Optimal apportionment of reliability and redundancy in seriessystems under multiple objectives

A multiobjective reliability apportionment problem for a series system with time-dependent reliability is presented. The resulting mathematical programming formulation determines the optimal level of component reliability and the number of redundant components at each stage. The problem is a multiobjective, nonlinear, mixed-integer mathematical programming problem, subject to several design constraints. Sequential unconstrained minimization techniques in conjunction with heuristic algorithms are used to find an optimum solution. A generalization of the problem in view of inherent vagueness in the objective and the constraint functions results in an ill-structured reliability apportionment problem. This multiobjective fuzzy optimization problem is solved using nonlinear programming. The computational procedure is illustrated through a numerical example. The fuzzy optimization techniques can be useful during initial stages of the conceptual design of engineering systems where the design goals and design constraints have not been clearly identified or stated, and for decision making problems in ill-structured situations     

Multi-path heuristic for redundancy allocation: the tree heuristic

A tree heuristic is presented for solving the general redundancy allocation problem in reliability optimization. The tree heuristic can obtain several local optima by branching off the main searching path when some criterions are satisfied. Then, the best local optima is selected for the final solution. The tree heuristic is a simple, efficient, iterative heuristic for any integer nonlinear programming problems with increasing constraint functions. Iterative heuristics are normally trapped in a local optimum. However, the tree heuristic can overcome local optima by branching the solution path. The experiments show that the proposed heuristic is very efficient in terms of solution quality, and computation time.     

System reliability design with deteriorative components

In constrained optimum system reliability problems, the reliability of each component is usually assumed to be fixed, and the optimal number of redundancies at each stage is determined. However, in real world the component reliability decreases as component deteriorates; i.e. the component reliability is dependent on its age. This paper presents a system reliability optimization problem with deteriorative components. We formulate this problem as a parametric nonlinear integer programming problem where the objective function has a time parameter t. A solution method is proposed for solving it. We believe that this model can provide very useful information for decision makers and reliability designers.     

A Sequential Approach for Optimal Broadcast Scheduling in Packet Radio Networks

An important problem that arises in the design of packet radio networks is that of scheduling access to the high speed communications channel in such a way as to avoid interference while keeping the frame length to a minimum. The broadcast scheduling problem is known to be NP-hard and to date, this problem has been formulated as a nonlinear discrete optimization problem for a given frame length, and solved via heuristic approaches by parametrically varying the length of the frame. This paper presents a linear integer programming formulation for the composite problem of maximizing channel utilization while minimizing the length of the frame. It then introduces a solution approach based on solving two relatively easier (though still NP-complete) integer programs in succession. Computational experiments are conducted on a set of benchmark cases and additional randomly generated problem instances. Results show that this sequential integer programming approach is very effective, solving all the problems optimally within a few seconds. These results imply that optimal solutions can be identified in very little time for problems of realistic size, and that heuristic approaches will be needed only when problems get much larger than those considered in the literature to date.     

Reliability optimization of systems by a surrogate-constraintsalgorithm

A method for solving the problem of optimizing both, redundancy (number of redundant components) and component reliability in each stage of a system under multiple constraints is presented. A mixed-integer nonlinear programming formulation and the surrogate dual method are used. The solution of the surrogate dual problem is not always feasible in the original problem, that is, a `surrogate gap' exists. Two countermeasures to surrogate gaps are considered: (1) modifying the original problem to tighten the constraints, with the modification being continued until the solution of the surrogate dual problem of the modified problem becomes feasible in the original problem, and (2) decreasing component reliabilities in the vertical direction to the tangential plane of the objective function. The method applies to reliability optimization problems for general systems, enabling complex systems such as communication networks to be treated. Some computational results are shown and compared with other approaches; they show the efficiency of the method     

Redundancy Allocation for Series-Parallel Systems Using Integer Linear Programming

We consider the problem of maximizing the reliability of a series-parallel system given cost and weight constraints on the system. The number of components in each subsystem, and the choice of components are the decision variables. In this paper, we propose an integer linear programming approach that gives an approximate feasible solution, close to the optimal solution, together with an upper bound on the optimal reliability. We show that integer linear programming is a useful approach for solving this reliability problem. The mathematical programming model is relatively simple. Its implementation is immediate by using a mathematical programming language, and integer linear programming software. And the computational experiments show that the performance of this approach is excellent based on a comparison with previous results.      

