Threshold Accepting Algorithm Research Articles

Multi-Compartment Vehicle Routing Problem Considering Traffic Congestion under the Mixed Carbon Policy

The use of multi-compartment vehicles (MCVs) in urban logistics distribution is increasing. However, urban traffic congestion causes high carbon emissions in the logistics distribution, resulting in unsustainable development in urban transportation. In addition, the application of the mixed carbon policy has gradually become the first choice for energy conservation and emission reduction in some countries and regions. The transportation industry is a major carbon-emitting industry, which needs to be constrained by carbon emission reduction policies. In this context, the research on the multi-compartment vehicle routing problem (MCVRP) considering traffic congestion under the mixed carbon policy is carried out. Firstly, a mathematical model of MCVRP considering traffic congestion under the mixed carbon policy is constructed. Secondly, a two-stage variable neighborhood threshold acceptance algorithm (VNS-TA) is proposed to solve the above mathematical model. Thirdly, 14 adapted standard examples of the MCVRP are used to verify the effectiveness and optimization ability of the two-stage VNS-TA algorithm. A simulation example of the MCVRP considering traffic congestion under the mixed carbon policy is used to conduct sensitivity analyses for different scenarios. Finally, the following conclusions are drawn: (1) the two-stage VNS-TA algorithm is effective and has strong optimization ability in solving the basic MCVRP, and (2) the two-stage VNS-TA algorithm can solve and optimize the MCVRP considering traffic congestion under the mixed carbon policy, which has the effects of cost saving and energy conservation and emission reduction.

Plug-in hybrid electric refuse vehicle routing problem for waste collection

Commercial waste collection is an essential service requiring efficient and reliable provision for customers. At the operational level, one of the most challenging problems is to design a set of refuse vehicle routes to collect waste from a set of bins. To be used multiple times, these vehicles must be emptied regularly throughout the day. This paper investigates a waste collection problem with a homogeneous fleet of plug-in hybrid electric refuse vehicles powered by two different power sources, i.e., electricity and compressed natural gas (CNG). In addition, realistic fuel consumption functions are used to estimate total energy requirements for each type of fuel, including refueling and recharging, and the detailed energy consumption along the path between two nodes of interest. We propose a Hybrid Threshold Acceptance (HTA) algorithm for this problem and denote it as the Hybrid Waste Collection Problem (HWCP). Extensive computational experiments confirm that the proposed HTA algorithm provides good results against current state-of-the-art algorithms designed for the electric vehicle routing problem. Out detailed computational results demonstrate the performance of our method considering either full or partial recharging, as well as the effect of different battery/tank capacities. Compared to the standard CNG or electric vehicles, we also show the benefits of using a fleet of hybrid electric refuse vehicles in terms of operational costs and total distance traveled.

Complete Neighbourhood Search Heuristic Algorithm for Portfolio Optimization

In portfolio optimization, the fundamental goal of an investor is to optimally allocate investments between different assets. Mean-variance optimization methods make unrealistic assumptions to solve the problem of optimal allocation. On the other hand, when realistic constraints like holding size and cardinality are introduced it leads to optimal asset allocation which differ from the mean variance optimization. The resulting optimization problem become quite complex as it exhibits multiple local extrema and discontinuities. Heuristic algorithms work well for the complex problem. Therefore, a heuristic algorithm is developed which is based on hill climbing complete (HC-C). It is utilized to solve the extended portfolio optimization problem. In order to validate its performance, the proposed HC-C is tested with standard portfolio optimization problem. Experimental results are benchmarked with the quadratic programming method and threshold accepting (TA) algorithm.

TA algorithms for D-optimal OofA Mixture designs

In a mixture experiment, m components are mixed to produce a response. The total amount of the mixture is a constant. This classical experiment has been studied for a long time, but little attention has been given to the addition order of the components. In an Order-of-Addition (OofA) Mixture experiment, the response depends on both the mixture proportions of components and their order of addition. The overall goal of the OofA Mixture experiment is to identify the addition order and mixture proportions that produce an optimal response. Methodology for constructing full OofA Mixture designs is discussed, but the size of these full designs increases rapidly as m increases. A Threshold Accepting (TA) algorithm is used to find a subset of n rows of the full OofA Mixture design that maximize the D-optimality criterion, reducing the number of required runs. Neighborhood structures are proposed for OofA simplex lattice and general mixture designs. The TA algorithm is compared with the well-known Fedorov algorithm, and recommendations for the use of this algorithm are provided.

