01IP and QUBO: Optimization Methods for Redundancy Allocation in Complex Systems

This paper addresses the issue of optimal allocation of spare modules in large series-redundant systems in order to obtain a required reliability under cost constraints. Both cases of active and standby redundancy are considered. Moreover, for a subsystem with standby redundancy, two cases are examined: in the first case, all the spares are maintained in cold state (cold standby redundancy) and, in the second one, to reduce the time needed to put a spare into operation when the active one fails, one of the spares is maintained in warm conditions. To solve this optimization problem, for the simpler case of active redundancy an analytical method based on the Lagrange multipliers technique is first applied. Then the results are improved by using Pairwise Hill Climbing, an original fine-tuning algorithm. An alternative approach is an innovative evolutionary algorithm, RELIVE, in which an individual lives for several generations and improves its fitness based on local search. These methods are especially needed in case of very large systems.

Quantum Annealing is an algorithm for solving instances of quadratic unconstrained binary optimization (QUBO) that is implemented in hardware utilizing quantum effects to quickly find approximate solutions. However, QUBO can obviously also be solved by any classical optimization technique, for which various implementations exist. The UQ platform provides a unified interface to various means of solving QUBO that allows for a seamless switch between classical and quantum methods while implementing features such as load and user management.

통상적으로 표준적인 최적배분은 층별 조사비용을 고려하여 표본을 배분한다. 만일 조사단위당 비용이 서로 다를 경우 보다 현실적인 배분방법을 고려할 필요가 있다. 즉, 개별 조사단위의 특성에 따라 이익비용비를 최대로 하는 단위를 먼저 표본으로 고려하는 동적배분을 고려하였다. 이러한 관점에서 층별 표본수를 배분하고, 배분된 표본규모에 따라 임의로 표본을 선정하는 방식인 표준적인 최적배분과는 차이가 있다. 이 논문은 약물오용, 낙태, 알콜중독 등과 같은 민감한 특성을 조사하는 층화확률화 응답기법에 대해 각 층별로 표본을 배분할 경우 최적 동적배분을 고려하여 보다 현실적인 문제를 해결하고자 하였으며, 수치적 예제를 통해 동적배분 방법의 효과성을 증명하였다. Typically the standard optimal allocation method distributes the sample for each stratum considering survey cost. In case of varying survey cost for each survey unit, we need to consider more practical allocation method. In other words, according to characteristics of an individual unit, we consider the optimal dynamic allocation method which first selects the survey unit having maximum value of benefit cost ratio. In terms of this, the proposed allocation method is different from standard optimal allocation method which allocate samples for each stratum and selects the random sample according to each size of sample. This paper is considered the dynamic optimal allocation method for the stratified randomized response technique which surveys for sensitive characteristic of survey units such as drug abuse, abortion, alcoholic. We prove the practical usefulness of proposed method using the numerical example.

Lagrange multiplier method for optimal reliability allocation in a series system

A derivative based method for cost optimal area allocation in heat exchanger networks

Computer program for the minimization of development costs for offshore oil and gas fields

Allocation issues in LCA methodology: a case study of corn stover-based fuel ethanol

According to the maximum hollow circle strategy of the Voronoi diagram, Starting from the basic principles for equipment allocation of the chemical reconnaissance system, the capability range of the three kinds of chemical reconnaissance nodes is determined by the ideal model of chemical reconnaissance actions, and a optimization method for equipment allocation is established in the plane area which under the reconnaissance protection.The simulation experiment about the algorithm is carried out by taking a certain chemical reconnaissance protection as an example.Finally, the deficiencies of this method in theoretical significance and reality are analyzed, which provides a method and modeling foundation for the research on equipment application of chemical reconnaissance.

The postman problem is one of the optimization problems that has many applications in today’s world. With the progress of science, such optimization problems are used more. The postman’s problem is to find a route that has the minimum cost. The postman starts the route from one point and returns to the same point and must travel all the routes. If the round-trip costs are symmetric, in other words, the round-trip cost is the same, the problem is called the Chinese postman problem, and if the costs are asymmetric, that is, the round-trip cost is different from the return cost, the problem is called the windy postman problem (WPP). Here we describe two models of the WPP, which include the WPP and the rural WPP. The model for these problems in the real world needs to apply uncertainty theory. Liu expressed the theory of uncertainty. Here is a model of the windy postman uncertainty problem and a model of the windy rural postman uncertainty problem. So far, there has been no such uncertainty analysis on these models. To solve these problems, we use the Lagrangian heuristic method after turning it into a deterministic model. To solve these problems, after turning the problem into a deterministic problem, the heuristic Lagrangian method was used, and for the wind postman problem, we stated the corresponding Lagrangian algorithm and for the rural wind postman, the Lagrangian algorithm. Examples of these are problems and uncertainties. We expressed them and finally solved them by direct and Lagrangian methods.

