Solution Representation Scheme Research Articles

An effective hyper heuristic-based memetic algorithm for the distributed assembly permutation flow-shop scheduling problem

In this paper, an effective Hyper Heuristic-based Memetic Algorithm (HHMA) is proposed to solve the Distributed Assembly Permutation Flow-shop Scheduling Problem (DAPFSP) with the objective of minimizing the maximum completion time. A novel searching-stage-based solution representation scheme is presented for both improving the search efficiency and maintaining potential solutions. In the global search stage, Estimation of Distribution Algorithm (EDA) is employed as the high level strategy of EDA-based Hyper Heuristic (EDAHH) to find promising product sequences for further exploitation. Based on the newly found knowledge of critical-products, several efficient Low-Level Heuristics (LLHs) are well designed to construct the LLH set so that the powerful exploration ability of the EDAHH can be guaranteed. A simulated-annealing-like type of acceptance criterion is also embedded into each LLH to avoid premature convergence. Then a Critical-Products-based Referenced Local Search (CP-RLS) method is proposed to improve the quality of superior sub-population by operating on the sub-job-sequences derived from the critical products. The benefit of the presented CP-RLS lies in the excellent exploitation ability with substantially reduced computational cost. Finally, performance evaluation and comparison are both carried out on a benchmark set and the results demonstrate the superiority of HHMA over the state-of-the-art algorithms for the DAPFSP.

An energy-efficient multi-objective scheduling for flexible job-shop-type remanufacturing system

This work considers a multi-objective scheduling issue for the remanufacturing system (RMS) including parallel disassembly/reassembly workstations and flexible job-shop-type reprocessing shops with the purpose of reducing completion time and energy usage by deciding the allocation/sequence of disassembly/reassembly jobs and determining the operation sequencing and workstation assignment of reprocessing jobs. A multi-objective mixed-integer programming model is first constructed to describe this scheduling problem mathematically. An improved grey wolf optimization (IGWO) algorithm with the global criterion (GC) multi-objective method and integrated float-number solution representation scheme is introduced to realize high-efficient scheduling. Various local neighborhood search strategies, random disturbance methods, and weighted distance updating mechanisms are integrated into IGWO to enhance its performance. A series of numeral instances are systematically designed and implemented to validate the effectiveness of IGWO. Finally, a case study is deployed to evaluate IGWO’s capability to address the practical remanufacturing scheduling problem. Experimental results reveal that the developed IGWO performs better than other existing methods in terms of solution accuracy, computing speed, solution stability, and convergence performance. Furthermore, the results of case study demonstrate IGWO’s superiority in solving the real-world remanufacturing scheduling problem in lower energy usage and time cost.

Multi-Objective multi-skill resource-constrained project scheduling problem with skill switches: Model and evolutionary approaches

This paper proposes a new extension of the multi-skill resource-constrained project scheduling problem: MS-RCPSP with skill switches. In real-world environment, the switch between skills for a resource often incurs considerable extra operation time and cost to meet the requirement of task. A mixed-integer programming model, aiming to minimize project completion time and total cost, is developed. Then, to solve this new problem effectively, we investigate the related existing solution representations and schedule builders from previous literature. Based on the investigation, we propose a new flexible solution representation scheme with reduced search space and a novel greedy-like schedule builder scheme that reorders tasks to reduce skill switches. Besides, we select two efficient mutation operators, i.e., a swap operator and a resource-leveling operator. The swap operator adjusts the task assignment sequence while the resource-leveling operator reassigns the tasks to other resources based on the resource loads of the current schedule. This operator improves solutions by balancing resource loads. We embed all the proposed new components into a multi-objective evolution strategy (MOES) framework. We analyze different configurations of MOES in terms of representation, schedule builder, and mutation operators, and identify the best configuration. We compare the result of MOES with the state-of-the-art algorithms on a wide range of test instances, and the results show that our proposed representation scheme and schedule builder can improve the convergence of the Pareto Front, while the resource-leveling operator can greatly improve the spread and diversity of the front.

