Zero-one Integer Programming Problem Research Articles

Cyber Protection for Malware Attack Resistance in Cyber-Physical Power Systems

In this article, we study how to resist malware attacks in cyber-physical power systems (CPPSs) through cyber protection. A model that incorporates the power flow analysis, the cyber monitoring and control, and the factor of cyber protection is proposed to simulate malware attacks in CPPSs. Meanwhile, an evaluation method is also developed to estimate the effectiveness of different cyber protection strategies. Through simulations, we conduct case studies in a test CPPS generated by coupling the IEEE 118 Bus System with a scale-free communication network. The protection effects of three heuristic cyber protection strategies, namely, target protection, random protection, and acquaintance protection are compared and analyzed. Simulation results reveal that compared with the other two strategies, target protection can suppress malware propagation and resist malware attacks more effectively. Moreover, we also investigate the optimal cyber protection problem in CPPSs and formulate it as a zero-one integer programming problem. We solve the problem by genetic algorithm and find that some low-degree cyber nodes also play a significant role in resisting malware attacks in CPPSs, especially when the protection budget is tight.

Моделі оптимізації завантаження мережі розподілених ситуаційних центрів

The article substantiates the relevance of the creation and formulates a mathematical statement of the problem of technical interoperability maintenance in a network of distributed situational centers based on convergent technological solutions. Technical interoperability is considered in the context of optimizing the distribution of situational management tasks between individual situation centers in a distributed network and minimizing information processing time. For this purpose the model and algorithms of optimization of performance of tasks by participants of process of situational management in a network of the distributed situational centers are offered. The model of technical interoperability optimization is presented in the form of a zero-one integer programming problem with the search for the local extremum of the objective function. The information-analytical process is formed as a request that determines the need for information resources, analytical and expert capabilities and service time in each local situation center. The task of optimizing the load of the network of distributed situational centers is to redistribute the load between network nodes by equalizing the use of organizational, human, technical and information resources for timely and quality decision-making in situational centers that serve participants in situational management at different levels. The problem of minimizing service time in a network of distributed situational centers is dual to the primal problem of load redistribution and is solved using a stochastic quasigradient projection method. Algorithms for solving the formulated problems are developed and a test example of application is given. The potential for further improvement of situational systems of strategic planning management based on capability management for target systems is shown

Bi-criteria travelling salesman subtour problem with time threshold

This paper deals with the bi-criteria travelling salesman subtour problem with time threshold (BTSSP-T), which comes from the family of the travelling salesman problem (TSP) and is NP-hard in the strong sense. The problem arises in several application domains, mainly in routing and scheduling contexts. Here, the model focuses on two criteria: total travel distance and gains attained. The BTSSP-T aims to determine a subtour that starts and ends at the same city and visits a subset of cities at a minimum travel distance with maximum gains, such that the time spent on the tour does not exceed the predefined time threshold. A zero-one integer-programming problem is adopted to formulate this model with all practical constraints, and it includes a finite set of feasible solutions (one for each tour). Two algorithms, namely, the Lexi-Search Algorithm (LSA) and the Tabu Search (TS) algorithm have been developed to solve the BTSSP-T problem. The proposed LSA implicitly enumerates the feasible patterns and provides an efficient solution with backtracking, whereas the TS, which is metaheuristic, will give the better approximate solution. A numerical example is demonstrated in order to understand the search mechanism of the LSA. Numerical experiments are carried out in the MATLAB environment, on the different benchmark instances available in the TSPLIB domain as well as on randomly generated test instances. The experimental results show that the proposed LSA works better than the TS algorithm in terms of solution quality and, computationally, both LSA and TS are competitive.

A global optimal zero-forcing Beamformer design with signed power-of-two coefficients

In this paper, we investigate a zero-forcing beamformer design with signed power-of-two coefficients for rural applications. In this design, the minimum user information rate is taken as the performance measure, while a practical system design constraint, the per-antenna power constraint, is imposed. The problem is formulated as a constrained zero-one integer programming problem. Based on a transform between two different integer spaces, the problem is transformed into an equivalent constrained integer programming problem. A global optimal two-stage design is proposed for solving the problem. In the first stage, a polynomial time quantization method is applied to obtain an initial design. In the second stage, an auxiliary function method is used to find the global optimal design. For illustration, numerical examples under several different scenarios are studied and the results are compared with those obtained by an existing method. Furthermore, the impact of the mutual interference terms in the performance measure is also studied.