Construction of uniform designs over continuous domain in computer experiments

Limited by practical operation, most experimental designs were constructed on discrete space, even if the influencing factors themselves are continuous. While in computer experiments, one can explore more possibilities to improve the modeling performance without increasing the test cost. As a space-filling design, the construction of uniform designs (UDs) can be naturally extended from lattice domain to continuous domain, so as to obtain better uniformity. In this article, coordinate descent methods are employed to construct UDs over the continuous domain with an initialization derived by threshold accepting (TA) algorithm. Our approach is suitable for arbitrary L 2-discrepancy. In particular, we provide the coordinate gradients under centered L 2-discrepancy and mixture discrepancy, as well as the code package. Computer experiments built on Kriging models show that our method can not only obtain more uniform designs, but also perform better in modeling than previous records.

High Speed Hill Climbing Algorithm for Portfolio Optimization

Portfolio can be defined as a collection of investments. Portfolio optimization usually is about maximizing expected return and/or minimising risk of a portfolio. The mean-variance model makes simplifying assumptions to solve portfolio optimization problem. Presence of realistic constraints leads to a significant different and complex problem. Also, the optimal solution under realistic constraints cannot always be derived from the solution for the frictionless market. The heuristic algorithms are alternative approaches to solve the extended problem. In this research, a heuristic algorithm is presented and improved for higher efficiency and speed. It is a hill climbing algorithm to tackle the extended portfolio optimization problem. The improved algorithm is Hill Climbing Simple–with Reducing Thresh-hold Percentage, named HC-S-R. It is applied in standard portfolio optimization problem and benchmarked with the quadratic programing method and the Threshold Accepting algorithm, a well-known heuristic algorithm for portfolio optimization problem. The results are also compared with its original algorithm HC-S. HC-S-R proves to be a lot faster than HC-S and TA and more effective and efficient than TA.
 Keywords: Portfolio optimization; Hill climbing algorithm; Threshold percentage; Reducing sequence; Threshold Acceptance algorithm

Drone routing and optimization for post-disaster inspection

Aerial drones have received increased attention by humanitarian organizations due to their potential to serve/monitor a disaster-affected region. In this study, we propose a mixed-integer linear programming model for a Heterogeneous Fixed Fleet Drone Routing problem (HFFDRP) that minimizes the post-disaster inspection cost of a disaster-affected area by accounting a number of drone trajectory-specific factors into consideration, such as battery recharging costs, servicing costs, drone hovering, turning, accelerating, cruising, and decelerating costs, and many others. Two heuristic algorithms are proposed, namely, Adaptive Large Neighborhood Search (ALNS) algorithm and Modified Backtracking Adaptive Threshold Accepting (MBATA) algorithm, to solve the largest instances of our proposed optimization model in a reasonable amount of time. Computational results indicate that the proposed MBATA algorithm is capable of producing high-quality solutions consistently within a reasonable amount of time. Finally, a real-life case study is used to visualize and validate the model results and to draw managerial insights that reveal how network design decisions vary with key drone design parameters.

An improved imperfect maintenance strategy for multiperiod randomly failing equipment with stochastic repair times

PurposeIn this paper, a maintenance strategy based on improved imperfect maintenance actions with stochastic repair times for multiperiod randomly failing equipment is developed. The main objective is to minimize the total maintenance cost by jointly finding the optimal preventive maintenance (PM) cycle and planning horizon.Design/methodology/approachA model based on the mathematical theory of reliability is developed to minimize the total maintenance cost by jointly finding the optimal couple: PM cycle T* and planning horizon H*. The proposed model aims to characterize the evolutionary impact of imperfect PM actions on the equipment failure rate and the resulting mean number of failures. The conventional threshold accepting (TA) algorithm is implemented to solve the proposed model. A numerical example for a given set of input parameters is presented in order to show the usefulness of the proposed model. A sensitivity analysis of some of the key parameters is performed to demonstrate the coherence of the developed maintenance policy.FindingsThe obtained results showed a sensitive trade-off between PM frequency and the total maintenance cost. Performing PM actions more frequently helps significantly to reduce the expected number of corrective maintenance actions and the corresponding total cost. It has also been found that improving the efficiency of the PM actions allows for maintaining the equipment less frequently by increasing the time between successive PM actions.Research limitations/implicationsGiven the complexity of the objective function to be minimized and the stochastic nature of the model's parameters, the authors limited this study to equally cyclic production periods over the planning horizon.Practical implicationsThe present model aims to provide an integrated maintenance/production comprehensive framework to assist planners in establishing maintenance schedules considering multiperiod randomly failing production systems and the evolutionary impact of imperfect PM actions on the equipment failure rate.Originality/valueContrary to the majority of existing works in the literature dealing with maintenance strategies, the authors consider that repair times are stochastic to provide a more realistic framework. In addition, the developed model considers the impact of imperfect maintenance on the equipment's mean time to failure. Thus, the evolutionary impact of imperfect PM actions on the equipment failure rate and the resulting mean number of failures is characterized. Simultaneously, the production planning horizon along with the length of each PM cycle is optimized in order to minimize the total maintenance cost over the planning horizon.

