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An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding…
Logistics has gained great attentions with the prosperous development of commerce, which is often seen as the classic optimal vehicle routing problem. Meanwhile, electric vehicle (EV) has been widely used in logistic fleet to curb the…
Load Balancing is a fundamental technology for scaling cloud infrastructure. It enables systems to distribute incoming traffic across backend servers using predefined algorithms such as round robin, weighted round robin, least connections,…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
We consider a problem of multi-product scheduling in production. Each product can be produced by a family of alternative multi-machine technologies. Multi-machine technologies require more than one machine at the same time. A sequence…
We address the multi-satellite scheduling problem with limited observation capacities that arises from the need to observe a set of targets on the Earth's surface using imaging resources installed on a set of satellites. We define and…
Order picking is the problem of collecting a set of products in a warehouse in a minimum amount of time. It is currently a major bottleneck in supply-chain because of its cost in time and labor force. This article presents two exact and…
According to the structural balance theory, a signed graph is considered structurally balanced when it can be partitioned into a number of modules such that positive and negative edges are respectively located inside and between the…
In this paper, we design $MC^2$ algorithms for Mixed Integer and Linear Programming. By expressing a constrained optimisation as one of simulation from a Boltzmann distribution, we reformulate integer and linear programming as Monte Carlo…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from…
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
We present methods to synthesize cooperative strategies for multi-vehicle control problems using mixed integer linear programming. Complex multi-vehicle control problems are expressed as mixed logical dynamical systems. Optimal strategies…
In this paper we present the use of Constraint Programming for solving balanced academic curriculum problems. We discuss the important role that heuristics play when solving a problem using a constraint-based approach. We also show how…
In process mining, alignments quantify the degree of deviation between an observed event trace and a business process model and constitute the most important conformance checking technique. We study the algorithmic complexity of computing…
Dynamic Programming (DP) and Constraint Programming (CP) are well-established paradigms for solving combinatorial optimization problems. Usually, these two approaches are used separately. This paper aims to show that the two can be combined…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
Emerging analog computing substrates, such as oscillator-based Ising machines, offer rapid convergence times for combinatorial optimization but often suffer from limited scalability due to physical implementation constraints. To tackle…