A new dynamic programming method for reliability & redundancy allocation in a parallel-series system

Reliability & redundancy allocation is one of the most frequently encountered problems in system design. This problem is subject to constraints related to the design, such as required structural, physical, and technical characteristics; and the components available in the market. This last constraint implies that system components, and their reliability, must belong to a finite set. For a parallel-series system, we show that the problem can be modeled as an integer linear program, and solved by a decomposition approach. The problem is decomposed into as many sub-problems as subsystems, one sub-problem for each subsystem. The sub-problem for a given subsystem consists of determining the number of components of each type in order to reach a given reliability target with a minimum cost. The global problem consists of determining the reliability target of subsystems. We show that the sub-problems are equivalent to one-dimensional knapsack problems which can be solved in pseudopolynomial time with a dynamic programming approach. We show that the global problem can also be solved by a dynamic programming technique. We also show that the obtained method YCC converges toward an optimal solution.     

Shared Risk Link Group (SRLG)-Diverse Path Provisioning Under Hybrid Service Level Agreements in Wavelength-Routed Optical Mesh Networks

The static provisioning problem in wavelength-routed optical networks has been studied for many years. However, service providers are still facing the challenges arising from the special requirements for provisioning services at the optical layer. In this paper, we incorporate some realistic constraints into the static provisioning problem, and formulate it under different network resource availability conditions. We consider three classes of shared risk link group (SRLG)-diverse path protection schemes: dedicated, shared, and unprotected. We associate with each connection request a lightpath length constraint and a revenue value. When the network resources are not sufficient to accommodate all the connection requests, the static provisioning problem is formulated as a revenue maximization problem, whose objective is maximizing the total revenue value. When the network has sufficient resources, the problem becomes a capacity minimization problem with the objective of minimizing the number of used wavelength-links. We provide integer linear programming (ILP) formulations for these problems. Because solving these ILP problems is extremely time consuming, we propose a tabu search heuristic to solve these problems within a reasonable amount of time. We also develop a rerouting optimization heuristic, which is based on previous work. Experimental results are presented to compare the solutions obtained by the tabu search heuristic and the rerouting optimization heuristic. For both problems, the tabu search heuristic outperforms the rerouting optimization heuristic.     

An Improved Algorithm for Reliability Optimization

This paper proposes a modification of the Aggarwal et al. algorithm for reliability optimization by introducing a new heuristic criterion for selecting the subsystem where redundancy is to be added. This criterion accounts for the relative decrement in unreliability versus the largest of the relative increments in resources. The method applies to multiple separable constraint problems (which need not be linear) and to systems which may be complex or series. The method is simple, fast, and easily programmed. The results are compared with those of the Aggarwal et al. algorithm and are better in many problems.     

Application of the surrogate constraints algorithm to optimal reliability design of systems

This paper presents a solution method for the reliability optimization problem of series-parallel systems which is formulated as a mixed integer nonlinear programming problem with multiple constraints. In the solution method, the optimal solution is obtained by solving the surrogate dual problem. Surrogate problems with only one constraint which appear in the optimization process are solved by a technique using dynamic programming. Some computational experiences are shown along with the comparison with an existing approach.     

Towards efficient dynamic surface gateway deployment for underwater network

In underwater acoustic sensor network, deploying multiple surface-level radio capable gateways is an efficient way to alleviate the burdens of high propagation delay and high error probability during transmission. However, the locations of gateways need to be carefully selected to maximize the benefit in a cost-effective way. In this paper, we present our formulation of the surface gateway deployment problem as an integer linear programming (ILP) and we solve the problem with heuristic approaches to provide a realtime solution for large scale deployment problems. By applying the proposed heuristic algorithms to a variety of deployment scenarios, we show that they are nearly optimal for practical cases, which opens the door for dynamic deployment. Therefore, we extend our solution to a dynamic case and propose a modified framework that integrates Aqua-sim, a NS2-based underwater wireless sensor network simulator. Our simulation result shows the benefits of dynamic gateway redeployment over static deployment.     

Augmented Lagrangean Based Algorithms for Centralized Network Design

Capacitated spanning tree problems appear frequently as fundamental problems in many communication network design problems. An integer programming formulation and a new set of valid inequalities are presented for the linear characterization of the problem. A combination of a subgradient optimization procedure and an augmented Lagrangean-based procedure is used to generate tight lower bounds. The procedure begins with an explicit representation of a subset of the constraints, and the corresponding Lagrangean problem is solved. The solution is examined in order to identify implicit constraints that are violated. Those are added to the Lagrangean problem, forming an expanded problem, and an efficient dual ascent procedure is then applied. When no further improvement is possible through this procedure, a subgradient optimization procedure is invoked in order to further tighten the lower bound value. An exchange heuristic is applied to the nonfeasible Lagrangean solution, in an attempt to generate good feasible solutions to the problem. The procedure has been tested and has generated bounds that are significantly better than ones obtained through previously published procedures.     

