Related papers: Permutatorial Optimization via the Permutahedron
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
There is a wealth of combinatorial algorithms for classical min-cost flow problems and their simpler variants like max flow or shortest path problems. It is well-known that many of these algorithms are related to the Simplex method and the…
We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent…
The paper addresses a new class of combinatorial problems which consist in restructuring of solutions (as structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
The gravity fed water distribution network design (WDND) optimization problem consists in determining the pipe diameters of a water network such that hydraulic constraints are satisfied and the total cost is minimized. Traditionally, such…
In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem…
The paper focuses on a new class of combinatorial problems which consists in restructuring of solutions (as sets/structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
Real world problems always have different multiple solutions. For instance, optical engineers need to tune the recording parameters to get as many optimal solutions as possible for multiple trials in the varied-line-spacing holographic…
This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems,…
The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…
Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…
The share-of-choice (SOC) problem is a widely studied problem for product line design (PLD) where representative customers are sampled from a target population and the percentage of the ones who choose the offered products over outside…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
Reductions combine collections of input values with an associative and often commutative operator to produce collections of results. When the same input value contributes to multiple outputs, there is an opportunity to reuse partial…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
We propose an Extended Hybrid High-Order scheme for the Poisson problem with solution possessing weak singularities. Some general assumptions are stated on the nature of this singularity and the remaining part of the solution. The method is…