Related papers: Tropical optimization techniques in multi-criteria…
The optimization of open-loop shallow geothermal systems, which includes both design and operational aspects, is an important research area aimed at improving their efficiency and sustainability and the effective management of groundwater…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of…
Solving optimization problems with parallel algorithms has a long tradition in OR. Its future relevance for solving hard optimization problems in many fields, including finance, logistics, production and design, is leveraged through the…
We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents. The method alternates between fitting the numerator and denominator terms via tropical polynomial…
The Multi-Objective Mixed-Integer Programming (MOMIP) problem is one of the most challenging. To derive its Pareto optimal solutions one can use the well-known Chebyshev scalarization and Mixed-Integer Programming (MIP) solvers. However,…
Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently…
We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…
Markov decision processes are useful models of concurrency optimisation problems, but are often intractable for exhaustive verification methods. Recent work has introduced lightweight approximative techniques that sample directly from…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
In many important design problems, some decisions should be made by finding the global optimum of a multiextremal objective function subject to a set of constrains. Frequently, especially in engineering applications, the functions involved…
A linear vector equation in two unknown vectors is examined in the framework of tropical algebra dealing with the theory and applications of semirings and semifields with idempotent addition. We consider a two-sided equation where each side…
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
A number of Multiple Criteria Decision Analysis (MCDA) methods have been developed to rank alternatives based on several decision criteria. Usually, MCDA methods deal with the criteria value at the time the decision is made without…
The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of…
We consider the problem of model multiplicity in downstream decision-making, a setting where two predictive models of equivalent accuracy cannot agree on the best-response action for a downstream loss function. We show that even when the…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…