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An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such…
In this pedagogical work we reviewed the mathematical formalism and the physical interpretation, based on statistical mechanics, of the meta-heuristics called simulated annealing. Moreover, we presented the mathematical formulation of the…
Autonomous vehicles need to handle various traffic conditions and make safe and efficient decisions and maneuvers. However, on the one hand, a single optimization/sampling-based motion planner cannot efficiently generate safe trajectories…
Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an…
This paper considers multi-goal motion planning in unstructured, obstacle-rich environments where a robot is required to reach multiple regions while avoiding collisions. The planned motions must also satisfy the differential constraints…
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…
We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with…
We address the Diverse Traveling Salesman Problem (D-TSP), a bi-criteria optimization challenge that seeks a set of $k$ distinct TSP tours. The objective requires every selected tour to have a length at most $c|T^*|$ (where $|T^*|$ is the…
We study GCS-TSP, a new variant of the Traveling Salesman Problem (TSP) defined over a Graph of Convex Sets (GCS) -- a powerful representation for trajectory planning that decomposes the configuration space into convex regions connected by…
The optimal transmission switching problem (OTSP) is an established problem of changing a power grid's topology to obtain an improved operation by controlling the switching status of transmission lines. This problem was proven to be…
Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written…
Neural Combinatorial Optimization aims to learn to solve a class of combinatorial problems through data-driven methods and notably through employing neural networks by learning the underlying distribution of problem instances. While, so far…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
Applying machine learning to combinatorial optimization problems has the potential to improve both efficiency and accuracy. However, existing learning-based solvers often struggle with generalization when faced with changes in problem…
The Traveling Salesperson Problem (TSP) is one of the best-known combinatorial optimisation problems. However, many real-world problems are composed of several interacting components. The Traveling Thief Problem (TTP) addresses such…
In many real-world settings, problem instances that need to be solved are quite similar, and knowledge from previous optimization runs can potentially be utilized. We explore this for the Traveling Salesperson problem with time windows…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
This paper studies a survivable traffic grooming problem in large-scale optical transport networks under double-link failures (STG2). Each communication demand must be assigned a route for every possible scenario involving zero, one, or two…
Generating overtaking trajectories in high-speed scenarios is typically addressed through hierarchical planning, which often suffers from local optima due to single initial solutions and low computational efficiency during numerical…
Most of the recent studies tackling routing problems like the Traveling Salesman Problem (TSP) with machine learning use a transformer or Graph Neural Network (GNN) based encoder architecture. However, many of them apply these encoders…