We study the combinatorial assignment domain, which includes auctions and course allocation. The main challenge in this domain is that bundle space grows exponentially number of items. To address this, several papers have recently proposed machine learning-based preference elicitation algorithms aim to elicit only most important information from agents. However, shortcoming prior work it does n...

Real-world problems are becoming highly complex and therefore have to be solved with combinatorial optimization (CO) techniques. Motivated by the strong increase in publications on CO, 8393 articles from this research field subjected a bibliometric analysis. The corpus of literature is examined using mathematical methods novel algorithm for keyword In addition most relevant countries, organizat...

This paper briefly describes three well-established frameworks for handling uncertainty in optimization problems. Our focus is mainly on combinatorial optimization and on the development of approximation algorithms under the discussed frameworks. In particular, we give a brief overview of Stochastic Programming, Robust Optimization, and Probabilistic Combinatorial Optimization, and list approxi...

Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and diverse problems ranging from congestive to partitioning problems. In particular, every standard combinatorial optimization problem has its shifted counterpart, ...

3 Solution techniques 13 3.1 Combinatorial approach : : : : : : : : : : : : : : : : : : : : : : : : : : 13 3.2 Continuous approach : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 3.2.1 Examples of embedding : : : : : : : : : : : : : : : : : : : : : : 14 3.2.2 Global approximation : : : : : : : : : : : : : : : : : : : : : : : 15 3.2.3 Continuous trajectories : : : : : : : : : : : : : ...

Difficult nonconvex optimization problems contain a combinatorial number of local optima, making them extremely challenging for modern solvers. We present a novel nonconvex optimization algorithm that explicitly finds and exploits local structure in the objective function in order to decompose it into subproblems, exponentially reducing the size of the search space. Our algorithm’s use of decom...