Threshold Accepting Algorithm Research Articles

Integración de investigación y docencia de posgrado a través del diseño eficiente de estructuras

This paper describes, with a case study, the teaching methodology in which a research perspective is introduced in a master program. Throughout the semester, students are asked to apply and analyze the results obtained with the implementation of different heuristic algorithms for the optimal design of a concrete structure. As a final report, students should implement a heuristic algorithm different to those implemented in class for the optimal design of the concrete structure. The results obtained should be presented in the format of a scientific paper. The case study presented in this paper consists on the optimization of the mix design of simply supported beams made of high-performance concrete (HPC). The optimization algorithm implemented is an hybrid strategy based on a variable neighborhood search and threshold acceptance algorithm. This paper begins by defining the optimization problem. It will then go on to present the results of applying the optimization algorithm. Finally, a parametric study is undertaken, analyzing beams with lengths varying from 10 to 20 m. The application of this teaching methodology has supposed an aditional challenge to postgraduate students, as they not only have to adquire the technical competences of the subject but they also have to apply them in a practical example and publish the results in the format of a scientific journal.

A threshold accepting algorithm for the uncapacitated single allocation hub location problem

Hub location problem simultaneously determines the number and locations of hubs, and customer allocations. In this study, we tackle the uncapacitated single allocation hub location problem (USAHLP) that has no capacity constraint on hubs and all non-hub nodes must be allocated to a single hub so that the total flow cost is minimized. Since USAHLP is NP-hard, we propose a threshold accepting (TA) algorithm to solve the problem. Our algorithm was tested on two sets of benchmark instances, Civil Aeronautics Board and Australia Post (AP), and two sets of new larger and modified AP instances from the literature. The computational experiments and comparisons with other metaheuristics are reported. The results show that TA is competitive with other well-known algorithms and able to update numerous new best solutions.

A PARTICLE SWARM OPTIMIZATION-THRESHOLD ACCEPTING HYBRID ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

In this paper, we propose a novel hybrid metaheuristic algorithm, which integrates a Threshold Accepting algorithm (TA) with a traditional Particle Swarm Optimization (PSO) algorithm. We used the TA as a catalyst in speeding up convergence of PSO towards the optimal solution. In this hybrid, at the end of every iteration of PSO, the TA is invoked probabilistically to refine the worst particle that lags in the race of finding the solution for that iteration. Consequently the worst particle will be refined in the next iteration. The robustness of the proposed approach has been tested on 34 unconstrained optimization problems taken from the literature. The proposed hybrid demonstrates superior preference in terms of functional evaluations and success rate for 30 simulations conducted.

Sixty-phase Sequences Design with Good Autocorrelation Properties

A new Hybrid Algorithm (HA) is proposed as a statistical technique for obtaining approximate solutions to combinatorial optimization problems. The proposed algorithm is a combination of Threshold Accepting (TA) and Hamming Scan algorithms. It combines the good methodologies of these algorithms, such as global minimum converging property of TA algorithm and fast convergence rate of Hamming scan algorithm. HA is used to design sixty-phase sequences, which have good autocorrelation properties. Sixty-phase Barker sequences with length up to 18 only were reported in the literature. Whereas in this paper, sixty-phase Barker sequences up to lengths 26 are presented. The merit factors of synthesized sixty-phase Barker sequences are better than well-known binary Barker sequences. The sequences up to length 441 have autocorrelation peak sidelobe values better than well-known Frank codes. The synthesized sequences are promising for practical applications to radar and in communication. These sequences have complex structure and very difficult to detect and analyze by an enemy’s electronic support measures (ESMs). The convergence rate of HA is found to be good.

A fuzzy based threshold policy for a single server retrial queue with vacations

In this paper we deal with a single server retrial queue with vacations. The server serves the customers until the system becomes empty, then it takes a vacation. The system consists of two types of costs. The blocking cost is considered whenever a customer is blocked either because of the server is busy or off. There is also a cost each time the server is turned on. The problem is to find an effective policy for turning on the dormant server. We propose a Fuzzy Based Threshold Policy (FBTP) to control the server, substitute for conventional threshold policies. The FBTP is based on four input parameters, an inference stage and it is tuned up using a stochastic List Based Threshold Accepting (LBTA) algorithm. Simulation models are developed to validate the fuzzy controller. Numerical experiments are provided to show that the proposed method is superior to crisp threshold policies.