Stackelberg–Nash equilibrium of pricing and inventory decisions in duopoly supply chains using a nested evolutionary algorithm

Pricing and inventory control in a competing environment, as separate entities, have attracted much attention from academics and practitioners. However, integrating these decisions in a competitive setting has not been significantly analyzed by academics, but is of great significance to practitioners. In this study, the joint decision on price and inventory control of a deterioration product is investigated in a duopoly setting. We consider two competing supply chains, each consisting of one manufacturer and one retailer. Each manufacturer, as the leader of their supply chain determines the wholesale price to maximize their profit, while the retailer as the follower should determine the retail price and inventory cycle to maximize his or her profit. Using a game theoretic approach, we formulate in-chain, and chain-to-chain competition as a bi-level programming problem, and analyze Stackelberg–Nash equilibrium of the problem. Furthermore, two versions of a nested algorithm are proposed to obtain the equilibrium. Both versions employ a modified threshold-accepting (TA) algorithm to solve the first level of the problem. However, while the first version utilizes the modified TA algorithm to deal with the second level of the problem, the second version applies a differential evolution (DE) approach. Eventually, a numerical study is carried out not only to compare two developed versions of the algorithm, but also to implement the sensitivity analysis of main parameters. Based on numerical experiments, although the accuracy of both versions of algorithm are alike, using TA is more computationally efficient than using DE. Furthermore, despite the permissibility of partial backlogging, it has never occurred in equilibrium points due to in-chain and chain-to-chain competition.

Construction of uniform designs via an adjusted threshold accepting algorithm

The threshold accepting (TA) algorithm, a stochastic heuristic technique, has been proposed as an effective method for constructing uniform designs (UDs). However, some flaws of this algorithm have been detected recently, especially when optimizing designs with large sizes. This paper proposes an adjusted TA algorithm that can overcome the defects of traditional TA. This new algorithm successfully updated the website UD tables by designs with better uniformity. Furthermore, the adjusted TA helps us to obtain a new UD with 27 runs and 13 factors each having 3 levels under the mixture L2-discrepancy. This UD is a minimum aberration design.

Construction of uniform [formula omitted]-designs

Orthogonal array-based Latin hypercubes, also called U-designs, have popularly been adopted for designing a computer experiment. The relationship between the averaged discrepancy of all U-designs generated from a given orthogonal array and the generalized wordtype pattern of the orthogonal array is established. Motivated by the relationship, we define a weighted wordtype pattern and a minimum weighted aberration criterion to compare orthogonal arrays of the same parameters. U-designs generated from an orthogonal array with less weighted aberration are shown to have low discrepancies on average. Then, an algorithm to construct uniform U-designs is proposed. It begins with a minimum weighted aberration orthogonal array and its advantage is illustrated by comparing with the threshold-accepting algorithm.

Application of Genetic Algorithms (GA) and Threshold Acceptance (TA) to a Ternary Liquid-Liquid Equilibrium System

In this study we present the results of the simulation of ternary liquid-liquid equilibrium (LLE) using Genetic Algorithm and Threshold Acceptance Algorithm with two hybrid functions (Nelder-Mead Simplex method: NMS and Quasi-Newton method: QN). These methods show that the hybridization of both GA and TA algorithms give good values of tie-lines. The RMSD values obtained were compared to UNIQUAC and NRTL models using GA and TA algorithms with NMS and QN hybrid functions. The Levy function was used in the test performances of GA and TA algorithms. The experimental protocol considered in this work was a ternary system (Trichloromethane-Acetic acid-Water) at two different temperatures. The thermodynamic models considered for the calculation of the interaction parameter are UNIQUAC and NRTL models. The interaction parameters were presented; the experimental and theoretical tie-lines were plotted on triangular coordinates.