A decomposition method for optimization of large-system reliability

The authors consider a decomposition approach for optimization of the reliability of a large system with a general network structure. A three-level methodology is developed for optimal allocation of available resources among subsystems in order to ensure maximization of system reliability. The decentralized nature of this methodology greatly reduces the complexity of the large problem and facilitates seeking the optimal solution. Two examples show that the complexity of a large system can be greatly reduced by solving several smaller-dimensional subproblems iteratively. Subproblems whose dimensions are small can be efficiently solved by an existing nonlinear programming method. Another important feature of the approach is the possible simplification of the objective function during the solution. This leads in some cases to an analytic solution for the lower-level optimization problems in the three-level decomposition solution     

Optimal Design of a Series-Parallel System with Time-Dependent Reliability

The paper formulates an optimal reliability design problem for a series system made of parallel redundant subsystems. The variables for optimization are the number of redundant units in each subsystem and the reliability of each unit. There is a cost-constraint. The time for which the system reliability exceeds a specified value is to be maximized. Similarly the cost could be minimized for a constraint on the mission time and reliability. A solution method for the formulated problems is presented along with an example.     

基于GA的系统冗余可靠性设计多目标优化模型

系统冗余可靠性多目标设计是一个复合最优化问题。传统的用于解决此类问题的方法,如拉格朗日乘子法、动态规划法、直接寻查法等,在系统单元较多的情况下存在着计算量大、难以获取全局最优解等问题。针对此问题,本文建立了基于遗传算法（GA）的系统冗余可靠性设计的多目标优化模型,该模型可在系统可靠性约束条件下,使系统的成本费用、体积、重量等指标达到最优设计。     

基于LINGO的城市物流配送路径优化简

为了提高城市物流配送效率,降低配送成本,以配送成本最低为目标,建立了物流配送路径优化问题的数学模型。利用LINGO软件能够快速求得线性规划问题最优解的特点,编写了求解配送路径优化问题的LINGO程序代码．通过实例验证,可以快速有效求得此问题的最优解。     

Determining Component Reliability and Redundancy for Optimum System Reliability

The usual constrained reliability optimization problem is extended to include determining the optimal level of component reliability and the number of redundancies in each stage. With cost, weight, and volume constraints, the problem is one in which the component reliability is a variable, and the optimal trade-off between adding components and improving individual component reliability is determined. This is a mixed integer nonlinear programming problem in which the system reliability is to be maximized as a function of component reliability level and the number of components used at each stage. The model is illustrated with three general non linear constraints imposed on the system. The Hooke and Jeeves pattern search technique in combination with the heuristic approach by Aggarwal et al, is used to solve the problem. The Hooke and Jeeves pattern search technique is a sequential search routine for maximizing the system reliability, RS (R, X). The argument in the Hooke and Jeeves pattern search is the component reliability, R, which is varied according to exploratory moves and pattern moves until the maximum of RS (R, X) is obtained. The heuristic approach is applied to each value of the component reliability, R, to obtain the optimal number of redundancies, X, which maximizes RS (R, X) for the stated R.     

Cell Planning in WCDMA Networks for Service Specific Coverage and Load Balancing

Third-generation (3G) Wideband Code Division Multiple Access network is an evolutionary network which supports services from circuit-based voice service to high and low rate packet-based data services. Unlike the voice oriented second-generation service, the 3G network is enhanced to support services with different data rate, different asymmetry, and different coverage. We thus need to investigate the coverage of multiple services and the capacity of a cell in cell planning for the advanced network. Service specific uplink coverage and downlink capacity with load balancing are considered in our cell planning. The problem is formulated as a linear integer programming optimization model. An efficient tabu search heuristic is developed to solve the NP-hard problem. Very promising computational results are demonstrated, where the solution gap from the optimal to the lower bound by CPLEX is within 0.9% in problems to cover all service traffic in the system. It is demonstrated that higher load factor effectively reduces cell sites for multiple service classes. Load balancing among cells is also demonstrated with different coverage ratio.     

Alphabet Partitioning Techniques for Semiadaptive Huffman Coding of Large Alphabets

Practical applications that employ entropy coding for large alphabets often partition the alphabet set into two or more layers, and encode each symbol by using some suitable prefix coding for each layer. In this paper, we formulate the problem of finding an alphabet partitioning for the design of a two-layer semiadaptive code as an optimization problem, and give a solution based on dynamic programming. However, the complexity of the dynamic programming approach can be quite prohibitive for a long sequence and a very large alphabet size. Hence, we also give a simple greedy heuristic algorithm whose running time is linear in the length of the input sequence, irrespective of the underlying alphabet size. Although our dynamic programming and greedy algorithms do not provide a globally optimal solution for the alphabet partitioning problem, experimental results demonstrate that superior prefix coding schemes for large alphabets can be designed using our new approach