Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the computationally hard (NP-hard) graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of run time and system size. The method has a single free para...

The minimum weight vertex cover problem is an interesting and applicable NP-hard problem that has been investigated from many different aspects. The ant colony optimization metaheuristic is a relatively new technique that was successfully adjusted and applied to many hard combinatorial optimization problems, including the minimum weight vertex cover problem. Some kind of hybridization or exploi...

Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectiv...

Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve because they belong to the NP-hard class, namely algorithms that always find a solution in polynomial time are not known. Over the past decades, research has...

This paper addresses a multiple objective optimization model to determine the file allocation and query routing assignment in a distributed information system. The problem is formulated as a zero-one integer nonlinear programming problem with multiple objectives. The optimization problem under consideration is shown to be NP-hard. We adopt an iterative improvement procedure, which gives the Par...

Partitioning a set of data points which are characterized by their mutual dissimilarities instead of an explicit coordinate representation is a difficult, NP-hard combinatorial optimization problem. We formulate this optimization problem of a pairwise clustering cost function in the maximum entropy framework using a variational principle to derive corresponding data partitionings in a d-dimensi...

this paper presents a new meta-heuristic solution to find the efficient frontier using the mean-variance approach. portfolio optimization problem is a quadratic programming model and, changes to np-hard if the number of assets and constraints has increased, and it cannot be solved using common mathematical methods in a reasonable time. therefore, a heuristic or meta-heuristic algorithm should b...

Recent advancements in Internet technology research, as well as the widespread of commercial content delivery networks, motivates the need for optimization algorithms designed to work in decentralized manner. In this paper we formulate data placement problem, a special case of universal facility location problem with quadratic terms in objective function. The considered combinatorial optimizati...

This paper proposes a robust model for optimizing collaborative reverse supply chains. The primary idea is to develop a collaborative framework that can achieve the best solutions in the uncertain environment. Firstly, we model the exact problem in the form of a mixed integer nonlinear programming. To regard uncertainty, the robust optimization is employed that searches for an optimum answer wi...