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The selection of branching variables is a key component of branch-and-bound algorithms for solving Mixed-Integer Programming (MIP) problems since the quality of the selection procedure is likely to have a significant effect on the size of…
This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to solve…
A method is given for generating a bounded invariant of a differential system with a given set of initial conditions around a point $x_0$. This invariant has the form of a tube centered on the Euler approximate solution starting at $x_0$,…
We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it.…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
In this article we develop a max-strategy improvement algorithm for computing least fixpoints of operators on on the reals that are point-wise maxima of finitely many monotone and order-concave operators. Computing the uniquely determined…
Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Non-deterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal…
We investigate meandric systems with a large number of loops using tools inspired by free probability. For any fixed integer $r$, we express the generating function of meandric systems on $2n$ points with $n-r$ loops in terms of a finite…
We study the labeled multi-robot path planning problem in continuous 2D and 3D domains in the absence of obstacles where robots must not collide with each other. For an arbitrary number of robots in arbitrary initial and goal arrangements,…
We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We…
When we consider a finite abelian group acting linearly on a polynomial ring, we can find monomial generators for the subring of invariants. By Noether's degree bound and Hilbert's finiteness theorem, we know that there are finitely many…
We propose a data-driven algorithm for numerical invariant synthesis and verification. The algorithm is based on the ICE-DT schema for learning decision trees from samples of positive and negative states and implications corresponding to…
This paper presents a Genetic Programming (GP) approach to solving multi-robot path planning (MRPP) problems in single-lane workspaces, specifically those easily mapped to graph representations. GP's versatility enables this approach to…
In this paper we study the robust invariant sets generation problem for discrete-time switched polynomial systems subject to disturbance inputs within the optimal control framework. A robust invariant set of interest is a set of states such…
Automatic software generation based on some specification is known as program synthesis. Most existing approaches formulate program synthesis as a search problem with discrete parameters. In this paper, we present a novel formulation of…
Multi Expression Programming (MEP) is a Genetic Programming variant that uses a linear representation of chromosomes. MEP individuals are strings of genes encoding complex computer programs. When MEP individuals encode expressions, their…
Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection…
Programmers frequently maintain implicit data invariants, which are relations between different data structures in a program. Traditionally, such invariants are manually enforced and checked by programmers. This ad-hoc practice is difficult…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
We propose an iterative programmatic planning (IPP) framework for solving grid-based tasks by synthesizing interpretable agent policies expressed in code using large language models (LLMs). Instead of relying on traditional search or…