Design of prestressed concrete precast pedestrian bridges by heuristic optimization

This paper deals with the economic optimization of prestressed concrete precast pedestrian bridges typically used in public works construction. These bridges are made of a precast concrete beam that integrates an upper reinforced concrete slab for the pedestrian traffic. The beam has a U-shape cross-section. Typical span lengths range from 20 to 40m and the width ranges from 3.00 to 6.00m. The study shows the efficiency of heuristic optimization by the simulated annealing (SA) and the threshold accepting (TA) algorithms. The evaluation of solutions follows the Spanish code for structural concrete. Stress resultants and envelopes of these structures are computed by direct calculation. Design loads are in accordance to the national IAP code for road bridges. The algorithms are applied to a typical pedestrian bridge of 40m of span length and 6.00m of width. This example has 59 discrete design variables for the geometry of the beam and the slab, materials in the two elements and active and passive reinforcement. The evaluation module includes the limit states that are commonly checked in design: flexure, shear, deflections, etc. The application of the SA and TA algorithms requires the calibration of the initial temperature and threshold, the number of variables modified in each iteration, the length of the Markov chains and the reducing coefficient. Each heuristic is run nine times so as to obtain statistical information about the minimum, average and deviation of the results. Best result has a cost of 38,[email protected]? for the SA algorithm and 38,[email protected]? for the TA algorithm. Finally, solutions and run times indicate that heuristic optimization is a forthcoming option for the design of real prestressed structures.

Heuristic optimization of RC bridge piers with rectangular hollow sections

This paper deals with the economic optimization of reinforced concrete (RC) bridge piers with hollow rectangular sections and describes the efficiency of three heuristic algorithms: two new variants of the ant colony optimization (ACO) algorithm, the genetic algorithm (GA) and the threshold acceptance (TA) algorithm. The GA and TA are used for comparison with the new ACO algorithms. The total number of variables is 95. All variables are discrete in this analysis. The calibration of the new ACO algorithm recommended a 250-member ant population and 100 stages. The best solution costs 69,467 euros, which means savings of about 33% as compared to experience-based design. Finally, results indicate that the new ACO algorithms are potentially useful for optimizing the costs of real RC structures.

Threshold accepting and Ant-colony optimization algorithms for scheduling m-machine flow shops with lot streaming

This paper addresses the problem of making sequencing and scheduling decisions for n jobs m machines flow shops under lot sizing environment. Lot streaming (lot sizing) is the process of creating sublots to move the completed portion of a production sublots to down stream machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. On this concern this paper proposes Ant-colony optimization algorithm (ACO) and threshold accepting algorithm (TA) to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and setup time. The following two algorithms are used to evaluate the performance of the proposed ACO and TA: (i) Baker's algorithm (BA), an optimal solution procedure for two-machine flow shop problem with lot streaming and makespan objective criterion and (ii) genetic and hybrid genetic algorithm for m-machine flow shop problem with lot streaming and makespan and total flow time criteria.

A faster, more reliable solver of regular-grid TSPs: single value threshold accepting

The main point of this paper is to provide a simple and efficient threshold value for the threshold accepting (TA) algorithm to attempt an optimal solution for the regular grid travelling salesman problems (TSPs) in a reliable way. This new algorithm is named the single value threshold accepting algorithm (SVTA). The number of the threshold value is one and its value is: % MathType!MTEF!2!1!+- % feaafaart1ev1aaatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakabbaaaaaaaatngA3fMC6bWdbeaapaWaaCWaaeaadaqadaqaaiaa % ikdacqGHsisldaGcaaqaaiaaikdaaSqabaaakiaawIcacaGLPaaaca % WGNbGaaiOkaiaaigdacaaIWaGaaiilaiaaicdacaaIWaGaaGimaaGa % ayP74laawMp+aiaac+cacaaIXaGaaGimaiaacYcacaaIWaGaaGimai % aaicdaaaa!50A7! $$\left\lceil {\left( {2 - \sqrt 2 } \right)g*10,000} \right\rceil /10,000$$ where g is the grid size and % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbb % a9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0-vr % 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaahmaabaGaam % iEaaGaayP74laawMp+aaaa!3BF0! $$\left\lceil x \right\rceil$$ is the smallest integer not less than a real number x. For the regular-grid TSPs, g can be set as % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY-Hhbbf9v8qqaqFr0xc9pk0xbb % a9q8WqFfeaY-biLkVcLq-JHqpepeea0-as0Fb9pgeaYRXxe9vr0-vr % 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaigdacaGGVa % WaaOaaaeaacaWGUbaaleqaaaaa!385A! $$1/\sqrt n$$ where n is the problem size. It is shown empirically, with 100 independent simulations performed with 441 cities, in 16 different cases, that the SVTA is far superior to (at least five times faster on average than) the previous double threshold accepting (DTA) with respect to the speed of finding a global optimal reliably. Particularly in the case of the 441 cities, the proposed algorithm is at least 21 times faster and rises up to 96 times on average and optimistically 284 times faster than the previous one. Important insight is provided that reveals how the formula works and why it works successfully.

