Algorithm for Solving the Component Assignment Problem in a Multistate Sliding Window System

2021 ◽  
pp. 2140001
Author(s):  
Taishin Nakamura
Keyword(s):  
Branch And Bound ◽  
System Reliability ◽  
Assignment Problem ◽  
Heuristic Algorithms ◽  
Sliding Window ◽  
Maximum Effect ◽  
Global Optimality ◽  
Recursive Method ◽  
Optimal Arrangement ◽  
Window System

The multistate sliding window system (SWS) comprises [Formula: see text] multistate components arranged in a line; each group of [Formula: see text] consecutive multistate components is considered as a window. If the total performance rate in a window does not meet the predetermined demand [Formula: see text], then that window is regarded as a failure. The SWS fails if and only if there exists at least one failed window. Several researchers have considered the component assignment problem for the SWS with the aim of finding an appropriate component arrangement that maximizes system reliability. Such an arrangement is called the optimal arrangement. Although several metaheuristic and heuristic algorithms have been proposed, an exact algorithm for solving the component assignment problem of the SWS has not been developed thus far. Therefore, in this study, a branch-and-bound-based algorithm is developed to determine the optimal arrangement of the SWS efficiently. Furthermore, a recursive method is proposed to compute the system reliability. Combining the branch-and-bound-based algorithm with the recursive method enables reduction of the complexity of the reliability computations for determining the optimal arrangement. To investigate the efficiency of the branch-and-bound-based algorithm, numerical experiments were conducted; it was observed that the parameters [Formula: see text] and [Formula: see text] have the maximum effect on computation time, whereas parameter [Formula: see text] has minimal effect. The proposed algorithm is useful for improving the reliability of a practical system that can be expressed as an SWS. In addition, the optimal arrangements can be used to measure the heuristic and metaheuristic performances because they guarantee global optimality.

scholarly journals Identification of mechanical properties of arteries with certification of global optimality

2021 ◽  
Author(s):  
Jan-Lucas Gade ◽  
Carl-Johan Thore ◽  
Jonas Stålhand
Keyword(s):  
Global Solution ◽  
Branch And Bound ◽  
Clinical Data ◽  
Minimization Problem ◽  
Branch And Bound Algorithm ◽  
Stationary Points ◽  
Model Parameters ◽  
Global Optimality ◽  
Clinical Value ◽  
Non Linear

AbstractIn this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.

Conflict Analysis for MINLP

2021 ◽  
Author(s):  
Timo Berthold ◽  
Jakob Witzig
Keyword(s):  
Nonlinear Optimization ◽  
Branch And Bound ◽  
Computational Study ◽  
General Purpose ◽  
Conflict Analysis ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Global Optimality ◽  
Nonlinear Programs ◽  
The Impact

The generalization of mixed integer program (MIP) techniques to deal with nonlinear, potentially nonconvex, constraints has been a fruitful direction of research for computational mixed integer nonlinear programs (MINLPs) in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers toward the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared toward two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. Summary of Contribution: This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed integer nonlinear programs (MINLPs). It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be transferred to nonlinear optimization. Further, it develops theory for how nonlinear dual infeasibility proofs can be derived from a nonlinear relaxation. This paper features a thoroughly computational study regarding the impact of conflict analysis techniques on the overall performance of a state-of-the-art MINLP solver when solving MINLPs to global optimality.

AN IMPROVED HYBRID OPTIMIZATION ALGORITHM FOR THE QUADRATIC ASSIGNMENT PROBLEM

2005 ◽  
Vol 9 (2) ◽  
pp. 149-168 ◽  
Author(s):  
A. Misevičius
Keyword(s):  
Simulated Annealing ◽  
Tabu Search ◽  
Optimization Algorithm ◽  
Assignment Problem ◽  
Optimization Problem ◽  
Heuristic Algorithms ◽  
Quadratic Assignment Problem ◽  
Hybrid Optimization ◽  
Quadratic Assignment ◽  
Hybrid Optimization Algorithm

In this paper, we present an improved hybrid optimization algorithm, which was applied to the hard combinatorial optimization problem, the quadratic assignment problem (QAP). This is an extended version of the earlier hybrid heuristic approach proposed by the author. The new algorithm is distinguished for the further exploitation of the idea of hybridization of the well‐known efficient heuristic algorithms, namely, simulated annealing (SA) and tabu search (TS). The important feature of our algorithm is the so‐called “cold restart mechanism”, which is used in order to avoid a possible “stagnation” of the search. This strategy resulted in very good solutions obtained during simulations with a number of the QAP instances (test data). These solutions show that the proposed algorithm outperforms both the “pure” SA/TS algorithms and the earlier author's combined SA and TS algorithm. Key words: hybrid optimization, simulated annealing, tabu search, quadratic assignment problem, simulation.

