Ordinal Optimization Algorithm Research Articles

Research on security-constrained unit commitment based on an improved ordinal optimization algorithm

It is of great significance for the development of intermittent renewable energy and the marketization of electricity to study an efficient and accurate algorithm for solving the unit commitment problem with security constraints. Based on the existing constrained ordinal optimization (COO) algorithm, an improved ordinal optimization (OO) algorithm is proposed, which can be applied to solve SCUC problems. In order to solve the rough model and the accurate model, the discrete variable identification strategy and the effective safety constraint reduction strategy are adopted, respectively. Compared with the traditional object-oriented algorithm, the improved object-oriented algorithm not only gives full play to the computational efficiency of the traditional object-oriented algorithm but also further improves the compactness and reduces the computational redundancy. IEEE 118 simulation results verify the correctness and effectiveness of the algorithm.

Redundancy optimization for multi-state series-parallel systems using ordinal optimization-based-genetic algorithm

Multi-state series-parallel systems (MSSPSs) are widely-used for representing engineering systems. In real-life cases, engineers need to design an optimal MSSPS structure by combining different versions and number of redundant components. The objective of the design is to ensure reliability requirements using the least costs, which could be formulated as a redundancy optimization problem under reliability constraints. The genetic algorithm is one of the most frequently used method for solving redundancy optimization problems. In traditional genetic algorithms, the population size needs to be determined based on the experience of the modeler. Often, this ends up creating a large number of unnecessary samples. As a result, the computational burden can be huge, especially for large-scale MSSPS structures. To solve these problems, this paper proposes an optimal structure designing method named as redundancy ordinal optimization. The universal generating function technique is applied to evaluate the reliabilities of the MSSPSs. Based on the reliabilities, an ordinal optimization algorithm is adapted to update the parent populations and the stopping criterion of genetic algorithm, so that the unnecessary structure designs can be eliminated. Numerical examples show that the proposed method improves the computational efficiency while remaining satisfactorily accurate.

Redundancy Optimization for Multi-Performance Multi-State Series-Parallel Systems Considering Reliability Requirements

Various engineering systems operating with multiple performance measures are multi-state in nature. These systems are usually modelled as multi-performance multi-state series-parallel systems (MPS). In real-life cases, engineers need to design an optimal MPS structure by combining different versions and number of redundant multi-performance components. Moreover, to design a reliable structure, reliability evaluation is inevitable. However, the conventional redundancy optimization measured by single performance is difficult to model the optimal MPS structure. Furthermore, as the most frequently used method, randomly sizing of parent populations and stopping criterion of traditional genetic algorithm (GA) may lead to massive unnecessary structures. The computational burden may be huge for the redundancy optimization considering multi-performance measures. This paper proposes a redundancy optimization model considering multi-performance measuring systems. The optimization objective and the reliability constraints are described by multiple performance measures. The universal generating function technique is applied to evaluate the reliability. Based on the reliability, the efficient optimization method combining with ordinal optimization and genetic algorithms is proposed to design the optimal MPS structure. The ordinal optimization algorithm is employed to modify both the parent populations and stopping criterion of genetic algorithm. Finally, the proposed model and method are illustrated by numerical examples.

Optimal structure screening for large-scale multi-state series-parallel systems based on structure ordinal optimization

Multi-state series-parallel systems are widely-used for representing engineering systems. In real-life cases, engineers need to select an optimal system structure among many different multi-state series-parallel system structures. Screening of system structures is meaningful and critical. Moreover, to design a reliable structure, reliability evaluation is an indispensable part of the process. Due to the large number of available system structures, the computational burden can be huge when selecting the optimal one. Also, the number of components and possible states of each system can be enormous when the system scale is large, which causes significant complexity in exact reliability evaluation. To effectively select the optimal structure among numerous multi-state series-parallel systems under a reliability constraint, this article proposes an optimal structure screening method called the structure ordinal optimization. The proposed method combines the fuzzy universal generating function technique with an ordinal optimization algorithm. The fuzzy universal generating function technique is applied to reduce the computational time by approximately evaluating the reliability. Based on the approximate reliabilities, ordinal optimization helps to reduce the number of structure options and thus accelerate the screening process. Numerical examples show that the structure ordinal optimization method has advantages in computational efficiency with satisfactory accuracy.