Ring–mesh topology design in a SONET–WDM network

This article deals with a ring–mesh network design problem arising from the deployment of an optical transport network. The problem seeks to partition the set of demand pairs to a number of rings and a mesh cluster, and to determine the location of the optical cross-connect system (OXC), while minimizing the total cost of optical add-drop multiplexers (OADMs), OXCs, and fiber links. We formulate this problem as a zero-one integer programming problem. In strengthening the formulation, we develop some valid inequalities for the zero-one quadratic (knapsack) polytope and a column generation formulation that eliminates the symmetry of ring configurations. Also, we prescribe an effective tabu search procedure for finding a good quality feasible solution, which is also used as a starting column for the column generation procedure. Computational results show that the proposed solution procedure provides tight lower and upper bounds within a reasonable time bound.

Value-at-Risk-Based Two-Stage Fuzzy Facility Location Problems

Reducing risks in location decisions when coping with imprecise information is critical in supply chain management so as to increase competitiveness and profitability. In this paper, a two-stage fuzzy facility location problem with value-at-risk (VaR), called VaR-FFLP, is proposed, which results in a two-stage fuzzy zero-one integer programming problem. Some properties of the VaR-FFLP, including the value of perfect information (VPI), the value of fuzzy solution (VFS), and the bounds of the fuzzy solution, are discussed. Since the fuzzy parameters of the location problem are represented in the form of continuous fuzzy variables, the determination of VaR is inherently an infinite-dimensional optimization problem that cannot be solved analytically. Therefore, a method based on the discretization of the fuzzy variables is proposed to approximate the VaR. The approximation approach converts the original problem into a finite-dimensional optimization problem. A pertinent convergence theorem for the approximation approach is proved. Subsequently, by combining the simplex algorithm, the approximation approach, and a mechanism of genotype-phenotype-mutation-based binary particle swarm optimization (GPM-BPSO), a hybrid GPM-BPSO algorithm is being exploited to solve the VaR-FFLP. A numerical example illustrates the effectiveness of the hybrid GPM-BPSO algorithm and shows its enhanced performance in comparison with the results obtained by other approaches using genetic algorithm (GA), tabu search (TS), and Boolean BPSO (B-BPSO).

Recursive algorithm with C++ program for floating-point arithmetic

Floating point Arithmetic is a topic included in virtually all textbooks for Computer Systems (CS 3: ACM's Curriculum Recommendation) or for Computer Organization (CS 4: ACM's Curriculum Recommendation). This paper presents a mathematical optimization model for the topic. The problem of converting real (float) numbers into binary equivalents is first modeled as a Zero-One Integer Programming problem. Then, a Recursive Algorithm is formulated for Floating-Point Formats. Computer programs are written in both C and C++ for a 32-bit floating-point format, using the recursive algorithm. [The computer programs are available at the email

Stochastic network project scheduling with non-consumable limited resources

This paper presents a newly developed resource constrained scheduling model for a PERT type project. Several non-consumable activity related resources, such as machines or manpower, are imbedded in the model. Each activity in a project requires resources of various types with fixed capacities. Each type of resource is in limited supply with a resource limit that is fixed at the same level throughout the project duration. For each activity, its duration is a random variable with given density function. The problem is to determine starting time values S ij for each activity ( i, j) entering the project, i.e., the timing of feeding-in resources for that activity. Values S ij are not calculated beforehand and are random values conditional on our decisions. The model's objective is to minimize the expected project duration. Determination of values S ij is carried out at decision points when at least one activity is ready to be operated and there are free available resources. If, at a certain point of time, more than one activity is ready to be operated but the available amount of resources is limited, a competition among the activities is carried out in order to choose those activities which can be supplied by the resources and which have to be operated first. We suggest carrying out the competition by solving a zero-one integer programming problem to maximize the total contribution of the accepted activities to the expected project duration. For each activity, its contribution is the product of the average duration of the activity and its probability of being on the critical path in the course of the project's realization. Those probability values are calculated via simulation. Solving a zero-one integer programming problem at each decision point results in the following policy: the project management takes all measures to first operate those activities that, being realized, have the greatest effect of decreasing the expected project duration. Only afterwards, does the management take care of other activities. A heuristic algorithm for resource constrained project scheduling is developed. A numerical example is presented.

