Population-based Simulated Annealing Research Articles

Urban freight distribution with electric vehicles: comparing some solution procedures

The Vehicle Routing Problem (VRP) is a well-known discrete optimization problem that has an impact on theoretical and practical applications. In this paper, a freight distribution model that includes a charging system located at the depot, making it feasible for real world-implementation, is proposed. Two different solution methods are proposed and compared: a genetic algorithm (GA) and a population-based simulated annealing (PBSA) with the number of moves increasing during the iterations. Among the variety of algorithm used to solve the VRP, population-based search methods are the most useful, due to the ability to update the memory at each iteration. To demonstrate the practical aspects of the proposed solution a case study is solved using travel time on a real network to evaluate the potentiality for a real-world application.

Adaptive population-based simulated annealing for resource constrained job scheduling with uncertainty

Transporting ore from mines to ports is of significant interest in mining supply chains. These operations are commonly associated with growing costs and a lack of resources. Large mining companies are interested in optimally allocating resources to reduce operational costs. This problem has been previously investigated as resource constrained job scheduling (RCJS). While a number of optimisation methods have been proposed to tackle the deterministic problem, the uncertainty associated with resource availability, an inevitable challenge in mining operations, has received less attention. RCJS with uncertainty is a hard combinatorial optimisation problem that is challenging for existing optimisation methods. We propose an adaptive population-based simulated annealing algorithm that can overcome existing limitations of methods for RCJS with uncertainty, including pre-mature convergence, excessive number of hyper-parameters, and the inefficiency in coping with different uncertainty levels. This new algorithm effectively balances exploration and exploitation, by using a population, modifying the cooling schedule in the Metropolis-Hastings algorithm, and using an adaptive mechanism to select perturbation operators. The results show that the proposed algorithm outperforms existing methods on a benchmark RCJS dataset considering different uncertainty levels. Moreover, new best known solutions are discovered for all but one problem instance across all uncertainty levels.

Realization and Optimization of Combinational Circuits Using Simulated Annealing and Partitioning Approach

Combinational logic circuits (CLCs) are basic building blocks of a system and optimization of these circuits in terms of reduced gates, transistors, or levels will lead to reduced area on chip, reduced power, and improved speed. Simulated annealing (SA) is a thermo-inspired metaheuristic used for solving various engineering and non-engineering problems. SA is also used for the realization and optimization of CLCs. Circuits with a large number of inputs and outputs require more generations for realization. Realization of the optimal circuit with fewer generations is desired as realization time increases with increase in the number of generations. In this paper, an attempt is made to realize circuits using population-based SA with fewer generations. SA with partitioning approach is proposed in this paper for circuits that could not be realized with fewer preset generations. To evaluate the performance of the proposed work, benchmark circuits from LGSynth'91 are considered, and it is observed that the success rate improved and realization time reduced with the proposed partitioning approach. During the evaluation, it is also observed that the gate count was reduced by 2.5–77.39% and the transistor count was reduced by 7.69–95.53% on using proposed work with fewer generations over circuits reported in the literature.

Design and Evaluation of Multipliers Using Simulated Annealing and Partitioning Approach

Multipliers are widely used in various fields of engineering, and they are considered to have complex designs. The efficient design of multipliers to meet various design requirements is still an active area of research. In this paper, a thermo-inspired metaheuristic called population-based simulated annealing algorithm, for the design of multipliers using four different resource types, is proposed. Metaheuristics suffers from the problem of scalability and non-convergence as the size and complexity of the circuit increase. Four types of partitioning approaches- output, input, input-output and hybrid-output partitioning are proposed to overcome the same. Proposed partitioning approaches have increased the success rate and reduced the time to realize the circuit. The multipliers designed are synthesized on Cadence Genus with 90 nm technology and compared with traditional designs such as Array, Wallace tree, Dadda and Booth multipliers to conclude that metaheuristics are capable of generating near-optimal solutions in terms of power, area and delay.

Designing an efficient vaccine supply chain network using a two-phase optimization approach: a case study of COVID-19 vaccine

The upsurge of the COVID-19 pandemic and its consequences on the world’s population has led to the accelerated production of vaccines across the world. The next challenge in the fight against COVID-19 is to distribute those vaccines to the right person in an optimized way by establishing an efficient vaccine supply network. Consequently, this paper studies an integrated two-phase planning framework for the vaccine distribution network. In the first phase, the population target is classified into several groups to determine their priority for vaccination using a multiple attribute decision making (MADM) technique. The second phase uses a mathematical model to decide on the location of distribution centers, inventory policies, and routing decisions to minimize the total procurement, inventory, and distribution costs. Since the proposed model falls into the category of NP-hard problems, a metaheuristic algorithm entitled population-based simulated annealing (PBSA) is developed to solve the presented model. Besides, the improved grey wolf optimizer (I-GWO) is customized and used as another solution method. A few generated datasets are utilized to evaluate and validate the performance of these solution methods. In addition, this methodology is implemented in a case study of the COVID-19 vaccine supply chain in Iran to demonstrate its practicability.