Dissipative systems are a particular class of complex systems with energy flowing through the systems to maintain their complexity. A dissipative system is characterised by its mass and energy rate (ER). Chaisson [2001] has proposed energy rate density (ERD = ER / mass) as a single, simple metric to describe the evolution of complexity over big time. The database with mass and ER data of dissipative systems of the previous study [van Duin, 2024] has been expanded with new data for “special” systems with very small or large mass and ER, as well as different energy processing mechanisms (3200 → 4000 rows with data). A new plot of ERD vs. mass shows much more clearly the ERD threshold of 105 W/kg, separating stable, dissipative systems from unstable, explosive systems. Simply stated, this ERD threshold is the result of too much energy being concentrated in a too small system in too short time. A lower ERD limit for systems just to stay “alive” is estimated at 10-8 W/kg. Evolution in the broadest sense can be viewed as the process of groups of systems exploring the ER vs. mass area between these ERD limits of 105 and 10-8 W/kg. Different groups of systems follow different ER vs. mass trajectories. Apparently, there is no universally preferred route for ER & mass evolution. Technological innovation is characterised by several ER vs. mass trajectories pointing in different directions, because of the conscious design of such technological systems in order to fit their different application requirements. ERD has decreased during the evolution of multicellular eukaryotes, hominins, and stellar populations, as well as over the lifetime of a human and the human society. These findings challenge the use of ERD as a universal metric of complexity over big time. Finally, a new hierarchy for complex systems is proposed, covering “all” systems relevant for big history. This scheme combines several ERD classes (conservative systems: 0 W/kg; stable, dissipative systems: 0 < ERD < 105 W/kg; explosive systems: > 105 W/kg; and abstract systems: ERD ill-defined) with two qualitative descriptors (self-organisation and adaptivity).

To satisfy the high speed transmission requirement, Fibre Channel (FC) network has been applied in the avionics system. Due to the complex structure of FC networks, traditional reliability allocation methods cannot be used directly. Advisory Group on the Reliability of Electronic Equipment (AGREE) allocation method, an objective method which considers the importance and complexity of the system, can only be applied to series-parallel systems. Aiming at allocating system reliability goal to network systems with complex structure, we have proposed two improved AGREE allocation methods based on heuristic algorithm using analytic algorithm and Monte Carlo simulation to compute network reliability, respectively. In this paper, we compare these three methods, and give application examples using a simple series-parallel system, which shows advantages of our proposed methods. Our proposed reliability allocation methods based on heuristic algorithm are applied for the FC network in avionics system. The allocation method using Monte Carlo simulation is more flexible to compute the reliability of complex networks, which is more practical in engineering.

To solve the question of guaranteeing the safety of a system with a complex structure and tight couplings, a new method of optimal allocation exploiting the dynamical planning theory is presented. Two key factors that can affect system safety, i.e., accident loss and accident rate are analyzed. Then, to measure comprehensively requirements of system safety, accident safety level is defined based on these two factors. Subsequently, optimal allocation for complex systems’ safety resource is implemented according to the network properties of the inherent structures of the systems and constraint conditions for safe investments. Finally, a case study shows that the method using dynamical planning for optimal allocation of system safety can ensure preferential allocations of the parts with high safety requirements. Besides, this optimal allocation method is feasible and valid.

Basically, complex systems are defined as a large number of autonomous entities in interaction, that create several levels of collective organization leading to emergent (and immergent) behavior. In short, complex systems are characterized by the observation that the whole is more than the sum of the parts (Aristotle). The aim of this paper is to address the issue of innovation systems in order to determine by how much they constitute complex systems.

The grooming node has the capability of grooming multicast traffic with the small granularity into established light at high cost of complexity and node architecture. In the paper, a grooming nodes optimal allocation (GNOA) method is proposed to optimize the allocation of the grooming nodes constraint by the blocking probability for multicast traffic in sparse WDM networks. In the proposed GNOA method, the location of each grooming node is determined by the SCLD strategy. The improved smallest cost largest degree (SCLD) strategy is designed to select the nongrooming nodes in the proposed GNOA method. The simulation results show that the proposed GNOA method can reduce the required number of grooming nodes and decrease the cost of constructing a network to guarantee a certain request blocking probability when the wavelengths per fiber and transmitter/receiver ports per node are sufficient for the optical multicast in WDM networks.

This paper suggests a stratified Kuk model to estimate the proportion of sensitive attributes of a population composed by a number of strata; this is undertaken by applying stratified sampling to the adjusted Kuk model. The paper estimates sensitive parameters when the size of the stratum is known by taking proportional and optimal allocation methods into account and then extends to the case of an unknown stratum size, estimating sensitive parameters by applying stratified double sampling and checking the two allocation methods. Finally, the paper compares the efficiency of the proposed model to that of the Su, Sedory and Singh model and the adjusted Kuk model in terms of the estimator variance.