Two- and three-level lower bounds for mixture [formula omitted]-discrepancy and construction of uniform designs by threshold accepting

The uniform experimental design (UD), a major kind of space-filling design, is widely used in applications. The majority of UD tables (UDs) with good uniformity are generated under the centralized L2-discrepancy (CD) and the wrap-around L2-discrepancy (WD). Recently, the mixture L2-discrepancy (MD) is proposed and shown to be more reasonable than CD and WD in terms of uniformity. In this paper we review lower bounds for MD of two-level designs from a different point of view and provide a new lower bound. Following the same idea we obtain a lower bound for MD of three-level designs. Moreover, we construct UDs under the measurement of MD by the threshold accepting (TA) algorithm, and finally we attach two new UD tables with good properties derived from TA under the measurement of MD.

Multi-agent list-based threshold-accepting algorithm for numerical optimisation

Traditional list-based threshold-accepting LBTA algorithm is similar with simulated annealing SA algorithm, depends on an intense local search method, and utilises a list filling procedure with threshold values to search the solution space effectively. Inspired by the learning ability of particle swarm optimisation PSO, multi-agent LBTA MLBTA involves the learning knowledge to guide its sampling, explores the solution space in a co-evolution mode. Compare with multi-agent SA MSA algorithm adapting the same local search version, MLBTA incorporates a dynamic list of threshold values which is adapted according to the topology of the solution space and tunes only one parameter. Dispense with sophisticated parameters as MSA, MLBTA balances the intensification and diversification iteratively. Computational results on functions optimisation and protein structure prediction PSP problems show that MLBTA algorithm achieves better or comparable performances with MSA.

Optimization of Cutting Conditions in Milling Process to Minimize Tool Wear Using Selected Soft Computing Techniques: A Comparative Study

The life of a tool is very significant in metal cutting because production time is a waste whenever a tool is replaced or reset. Because of prolonged use, cutting tools blunt and their effectiveness decreases over time. It is necessary to replace, index or resharpen, and reset the tool after certain time. Tool life is a measure of the length of time a tool will cut effectively. The life of a cutting tool is mostly affected by many factors, such as, the tool wear, material removal rate, microstructure of the material being cut, setup rigidity, and cutting fluid quality. In this paper, up-milling and down-milling are compared with respect to different input parameters mainly cutting speed, feed, and number of teeth, rake angle, and helix angle. A relationship between tool wear and these input parameters is established by using regression analysis and soft computing techniques are applied to minimize the tool wear. Five selected soft computing techniques viz. (i) Genetic Algorithm (GA), (ii) Simulated Annealing (SA), (iii) Hybrid GA with Pattern Search (PS), (iv) Particle Swarm Optimization (PSO), and (v) Threshold Acceptance Algorithm (TAA), are used for optimization of tool wear. The results obtained from each of them are also analyzed. The effect of input parameters on tool wear, the way it is different for up-milling and down-milling is addressed for each case with the help of five selected soft computing techniques. The results indicate that the tool wear is least in case of down-milling when compared to up-milling and hybrid GA gave the best results.

Construction of uniform designs without replications

A uniform design scatters its design points evenly on the experimental domain according to some discrepancy measure. In this paper all the design points of a full factorial design can be split into two subdesigns. One is called the complementary design of the other. The complementary design theories of characterizing one design through the other under the four commonly used discrepancy measures are investigated. Based on these complementary design theories, some general rules for searching uniform designs through their complementary designs are proposed. An efficient method to check if a design has repeated points is introduced and a modified threshold-accepting algorithm is proposed to search uniform or nearly uniform designs without replications. The new algorithm is shown to be more efficient by comparing with other existing methods. Many new uniform or nearly uniform designs without replications are tabulated and compared.

Optimization of the effect of welding heat input on the microstructure and mechanical properties of submerged arc welded joints by fuzzy-based multiobjective threshold acceptance algorithm

This article investigates the influence of welding heat input on the microstructure, hardness, ultimate tensile strength and toughness of submerged arc welding of plain carbon steel. An attempt was also made to find an optimal welding heat input conditions using Fuzzy logic–based multiobjective threshold acceptance algorithm. Phase analysis of weldments was evaluated at different welding conditions varying from 7.806 to 17.955 kJ/cm. Results revealed that the percentage of ferrite increases with the heat but pearlite percentage decreases and significant grain coarsening was observed in weld zone. Mechanical properties of the weld joints decrease with the increase of heat input. Fuzzy interference system has been adopted to solve the multiobjective problem to avoid the imprecision and uncertainty in weights of the responses. Threshold acceptance method has been introduced for finding optimal welding heat input condition. Finally, a confirmatory test was carried out using the optimal result to verify the effectiveness of this approach.

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.