A Hybrid Metaheuristic for the Unrelated Parallel Machine Scheduling Problem

The unrelated parallel machine scheduling problem aims to assign jobs to independent machines with sequence-dependent setup times so that the makespan is minimized. When many practical considerations are introduced, solving the resulting problem is challenging, especially when problems of realistic sizes are of interest. In this study, in addition to the conventional objective of minimizing the makespan, we further consider the burn-in (B/I) procedure that is required in practice; we need to ensure that the scheduling results satisfy the B/I ratio constrained by the equipment. To solve the resulting complicated problem, we propose a population-based simulated annealing algorithm embedded with a variable neighborhood descent technique. Empirical results show that the proposed solution strategy outperforms a commonly used commercial optimization package; it can obtain schedules that are better than the schedules used in practice, and it does so in a more efficient manner.

An efficient population-based simulated annealing algorithm for 0–1 knapsack problem

0–1 knapsack problem (KP01) is one of the classic variants of knapsack problems in which the aim is to select the items with the total profit to be in the knapsack. In contrast, the constraint of the maximum capacity of the knapsack is satisfied. KP01 has many applications in real-world problems such as resource distribution, portfolio optimization, etc. The purpose of this work is to gather the latest SA-based solvers for KP01 together and compare their performance with the state-of-the-art meta-heuristics in the literature to find the most efficient one(s). This paper not only studies the introduced and non-introduced single-solution SA-based algorithms for KP01 but also proposes a new population-based SA (PSA) for KP01 and compares it with the existing methods. Computational results show that the proposed PSA is the most efficient optimization algorithm for KP01 among all SA-based solvers. Also, PSA’s exploration and exploitation are stronger than the other SA-based algorithms since it generates several initial solutions instead of one. Moreover, it finds the neighbor solutions based on the greedy repair and improvement mechanism and uses both mutation and crossover operators to explore and exploit the solution space. Suffice to say that the next version of SA algorithms for KP01 can be enhanced by designing a population-based version of them and choosing the greedy-based approaches for the initial solution phase and local search policy.

Concurrent scheduling and layout of virtual manufacturing cells considering assembly aspects

Cell formation, scheduling, and facility layout are three main decisions in designing manufacturing cells. In this paper, we address the integration of these decisions in virtual manufacturing cells considering assembly aspects and process routing. We develop a mathematical model to determine the machine cells, the layout of machines and workstations on the shop floor, the processing route of parts, and the production sequence of operations on the machines. In this mathematical model, material handling costs and cycle time are minimized. To the best of our knowledge, this is the first paper that concurrently addresses the scheduling and layout of virtual manufacturing cells with assembly aspects and so-called criteria. To effectively solve the problem, a Population-based Simulated Annealing (PSA) combined with linear programming is proposed. The practical usability of the developed model is demonstrated in a case study. Finally, instances from the literature are solved to evaluate the performance of the PSA. The comparison results showed the superior performance of the PSA in comparison with CPLEX solver and standard simulated annealing.

Hybrid algorithm of harmony search for dynamic parallel row ordering problem

In the context of an automated assembly line and flexible manufacturing, good layout planning of the production facilities aids in improving production efficiency and reducing production costs. The current research on the facility layout problems mainly focuses on the static ones with the fixed flow between facilities, including the parallel row ordering problem (PROP). Based on existing research on the PROP, in this study, we first investigate the dynamic parallel row ordering problem (DPROP), considering the flexibility of the production line. This study proposes a DPROP model and utilises it to verify some PROP examples less than 15 facilities and some global optimal solutions are achieved. In addition, the performance of the model in solving DPROP is verified on some new small-scale examples designed based on the PROP. Owing to the limited performance of the exact methods for DPROP, this study proposes a hybrid algorithm of harmony search and tabu search to solve large-scale problems, and this new algorithm performs better than some existing ones so that some new better solutions for the PROP examples are obtained. The algorithm is first utilised to solve the small-scale PROP and DPROP and the results are compared with an exact methods. Moreover, by evaluating the large-scale PROP between 30 and 70 facilities, the results are compared with those of the improved genetic algorithm and the population-based simulated annealing algorithm, thereby 28.8 % of the current optimal solutions are improved. Finally, the hybrid algorithm of harmony search and tabu search is utilised to solve the large-scale DPROP with 30 and 40 facilities, and some optimal solution sequences are presented.