Neural network approach for allocation with capacity

In this paper we discuss neural network approach for allocation with capacity constraints problem. This problem can be formulated as zero-one integer programming problem. We transform this zero-one integer programming problem into an equivalent nonlinear programming problem by replacing zero-one constraints with quadratic concave equality constraints. We propose two kinds of neural network structures based on penalty function method and augmented Lagrangian multiplier method, and compare them by theoretical analysis and numerical simulation. We show that penalty function based neural network approach is not good to combinatorial optimization problem because it falls in the dilemma whether terminating at an infeasible solution or sticking at any feasible solution, and augmented Lagrangian multiplier method based neural network can alleviate this suffering in some degree.

Assigning slabs to orders: an example of appropriate model formulation

An important problem for a steel company is the assigning of slabs, i.e. semi-finished rectangular pieces of steel, to customer orders. Due to its discrete nature, the prolem can be formulated as a zero-one integer programming problem; however, real-world problems are too large (12,000–16,000 zero-one variable) to be solved exactly in a reasonable amount of computer time. In this paper we present a transportation formulation for this problem that can be efficiently solved using a network code of Bertsekas. Then, using rounding heuristics, the transportation solution can be transformed into a practical solution. An example is used to illustrate this approach. Empirical results indicate that excellent (low-cost) practical solutions can be generated for large-scale (300 orders and 3000 slabs) problems in less than 1 min on a 386 PC (25 MHZ).

Extending SQL with Graph Matching and Set Covering for Decision Support Applications

Graph matching, set covering, and partitioning problems are both theoretically and practically important in decision support systems. Numerous decision support applications have been modeled as graph matching, set covering, and partitioning problems. These include applications in the areas of task assignment, marriage problem, airline crew scheduling, truck deliveries or vehicle routing, political redistricting, and the like. Currently, these applications are supported through programs written in external (to the database system) programming languages that use only the data in the database system. Thus, decision makers or application programmers require extra effort to get required decision support information. As opposed to database systems, the purpose of a model management system (MMS) is to make a wide variety of models available to decision makers so they can apply these models without having to become involved in technical and/or procedural aspects of implementation. The goal of this research is to integrate database systems and model systems for zero-one integer programming problems especially concerning graph matching, set covering, and partitioning problems. Users utilize a single integrated language for both problem formulation and model execution. In order to achieve this goal, we extend relational operators and the query language SQL. The relational operators are extended with six operators, namely, match, maxmatch, cover, mincover, partition, and minpartition. Some of these operators may take a very long time to find an optimal solution. In this article, we adopted genetic algorithms to find a near-optimal solution of this kind of operators. We found they performed well both on the computational effort and on the quality of the solutions through a variety of test problems. These algorithms are bounded by a polynomial time. Therefore, they enable a DBMS to respond to queries involving proposed operators in a restricted amount of time.

A STATIONARY CYCLICAL PRODUCTION SCHEDULING PROBLEM UNDER A NONADDITIVE OUTPUT FUNCTION

Abstract The purpose of this paper is to formulate and solve a nonlinear mixed zero-one integer programming problem aimed to maximize total output by scheduling the operational time of N non-identical machines. Properties of the optimal solution are identified under restrictions imposed on machine availability and various budget constraints. A branch and bound algorithm to solve the problem is suggested.

Reliability and cost of fault tolerant multiprocessing networks with heterogeneous nodes

We present a reliability and cost model for a class of multiprocessing networks which consist of a large number of processing elements (PEs) and fail when there are less than K functioning PEs. The processing elements are of two types: a type 2 PE is more reliable and costly than a type 1 PE. The PEs in a network can be of the same type or of different type. A decision problem arises: how many PEs of each type should be used in order to (i) maximize the mean-time-to-failure given a cost budget and (ii) minimize the cost given a mean-time-to-failure requirement. We formulate these optimization problems as zero-one integer programming problems and propose efficient algorithms to solve them.

