Related papers: Efficient Local and Tabu Search Strategies for Lar…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…
We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by…
The need to explore and/or optimize expensive simulators with many qualitative factors arises in broad scientific and engineering problems. Our motivating application lies in path planning - the exploration of feasible paths for navigation,…
Tabu search is one of the most effective heuristics for locating high-quality solutions to a diverse array of NP-hard combinatorial optimization problems. Despite the widespread success of tabu search, researchers have a poor understanding…
We develop a variable depth search heuristic for the quadratic assignment problem. The heuristic is based on sequential changes in assignments analogous to the Lin-Kernighan sequential edge moves for the traveling salesman problem. We treat…
Formulation symmetry in mixed-integer programming (MIP) can hinder solver performance by inducing redundant search, but detecting such symmetries is also a significant computational challenge. This paper explores the potential for quantum…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…
The tabu and restart are two fundamental strategies for local search. In this paper, we improve the local search algorithms for solving the Maximum Weight Clique (MWC) problem by introducing new tabu and restart strategies. Both the tabu…
This paper investigates a new class of non-convex optimization, which provides a unified framework for linear precoding in single/multi-user multiple-input multiple-output (MIMO) channels with arbitrary input distributions. The new…
The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In…
Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several…
The Equitable Coloring Problem is a variant of the Graph Coloring Problem where the sizes of two arbitrary color classes differ in at most one unit. This additional condition, called equity constraints, arises naturally in several…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
The Quadratic Unconstrained Binary Optimization problem (QUBO) has become a unifying model for representing a wide range of combinatorial optimization problems, and for linking a variety of disciplines that face these problems. A new class…
We consider an extension of the set covering problem (SCP) introducing (i)~multicover and (ii)~generalized upper bound (GUB)~constraints. For the conventional SCP, the pricing method has been introduced to reduce the size of instances, and…
Quadratic Unconstrained Binary Optimization (QUBO) is a standard NP-hard optimization problem. Recently, it has gained renewed interest through quantum computing, as QUBOs directly reduce to the Ising model, on which quantum annealing…
We present a data mining approach for reducing the search space of local search algorithms in a class of binary integer programs including the set covering and partitioning problems. The quality of locally optimal solutions typically…
Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…