the EWMCP is unbounded. This result … Read more
Novel closed-loop controllers for fractional linear quadratic tracking systems
A new method for finding closed-loop optimal controllers of fractional tracking quadratic optimal control problems is introduced. The optimality conditions for the fractional optimal control problem are obtained. Illustrative examples are presented to show the applicability and capabilities of the method. ArticleDownload View PDF
Two approaches to piecewise affine approximation
The problem of approximation by piecewise affine functions has been studied for several decades (least squares and uniform approximation). If the location of switches from one affine piece to another (knots for univariate approximation) is known the problem is convex and there are several approaches to solve this problem. If the location of such switches … Read more