The pallet packing problem for non-uniform box sizes

We consider an important problem in the design of material handling systems in a flexible manufacturing environment; that of robotic palletization when the boxes to be palletized are of varying dimensions. The problem is formulated as a zero-one integer programming problem. The mathematical model includes the issue of multiple pallets and the orientation of boxes on the pallet. An illustrative problem is solved.

Optimal flow path design of unidirectional AGV systems

SUMMARY This paper describes an alternative formulation of the AGV flow path layout (FPL) problem which was first formulated by Gaskins and Tanchoco (1987) as a zero-one integer programming problem. A computationally efficient procedure is proposed which is based on the branch-and-bound technique. An algorithm for satisfying the reachability condition for nodes in the AGV flow path network is also presented. A simple illustrative example is discussed to demonstrate the procedure, and a more complex problem is also given.

A generalized optimal path-selection model for structural program testing

Economic and effective preparation of test cases involves identification of the minimal set of test paths that meets certain test requirements. Unlike traditional approaches that employ heuristic algorithms, we solve this problem on the basis of a rigid mathematical ground. This article discusses how the path-selection problem in structural program testing can be formulated as a zero-one integer programming problem. It is thus possible to find the solution through one of the most powerful problem-solving techniques in the realm of operations research. The model applies not only to common requirements such as statement and branch testing. This generalized model has greater merits. A large variety of constraints, cost functions, and coverage requirements can easily be handled as special cases of the same integer programming problem.

Forming the optimal union of multiple databases

Many organizations, best illustrated by libraries, have access to hundreds of databases possessing varying degrees of complimentary and overlapping records. While users may receive positive marginal benefits from data duplications, all databases and their services cannot be supported because of resource limitations. This paper attempts to conceptualize the problem of database collection in an environment of multiple databases, with differential content and performance characteristics, diverse users, and limited resources. It defines the database collection problem as a constrained zero-one integer programming problem and solves for the optimal combination or union of databases. Several extensions are shown, where special conditions are imposed on the relationships between databases and/or their availability.

The Multi-Depot Routing Allocation Problem

SYNOPTIC ABSTRACTCurrent mathematical models for analyzing distribution systems usually consider the long-term “strategic problem” of Distribution Center (DC) location, and the short-term “tactical problem” of vehicle routing, independently and sequentially. While in the short-term, both the capacities and variable costs at the DC's are given, existing vehicle routing models do not consider either the capacities of the variable costs at the DC's. The proposed Multi-Depot Routing Allocation Problem (MDRAP) is that of designing vehicle routes from multiple capacitated depots with different variable costs. It can be formulated as a zero-one integer programming problem. We present an efficient heuristic for the MDRAP based on a sequential savings approach. The computational analysis suggests that DC capacities and variable costs may have significant effects on vehicle routing.

Zero-one integer programs with few constraints —Lower bounding theory

The zero-one integer programming problem and its special case, the multiconstraint knapsack problem frequently appear as subproblems in many combinatorial optimization problems. We present several methods for computing lower bounds on the optimal solution of the zero-one integer programming problem. They include Lagrangean, surrogate and composite relaxations. New heuristic procedures are suggested for determining good surrogate multipliers. Based on theoretical results and extensive computational testing, it is shown that for zero-one integer problems with few constraints surrogate relaxation is a viable alternative to the commonly used Lagrangean and linear programming relaxations. These results are used in a follow up paper to develop an efficient branch and bound algorithm for solving zero-one integer programming problems.

The Optional Allocation of Inspection Effort in a Class of Nonserial Production Systems

Abstract The allocation of quality control inspection effort (QCIE) within a class of nonserial production systems permitting inspection errors is considered. If the allocation of QCIE is unconstrained, and providing inspected and uninspected items from an operation are aggregated, then, for the cost structure considered, this problem is shown to be equivalent to a nonlinear zero-one integer programming problem. This implies the existence of an optimal inspection policy involving only integer multiples of 100% inspection at each potential location. However, if the allocation of QCIE is constrained or the segregation of inspected and uninspected items is permitted, then the existence of such an optimal policy is no longer assured.