On a new polynomial algorithm for solving NPC problems

Intelligent systems generally face optimization problems when solving specific problems, and complex optimization problems are usually non-deterministic polynomial complete (NPC) problems. To solve such problems, approximation methods are generally adopted. This paper presents an accurate method fo r finding an optimal solution to probability 1 in polynomial time. It combines intelligent optimization algorithms such as ordinal optimization, simulated annealing, genetic algorithm (differential evolution algorithm), tabu search, ant colony algorithm, particle swarm optimization, space neighborhood sampling, time neighborhood sampling, number neighborhood sampling (knowledge neighborhood sampling). Then it draws on the matrix ideas of Riemann Hypothesis, prime distribution formula, random number generator, maximum entropy heuristics (proposed by this paper), and combines a new group ordinal optimization algorithm framework proposed by this paper to Traveling Salesman Problem (TSP, a NPC problem) as an example and constructs a polynomial algorithm. The theoretical time complexity is O(N^4) (considering parallel computing), and is verified based on some examples.

Reliability Evaluation and Selection in Multi-State System

The multi-state system is an essential tool to present engineering system and previous researches have been focusing on the reliability evaluation of multi-state system recently. The Analytical algorithm and Monte Carlo simulation are the major reliability evaluation methods. However, it is inefficient to apply these algorithms to find the optimal multi-state system with greatest reliability in numbers of systems, whose computational time may last for hours. Hence, this paper proposes a new method based on ordinal optimization algorithm and Monte Carlo simulation applied in reliability evaluation. Calculation methods concerning the characteristics of system are defined, which can dramatically and effectively shorten the computational time. An effective and convenient precision and efficiency verification according to the proposed method is illustrated.

Applying Hybrid Heuristic Approach to Identify Contaminant Source Information in Transient Groundwater Flow Systems

Simultaneous identification of the source location and release history in aquifers is complicated and time-consuming if the release of groundwater contaminant source varies in time. This paper presents an approach called SATSO-GWT to solve complicated source release problems which contain the unknowns of three location coordinates and several irregular release periods and concentrations. The SATSO-GWT combines with ordinal optimization algorithm (OOA), roulette wheel approach, and a source identification algorithm called SATS-GWT. The SATS-GWT was developed based on simulated annealing, tabu search, and three-dimensional groundwater flow and solute transport model MD2K-GWT. The OOA and roulette wheel method are utilized mainly to reduce the size of feasible solution domain and accelerate the identification of the source information. A hypothetic site with one contaminant source location and two release periods is designed to assess the applicability of the present approach. The results indicate that the performance of SATSO-GWT is superior to that of SATS-GWT. In addition, the present approach works very effectively in dealing with the cases which have different initial guesses of source location and measurement errors in the monitoring points as well as problems with large suspicious areas and several source release periods and concentrations.

Application of an Ordinal Optimization Algorithm to the Wafer Testing Process

In this correspondence, we have formulated a stochastic optimization problem to find the optimal threshold values to reduce the overkills of dies under a tolerable retest level in wafer testing process. The problem is a hard optimization problem with a huge solution space. We propose an ordinal optimization theory-based two-level algorithm to solve for a vector of good enough threshold values and compare with those obtained by others using a set of 521 real test wafers. The test results confirm the feature of controlling the retest level in our formulation, and the pairs of overkills and retests resulted from our approach are almost Pareto optimal. In addition, our approach spends only 6.05 min in total in a Pentium IV personal computer to obtain the good enough threshold values

Dynamical mobile terminal location registration in wireless PCS networks

In this paper, we propose a mobile terminal (MT) location registration/update model. In this model, the registration decision is based on two factors-the time elapsed since last call arrival and the distance the MT has traveled since last registration. It is established that the optimal registration strategy can be represented by a curve. Only when the state of the system reaches this curve is a registration performed. In order for an MT to calculate its traveled distance, an interactive implementation scheme and a distance calculation algorithm are developed. When the call interarrival times are independent and geometrically distributed, the proposed model becomes a distance-based model and, in this case, the optimal registration strategy is of threshold structure. For the distance-based model, a single sample path-based ordinal optimization algorithm is devised. In this algorithm, without any knowledge about the system parameters, the MT observes the system state transitions, estimates the ordinal of a set of strategies, and updates the registration strategy adaptively. Since only a single sample path is used, this algorithm can be implemented online. Several numerical examples are provided to compare the proposed model and the existing ones.

On the convergence rate of ordinal optimization for a class of stochastic discrete resource allocation problems

In Cassandras et al. (1998), stochastic discrete resource allocation problems were considered which are hard due to the combinatorial explosion of the feasible allocation search space, as well as the absence of closed-form expressions for the cost function of interest. An ordinal optimization algorithm for solving a class of such problems was then shown to converge in probability to the global optimum. In this paper, we show that this result can be strengthened to almost sure convergence, under some additional mild conditions, and we determine the associated rate of convergence. In the case of regenerative systems, we further show that the algorithm converges exponentially fast.