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The minimum common string partition problem is an NP-hard combinatorial optimization problem with applications in computational biology. In this work we propose the first integer linear programming model for solving this problem. Moreover,…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…
In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…
The optimal pricing problem is a fundamental problem that arises in combinatorial auctions. Suppose that there is one seller who has indivisible items and multiple buyers who want to purchase a combination of the items. The seller wants to…
Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…