Oleg V. Shylo

Restart strategies in optimization: parallel and serial cases

This paper addresses the problem of minimizing the average running time of the Las Vegas type algorithm, both in serial and parallel setups. The necessary conditions for the existence of an effective restart strategy are presented. We clarify the counter-intuitive empirical observations of super linear speedup and relate parallel speedup with the restart properties of serial algorithms. The general property of restart distributions is derived. The computational experiments involving the state-of-the-art optimization algorithm are provided.

An Algorithm for the Job Shop Scheduling Problem based on Global Equilibrium Search Techniques

The job shop scheduling problem is considered, and an algorithm based on the global equilibrium search method is proposed for its solution. Computational experiments using well-known benchmark problems are presented. Several new upper bounds for these problems are obtained.

Global equilibrium search applied to the unconstrained binary quadratic optimization problem

We describe a heuristic method for solving the unconstrained binary quadratic optimization problem based on a global equilibrium search framework. We investigate performance of the proposed approach and compare it with the best available solver [G. Palubeckis, Multistart tabu search strategies for the unconstrained binary quadratic optimization problem, Ann. Oper. Res., 131 (2004), pp. 259–282; G. Palubeckis, Unconstrained binary quadratic optimization. Available at http://www.soften.ktu.lt/∼gintaras/binqopt.html (Last accessed December 2006).] on well-known benchmarks instances. The reported computational results indicate a high efficiency of the heuristic.

Cardinality-Constrained Critical Node Detection Problem

We consider methodologies for managing risk in a telecommunication network based on identification of the critical nodes. The objective is to minimize the number of vertices whose deletion results in disconnected components which are constrained by a given cardinality. This is referred to as the CARDINALITY CONSTRAINED CRITICAL NODE PROBLEM (CC-CNP), and finds application in epidemic control, telecommunications, and military tactical planning, among others. From a telecommunication perspective, the set of critical nodes helps determine which players should be removed from the network in the event of a virus outbreak. Conversely, in order to maintain maximum global connectivity, it should be ensured that the critical nodes remain intact and as secure as possible. The presence of these nodes make a network vulnerable to attacks as they are crucial for the overall connectivity. This is a variation of the CRITICAL NODE DETECTION PROBLEM which has a known complexity and heuristic procedure. In this chapter, we review the recent work in this area, provide formulations based on integer linear programming and develop heuristic procedures for CC-CNP. We also examine the relations of CC-CNP with the well known NODE DELETION PROBLEM and discuss complexity results as a result of this relation.

Solving job shop scheduling problems utilizing the properties of backbone and big valley

In this paper, a new metaheuristic for the job shop scheduling problem is proposed. Our approach uses the backbone and “big valley” properties of the job shop scheduling problem. The results of the computational experiments have demonstrated the high efficiency of our approach. New upper bounds have been obtained for many problems.

Jamming communication networks under complete uncertainty

This paper describes a problem of interdicting/jamming wireless communication networks in uncertain environments. Jamming communication networks is an important problem with many applications, but has received relatively little attention in the literature. Most of the work on network interdiction is focused on preventing jamming and analyzing network vulnerabilities. Here, we consider the case where there is no information about the network to be jammed. Thus, the problem is reduced to jamming all points in the area of interest. The optimal solution will determine the locations of the minimum number of jamming devices required to suppress the network. We consider a subproblem which places jamming devices on the nodes of a uniform grid over the area of interest. The objective here is to determine the maximum grid step size. We derive upper and lower bounds for this problem and provide a convergence result. Further, we prove that due to the cumulative effect of the jamming devices, the proposed method produces better solutions than the classical technique of covering the region with uniform circles.

Periodic complementary binary sequences and Combinatorial Optimization algorithms

We establish a new formalism for problems pertaining to the periodic autocorrelation function of finite sequences, which is suitable for Combinatorial Optimization methods. This allows one to bring to bear powerful Combinatorial Optimization methods in a wide array of problems that can be formulated via the periodic autocorrelation function. Using this new formalism we solve all remaining open problems regarding periodic complementary binary sequences, in the context of the Bömer and Antweiler diagram and thus complete the program that they started in 1990.

Solving weighted MAX-SAT via global equilibrium search

In this note we investigate the performance of global equilibrium search based heuristics on the weighted MAX-SAT problem. Three variants of the approach are implemented and compared with other existing algorithms on publicly available benchmark instances. The reported computational results indicate high efficiency of the method considered.

The Surgical Patient Routing Problem: A Central Planner Approach

Many patients face difficulties when accessing medical facilities, particularly in rural areas. To alleviate these concerns, medical centers may offer transportation to eligible patients. However, the operation of such services is typically not tightly coordinated with the scheduling of medical appointments. Motivated by our collaborations with the U.S. Veterans Health Administration, we propose an integrated approach that simultaneously considers patient routing and operating room scheduling decisions. We model this problem as a mixed-integer program. Unfortunately, realistically sized instances of this problem are intractable, so we focus on a special case of the problem that captures the needs of low-volume (e.g., rural) hospitals. We establish structural properties that are exploited to develop a branch-and-price algorithm, which greatly outperforms a commercial solver on the original formulation. We discuss several algorithmic strategies to improve the overall solution efficiency. We evaluate the per...