Solving the Laser Cutting Path Problem Using Population-Based Simulated Annealing with Adaptive Large Neighborhood Search

This paper presents an alternative algorithm for solving the laser cutting path problem which was modeled as Generalized Traveling Salesman Problem (GTSP). The objective is to minimize the traveling distance of laser cutting of all profiles in a given layout, where a laser beam makes a single visit and then does the complete cut of individual profile in an optimum sequence. This study proposed a hybrid method combining population-based simulated annealing (SA) with an adaptive large neighborhood search (ALNS) algorithm to solve the cutting path problem. Recombination procedures were executed alternately using swap, reversion, insertion and removal-insertion through a fitness proportionate selection mechanism. In order to reduce the computing time and maintain the solution quality, the 35% proportion of population were executed in each iteration using the cultural algorithm selection method. The results revealed that the algorithm can solve several ranges of problem size with an acceptable percentage of error compared to the best known solution.

Solving a new cost-oriented assembly line balancing problem by classical and hybrid meta-heuristic algorithms

In this study, a new cost-oriented assembly line balancing problem is proposed and formulated. A single objective function consisting of minimizing the cost associated with equipment, labor wage, and station establishment is considered for the problem. This problem is more complicated comparing to the literature as worker qualification is considered for determining his/her wage. As this problem is of NP-hard optimization problems, some meta-heuristic solution approaches, e.g., simulated annealing, variable neighborhood search, genetic algorithm, tabu search, population-based simulated annealing, and their hybrid versions are proposed. In the proposed algorithms, a novel encoding–decoding scheme is applied. This scheme uses the Hungarian method to assign the workers to the station to reduce the total wage of the workers. To study the performance of the proposed meta-heuristic algorithms, ten test problems are generated randomly, and using one of them the parameters of the algorithms are tuned by the Taguchi method. The final experiments on the proposed algorithms and the test problems show that in the most of the experiments, among the proposed algorithms, the single-solution-based algorithms, except TS, perform better than the population-based algorithms, especially for the case of large size test problems.

A green vehicle routing problem with time windows considering the heterogeneous fleet of vehicles: two metaheuristic algorithms

In this paper, the green vehicle routing problem with time windows constraint is studied in the presence of a heterogeneous fleet of vehicles and filling stations. In addition, the number of vehicles and their fuel tank capacity are both limited. The main contribution of this study is the simultaneous consideration of these features, which makes the problem more practical. For this purpose, a mixed integer linear programming model that minimises the transportation costs and (or carbon dioxide) emissions, is proposed. Furthermore, a genetic algorithm and a population-based simulated annealing are developed to find high-quality solutions for large-scale instances. To validate the proposed model and algorithms, 28 instances are generated using a benchmark database. The computational results demonstrate that both algorithms provide efficient solutions regarding the objective function value and CPU time. Finally, a comprehensive sensitivity analysis is carried out to show the importance of features mentioned above. [Received: 7 October 2016; Revised: 27 December 2018; Accepted: 13 January 2019]

Robust optimisation of the intermodal freight transport problem: Modeling and solving with an efficient hybrid approach

In the present paper, we propose robust optimisation models for the intermodal freight transport problem for dealing with uncertainties in using costs, and the capacities of terminals and uncertainties in transportation costs. Moreover, we propose two solution approaches for efficiently solving the problem. The first one is a population-based simulated annealing (PBSA) with heuristics. The second one is a hybrid solution approach combining the PBSA with an exact method. In addition to a theoretical study of randomly-generated instances, a real network is addressed for testing the performance of the proposed methods and models and analysing the impact of robustness.

A bi-level bi-objective mathematical model for cellular manufacturing system applying evolutionary algorithms

The present study aimed to design a bi-objective bi-level mathematical model for multi-dimensional cellular manufacturing system. Minimizing the total number of voids and balancing the assigned workloads to cells are regarded as two objectives of the upper level of the model. However, the lower level attempts to maximize the workers' interest to work together in a special cell. To this aim, two nested bi-level metaheuristics including particle swarm optimization (NBL-PSO) and a population-based simulated annealing algorithm (NBL-PBSA) were implemented to solve the model. In addition, the goal programming approach was utilized in the upper level procedure of these algorithms. Further, nine numerical examples were applied to verify the suggested framework and the TOPSIS method was used to find the better algorithm. Furthermore, the best weights for upper level objectives were tuned by using a weight sensitivity analysis. Based on computational results, all three objectives were different from their ideal goals when decisions about inter and intra-cell layouts, and cell formation to balance the assigned workloads by considering voids and workers' interest were simultaneously madeby considering a wide assumption-made problem closer to the real world. Finally, NBL-PBSA could perform better than NBL-PSO, which confirmed the efficiency of the proposed framework.

Constraint programming models and population-based simulated annealing algorithm for finding graceful and $$\alpha $$ α -labeling of quadratic graphs

In this research, a new mathematical integer programming model is presented for the graph labeling problem of quadratic graphs. The advantages of this model are linearity and the existence of an objective function. Furthermore, two constraint programming models and a meta-heuristics algorithm are also developed to generate feasible graceful labeling and $$\alpha $$ -labeling for special classes of quadratic graphs. Experimental results on large sizes of graphs from the literature show the efficiency of the proposed model and approach.