A Technique for Resolution of the Assignment Problem Containers in a Container Terminal

2018 ◽  
pp. 120-132
Author(s):  
Khedidja Yachba ◽  
Zakaria Bendaoud ◽  
Karim Bouamrane
Keyword(s):  
Branch And Bound ◽  
Assignment Problem ◽  
Container Terminal ◽  
Software Tool ◽  
Storage Space ◽  
Space And Time ◽  
Complicated System

A container terminal is a complicated system made up of several components in interdependence. Several materials handle possible to move containers at the port to better meet the needs of ships awaiting loading or unloading. In order to effectively manage this area, it is necessary to know the location of each container. Containers search times can be considerable and lead to delays that cause financial penalties for terminal management operators. In this chapter, the authors propose an approach to solve the problem of placement of containers through the description of a model that optimizes available storage space to handle the distance travelled between the containers and the storage locations in a seaport. In other words, a model that minimizes the total number of unnecessary movement while respecting the constraints of space and time. This work develops a software tool enabling identification of the best location of a container using the methodological resolution Branch and Bound.

Optimal allocation of multi-state elements in a sliding window system with phased missions

2020 ◽  
pp. 1748006X2094616
Author(s):  
Kunxiang Yi ◽  
Gang Kou ◽  
Kaiye Gao ◽  
Hui Xiao
Keyword(s):  
Intelligent Transportation Systems ◽  
High Performance ◽  
Optimal Allocation ◽  
Sliding Window ◽  
Heating System ◽  
Degradation Process ◽  
Transportation Systems ◽  
Function Technique ◽  
Window System ◽  
Evaluation Algorithm

Many real-world engineering systems such as aerospace systems, intelligent transportation systems and high-performance computing systems are designed to complete missions in multiple phases. These types of systems are known as phased-mission systems. Inspired by an industrial heating system, this research proposes a generalized linear sliding window system with phased missions. The proposed system consists of N nodes with M multi-state elements that are subject to degradation. The linear sliding window system fails if the cumulative performance of any r consecutive nodes is less than the pre-determined demand in any phase. The degradation process of each element is modeled by a continuous-time Markov chain. A novel reliability evaluation algorithm is proposed for the linear sliding window system with phased missions by extending the universal generating function technique. Furthermore, the optimal element allocation strategy is determined using the particle swarm optimization. The effectiveness of the proposed algorithm is confirmed by a set of numerical experiments.

scholarly journals Bilinear Assignment Problem: Large Neighborhoods and Experimental Analysis of Algorithms

2020 ◽  
Vol 32 (3) ◽  
pp. 730-746
Author(s):  
Vladyslav Sokol ◽  
Ante Ćustić ◽  
Abraham P. Punnen ◽  
Binay Bhattacharya
Keyword(s):  
Experimental Analysis ◽  
Assignment Problem ◽  
Heuristic Algorithms ◽  
Analysis Of Algorithms ◽  
Quadratic Assignment Problem ◽  
Point Of View ◽  
Neighborhood Search ◽  
Quadratic Assignment ◽  
Neighborhood Structures ◽  
Experimental Analysis Of Algorithms

The bilinear assignment problem (BAP) is a generalization of the well-known quadratic assignment problem. In this paper, we study the problem from the computational analysis point of view. Several classes of neighborhood structures are introduced for the problem along with some theoretical analysis. These neighborhoods are then explored within a local search and variable neighborhood search frameworks with multistart to generate robust heuristic algorithms. In addition, we present several very fast construction heuristics. Our systematic experimental analysis disclosed some interesting properties of the BAP, different from those of comparable models. We have also introduced benchmark test instances that can be used for future experiments on exact and heuristic algorithms for the problem.

Reliability analysis of circular multi-state sliding window system with sequential demands

2020 ◽  
Vol 198 ◽  
pp. 106882 ◽  
Author(s):  
Wei Wang ◽  
Yongnian Fu ◽  
Peng Si ◽  
Mingqiang Lin
Keyword(s):  
Reliability Analysis ◽  
Sliding Window ◽  
Window System
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