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In this paper, we investigate two decomposition methods for their convergence rate which are used to solve security constrained economic dispatch (SCED): 1) Lagrangian Relaxation (LR), and 2) Augmented Lagrangian Relaxation (ALR). First,…
We formulate the Alternating Current Optimal Power Flow Problem (ACOPF) as a Linear Constrained Quadratic Program (LCQP) with many negative eigenvalues ($r$) and linear constraints, making it NP-hard. We propose two algorithms, Feasible…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
Existing disambiguation strategies for partial structured output learning just cannot generalize well to solve the problem that there are some candidates which can be false positive or similar to the ground-truth label. In this paper, we…
Neural Combinatorial Optimization (NCO) has emerged as a powerful framework for solving combinatorial optimization problems by integrating deep learning-based models. This work focuses on improving existing inference techniques to enhance…
In this paper, we study the shortest path problem (SPP) with multiple source-destination pairs (MSD), namely MSD-SPP, to minimize average travel time of all shortest paths. The inherent traffic capacity limits within a road network…
This paper explores minimum sensing navigation of robots in environments cluttered with obstacles. The general objective is to find a path plan to a goal region that requires minimal sensing effort. In [1], the information-geometric RRT*…
In this paper, we consider the linear programming (LP) formulation for deep reinforcement learning. The number of the constraints depends on the size of state and action spaces, which makes the problem intractable in large or continuous…
Path planning for multiple robots (MRPP) represents a task of finding non-colliding paths for robots through which they can navigate from their initial positions to specified goal positions. The problem is usually modeled using undirected…
Capacitated vehicle routing problem (CVRP) is being one of the most common optimization problems in our days, considering the wide usage of routing algorithms in multiple fields such as transportation domain, food delivery, network routing,…
Constrained Optimum Path (COP) problems appear in many real-life applications, especially on communication networks. Some of these problems have been considered and solved by specific techniques which are usually difficult to extend. In…
We present a novel framework that combines machine learning with mixed-integer optimization to solve the Capacitated Location-Routing Problem (CLRP). The CLRP is a classical NP-hard problem that integrates strategic facility location with…
In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we…
The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP…
We study a pair of budget- and performance-constrained weak-submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the…
Given a graph with a source vertex $s$, the Single Source Replacement Paths (SSRP) problem is to compute, for every vertex $t$ and edge $e$, the length $d(s,t,e)$ of a shortest path from $s$ to $t$ that avoids $e$. A Single-Source Distance…
High-level penetration of intermittent renewable energy sources (RESs) has introduced significant uncertainties into modern power systems. In order to rapidly and economically respond to the fluctuations of power system operating state,…
In this paper, we focus on the problem of robustifying reinforcement learning (RL) algorithms with respect to model uncertainties. Indeed, in the framework of model-based RL, we propose to merge the theory of constrained Markov decision…
We consider a constrained Markov Decision Problem (CMDP) where the goal of an agent is to maximize the expected discounted sum of rewards over an infinite horizon while ensuring that the expected discounted sum of costs exceeds a certain…
Optimization-based approaches are widely employed to generate optimal robot motions while considering various constraints, such as robot dynamics, collision avoidance, and physical limitations. It is crucial to efficiently solve the…