Analysis of maximal covering location-allocation model for congested healthcare systems in user choice environment

This paper attempts to shed light onto the formulation and the solution of a probabilistic maximal covering location model for determining the optimal location of facilities in congested healthcare systems with referral hierarchical structure. We will address healthcare systems operating in a competitive setting and when the customers choose the facilities they patronise, by the travel time to the hospitals and service costs at each hospital. The hospitals have several low-level sections for offering low level services (such as primary services) and several high-level sections for offering high level services (such as professional services) and the patients will refer to different sections of hospitals according to their requirements and their physical conditions. Our objective is to minimise the total amount of demand that is lost in the system. To solve the model, two meta-heuristic algorithms, including population-based simulated annealing (PBSA) and ant colony optimisation (ACO) have been executed and analysed using statistical test and TOPSIS method to determine which algorithm works better.

Analysis of maximal covering location-allocation model for congested healthcare systems in user choice environment

This paper attempts to shed light onto the formulation and the solution of a probabilistic maximal covering location model for determining the optimal location of facilities in congested healthcare systems with referral hierarchical structure. We will address healthcare systems operating in a competitive setting and when the customers choose the facilities they patronise, by the travel time to the hospitals and service costs at each hospital. The hospitals have several low-level sections for offering low level services (such as primary services) and several high-level sections for offering high level services (such as professional services) and the patients will refer to different sections of hospitals according to their requirements and their physical conditions. Our objective is to minimise the total amount of demand that is lost in the system. To solve the model, two meta-heuristic algorithms, including population-based simulated annealing (PBSA) and ant colony optimisation (ACO) have been executed and analysed using statistical test and TOPSIS method to determine which algorithm works better.

An Effective Harmony Search Algorithm for Solving a No-Wait Hybrid Flow Shop Scheduling Problem with Machine Availability Constraint

This research investigates a no-wait hybrid flow shop scheduling problem. Minimizing the mean tardiness is considered as the objective to develop the optimal scheduling algorithm. Characteristics of our considered problem leads to the complexity of problem. First, no-wait operations. Second, setup time of each job is separated from its processing time and depends upon its preceding job. Third, all of jobs aren’t available at the first of scheduling. In other word, each job has individual ready time. Finally, machines are not continuously available due to the preventive maintenance. An effective harmony search algorithm is used to tackle the mentioned problem. A series of computational experiments is conducted by comparing our algorithm with previous meta-heuristic algorithms like population based simulated annealing (PBSA), Adopted imperialist competitive algorithm (ICA) and hybridization of PBSA and ICA (ICA+PBSA). To achieve reliable results, Taguchi approach is used to define robust parameters’ values for our proposed algorithm. The computational results with random test problems suggest that our proposed harmony search outperforms the three foregoing algorithms.

A new hybridized algorithm based on Population-Based Simulated Annealing with an experimental study of phase transition in 3-SAT

This paper is about experiments for satisfiability problem using a new algorithm (GR-MM-PBSA) that improves the algorithm Population-Based Simulated Annealing (PBSA). GR-MM-PBSA runs in a parallel way Simulated Annealing (SA) and Threshold Annealing (TA) algorithms with a Golden Ratio space search strategy and Markovian Model to select initial and final temperature. In this paper we execute differents hybridized Simulated Annealing (or Threshold Accepting) algorithms and compares the efficiency of these, using a metric based on transition phase effect. Simulated Annealing Algorithms (SAA) theoretically can reach the optimum if the control parameters and cooling scheme are chosen correctly. All algorithms are compared with a metric based on transition phase obtained for 3-SAT instances. This paper shows the results of SAA hybridizations are more efficient than the original algorithm, without increasing their computational complexity. We also show the experimental data about runs with 820 3-SAT instances with ratio clauses-variables between 2.0 to 6.0.

An efficient population-based simulated annealing algorithm for the multi-product multi-retailer perishable inventory routing problem

This paper presents an inventory routing problem (IRP) involving perishable products with a fixed lifetime. It involves a multi-period multi-product IRP in two-level supply chains, where products are produced and delivered from a single manufacturer to several retailers utilizing multiple shipping strategies through a fleet of appropriately capacitated vehicles. The goal is to minimize total cost while ensuring that no stock out occurs. A mathematical model is presented. A population-based simulated annealing (PBSA) algorithm is proposed. This PBSA algorithm is compared with simulated annealing (SA) and genetic algorithms (GA) which shows the superiority of the PBSA algorithm. CPLEX solver, branch-and-cut method, and different relaxation methods also were used, so as to obtain upper and lower bounds. The computational experiments show the high efficiency of the PBSA algorithm.