A novel threshold accepting meta-heuristic for the job-shop scheduling problem

A novel list based threshold accepting (LBTA) algorithm is proposed for solving the job-shop scheduling problem. The LBTA algorithm belongs to the class of threshold accepting algorithms but the acceptance probability decreases based on a list that is rejuvenated and adapted according to the topology of the solution space of the problem. A probabilistic steepest optimization strategy was adapted to search the solution space effectively. The most prominent advantage of the LBTA algorithm over other local search methods is that it is simple and easy to implement, needs less problem specific knowledge, and is effectively tuning free. Computational experiments on a set of benchmark problems show that the proposed method gives optimal and very near-optimal solution results within a short computation time.

List-Based Threshold-Accepting Algorithm for Zero-Wait Scheduling of Multiproduct Batch Plants

A novel list-based threshold-accepting (LBTA) algorithm is proposed for solving the zero-wait (ZW) scheduling problem. The LBTA algorithm belongs to the class of threshold-accepting algorithms, but the acceptance probability decreases based on a list that is rejuvenated and adapted according to the topology of the solution space of the problem. A probabilistic steepest optimization strategy was adapted to search the solution space effectively. The effectiveness of the LBTA method is illustrated through case studies from scheduling literature which were formulated as mixed-integer linear programming and mixed-integer nonlinear programming models. The performance of the LBTA algorithm is also compared with that of the simulated annealing (SA) algorithm for a large number of various problem sizes. The proposed algorithm gives optimal solutions for small- to moderate-size ZW scheduling problems within a very short time and shows much superior computational performance compared to SA for large-size problems.

Long-Term Scheduling of Cleaning of Heat Exchanger Networks: Comparison of Outer Approximation-Based Solutions with a Backtracking Threshold Accepting Algorithm

Management of cleaning of heat exchanger networks (HENs) subject to significant fouling plays an important role in oil refinery heat recovery network economics. Recent studies have shown that where this can be applied1,2, significant benefits can be achieved in, for instance, reducing fired-heater duties over the operating horizon considered. These previous approaches have focused on using outer approximation (OA) based formulations and solution techniques to solve the associated mixed integer-nonlinear programming problem (MINLP) involving binary decision variables describing when and which unit to clean in a multi-period formulation. In parallel to this avenue, this work explores the options offered by stochastic optimization techniques for combinatorial problems applied to the HEN cleaning problem. A particular method, the backtracking threshold accepting algorithm (BTA) is developed, derived from the standard threshold accepting algorithm (TA), which is related to the class of methods typified by simulated annealing (SA). Two large-scale case studies are considered: one involving 14 heat exchanger units, and one involving 25 units. Both are tackled by the OA and BTA approaches: the latter proved able to handle larger problems, for example, with more time intervals or exchangers, than the commercial OA solver used.

A Backtracking Adaptive Threshold Accepting Algorithm for the Vehicle Routing Problem

The aim of this study is to describe a new stochastic search metaheuristic algorithm for solving the capacitated Vehicle Routing Problem, termed as the Backtracking Adaptive Threshold Accepting (BATA) algorithm. Our effort focuses on developing an innovative method, which produces reliable and high quality solutions in a reasonable amount of time, without requiring substantial parameter tuning. BATA belongs to the class of threshold accepting algorithms. Its main difference over a typical threshold-accepting algorithm is that during the optimization process, the value of the threshold not only is lowered but also raised, or backtracked, depending on the success of the inner loop iterations to provide an acceptable new configuration (set of routes) replacing the previous one. This adaptation of the value of the threshold, plays an important role in finding the high quality solutions demonstrated in computational results presented in this study.

A List Based Threshold Accepting Algorithm for the Capacitated Vehicle Routing Problem

The aim of this study is to describe a new stochastic search meta-heuristic algorithm for solving the Capacitated Vehicle Routing Problem (CVRP), termed as the List Based Threshold Accepting (LBTA) algorithm. The main advantage of this algorithm over the majority of other meta-heuristics is that it produces quite satisfactory solutions in reasonable amount of time by tuning only one parameter of the algorithm. This property makes this algorithm a reliable and a practical tool for every decision support system designed for solving real life vehicle routing problems.

Distribution of fresh meat

This paper deals with a real-life distribution problem formulated as an open multi-depot vehicle routing problem (OMDVRP) that was encountered by a major Greek industry distributing fresh meat from depots to its customers (butchers' shops) located in an area of the city of Athens. To solve the problem, a new stochastic search meta-heuristic algorithm termed as the list-based threshold accepting (LBTA) algorithm is proposed. The proposed routing plan gives answers to a number of operational decision problems and provides significant economic benefits for the company.

AN EFFICIENT META-HEURISTIC ALGORITHM FOR ROUTING PRODUCT COLLECTING VEHICLES OF DEHYDRATION PLANTS. I. ALGORITHM DEVELOPMENT

Dehydration plants are characterized by a multi-product nature chiefly attributed to the utilization of different raw materials to be processed in parallel so that demand constraints are met. The Just-In-Time production planning policy of these plants require the collection of raw materials to be dehydrated shortly before the actual processing, immediately after harvesting.One of the most important aspects in collection of plant fresh products, is routing of collecting vehicles, so that total collection time is minimized.The aim of this study is to describe a new stochastic search meta-heuristic algorithm for solving the Vehicle Routing Problem (VRP), termed as the Backtracking Adaptive Threshold Accepting (BATA) algorithm. Our effort focuses on developing an innovative method, which produces reliable and high quality solutions, requiring reasonable computing effort. The main innovation of the algorithm, toward a typical threshold accepting algorithm, is that during the optimization process the value of the threshold is not only lowered, but also raised or backtracked according to how effective a local search is. This adaptation of the value of the threshold, plays an important role in finding high quality routing solutions. BATA is described in detail while its performance and characteristic case studies are presented by Tarantilis and Kiranoudis (2000).

Faster magnet sorting with a threshold acceptance algorithm

We introduce here a new technique for sorting magnets to minimize the field errors in permanent magnet insertion devices. Simulated annealing has been used in this role, but we find the technique of threshold acceptance produces results of equal quality in less computer time. Threshold accepting would be of special value in designing very long insertion devices, such as long free electron lasers (FELs). Our application of threshold acceptance to magnet sorting showed that it converged to equivalently low values of the cost function, but that it converged significantly faster. We present typical cases showing time to convergence for various error tolerances, magnet numbers, and temperature schedules.

Structural optimization of vapor pressure correlations using simulated annealing and threshold accepting: Application to R134a

This paper reports the use of two methods, simulated annealing (SA) and threshold accepting (TA), to determine a set of optimal terms (the structure) of the vapor pressure correlation for the R134a. The SA algorithm with the Lundy and Mees annealing schedule, and the TA algorithm with the Aarts and VanLaarhoven schedule gave the best performance, based on minimal computational time for a given performance. SA and TA appear to be versatile, powerful and computationally simple methods for determining the structure of empirical correlations of thermophysical property data.

New Optimization Heuristics: The Great Deluge Algorithm and the Record-to-Record Travel

In a former paper we introduced a very effective new general purpose optimization principle. We compared this method, which we called threshold accepting (TA), with the well-known simulated annealing (SA) method for discrete optimization. The empirical results demonstrated the superiority of the TA algorithm. In further experiments with the TA principle we discovered two new powerful optimization heuristics: The great deluge algorithm (GDA) and the record-to-record travel (RRT). These algorithms resemble in their structure the formerly studied TA and the SA method. The differences lie in their acceptance rules for worse intermediate solutions. Both, the GDA and the RRT, are essentially one-parameter algorithms; i.e., for the achievement of best possible performance, a good choice is necessary only for a single parameter. This is in contrast for instance to the classical AS algorithm, where it is necessary to choose carefully a certain sequence of parameters, the so-called annealing schedule. The quality of the computational results obtained so far by RRT and GDA shows that the new algorithms behave equally well as TA and thus a fortiori better than SA.

New concepts and algorithms for portfolio choice

AbstractThe paper studies the design of optimal (bond) portfolios taking into account various possible utility functions of an investor. The most prominent model for portfolio optimization was introduced by Markowitz. A real solution in this model can be achieved by quadratic programming routines for mean‐variance analysis. Of course, there are many reasons for an investor to prefer other utility criteria than return/variance of return in the Markowitz model. In the last few years, many efficient multiple purpose optimization heuristics have been invented for the needs in optimizing telephone nets, chip layouts, job shop scheduling etc. Some of these heuristics have essential advantages: they are extremely flexible and very easy to implement on computers. One example of such an algorithm is the threshold‐accepting algorithm (TA). TA is able to optimize portfolios under nearby arbitrary constraints and subject to nearly every utility function. In particular, the utility functions need neither to be convex, differentiable nor ‘smooth’ in any sense. We implemented TA for bond portfolio optimization with different utility criteria. The algorithms and computational results are presented. Under various utility functions, the ‘best’ portfolios look surprisingly different and have quite different qualities. Thus, for a portfolio manager it might be useful to provide himself with such a ‘multiple‐taste’ optimizer in order to be able easily to readjust it according to his own personal utility considerations.