A bi-population immune algorithm for weapon transportation support scheduling problem with pickup and delivery on aircraft carrier deck

The weapon transportation support scheduling problem on aircraft carrier deck is the key to restricting the sortie rate and combat capability of carrier-based aircraft. This paper studies the problem and presents a novel solution architecture. Taking the interference of the carrier-based aircraft deck layout on the weapon transportation route and precedence constraint into consideration, a mixed integer formulation is established to minimize the total objective, which is constituted of makespan, load variance and accumulative transfer time of support unit. Solution approach is developed for the model. Firstly, based on modeling the carrier aircraft parked on deck as convex obstacles, the path library of weapon transportation is constructed through visibility graph and Warshall-Floyd methods. We then propose a bi-population immune algorithm in which a population-based forward/backward scheduling technique, local search schemes and a chaotic catastrophe operator are embedded. Besides, the random-key solution representation and serial scheduling generation scheme are adopted to conveniently obtain a better solution. The Taguchi method is additionally employed to determine key parameters of the algorithm. Finally, on a set of generated realistic instances, we demonstrate that the proposed algorithm outperforms all compared algorithms designed for similar optimization problems and can significantly improve the efficiency, and that the established model and the bi-population immune algorithm can effectively respond to the weapon support requirements of carrier-based aircraft under different sortie missions.

Solution Representation in Proportionate Multiprocessor Open Shop

Proportionate multiprocessor open shop is considered in this study. It is a shop model where a set of jobs follow no predefined route to visit several stages with at least one having two or more parallel machines to carry out the same task. Proportionality means that processing times depend only on stages and are independent of jobs, hence is defined as stage-wise. The shop model has various application areas in industry but the literature on the field is still limited. In this study, a novel solution representation scheme is proposed for the proportionate multiprocessor open shop. The scheme is based on permutation of stages and encodes the cumulative number of job assignments to a stage. The proposed scheme is shown to generate higher quality random solutions compared to the common operation permutation representation for the shop model. The approach proposed in this study to design a solution representation for a scheduling problem is a new and favorable approach that takes into account the specific machine environment, job characteristics and objective function of the problem under consideration. This way of designing solution representation schemes would increase the solution quality or decrease the computational time required in solution algorithms for scheduling problems.

New variable-length data compression scheme for solution representation of meta-heuristics

Solution representation is an important aspect of the development of a meta-heuristic. However, most meta-heuristics focus on the algorithm aspect rather than the solution representation. As the scale of the optimization problem under study rises, the solution representation becomes ever more crucial because the computational performance tends to deteriorate for three reasons: (1) increased landscape complexity, (2) exponential growth of search space, and (3) costly function evaluation. In this study, data compression of solution representation is explored to improve the performance of meta-heuristics in terms of compression efficiency and solution quality. A proposed new data compression scheme – variable-length solution representation compression for meta-heuristics – is developed and tested against benchmarked problem instances from the quadratic assignment problem library (QAPLIB) and additional large problem instances. The analyzed results indicate that the compressed solution representation scheme under a meta-heuristic framework performs well against the QAPLIB and large problem instances with less space complexity and computation time.

Integration of process planning and scheduling for distributed flexible job shops

This paper addresses a problem regarding the joint decision of process planning and scheduling in the context of a distributed flexible job shop (DFJS). The joint decision is called integrated process planning and scheduling (IPPS). Therefore, the problem is called an IPPS/DFJS problem. This research develops a genetic algorithm (called GA_X) to solve the IPPS/DFJS problem. The GA_X algorithm is meritorious insofar as it entails the development of an incomplete modeling scheme (chromosome Φs) to represent an IPPS/DFJS solution. In chromosome Φs, only some decisions are explicitly modeled, and the remaining decisions are implicitly determined using heuristic rules that ensure load balancing among manufacturing resources. Therefore, GA_X generates load-balanced solutions and is more likely to search effectively. We optimize the genetic parameters of GA_X by conducting a full factorial experiment. Three experiments are conducted to compare GA_X with other algorithms. Experiment I involves two light-loading IPPS/DFJS instances. Experiment II involves 15 light-loading IPPS/flexible job shop (FJS) instances (degenerated cases of IPPS/DFJS problems). Experiment III involves 17 heavy-loading IPPS/DFJS instances. GA_X outperforms benchmark algorithms, and Φs (the proposed incomplete chromosome representation) has considerable merit. This finding highlights a promising direction in developing “incomplete solution representation schemes” when solving complex space-search problems with genetic or other metaheuristic algorithms.

Resource Management for Improving Soft-Error and Lifetime Reliability of Real-Time MPSoCs

Multiprocessor system-on-chip (MPSoC) has been widely used in many real-time embedded systems where both soft-error reliability (SER) and lifetime reliability (LTR) are key concerns. Many existing works have investigated them, but they focus either on handling one of the two reliability concerns or on improving one type of reliability under the constraint of the other. These techniques are thus not applicable to maximize SER and LTR simultaneously, which is highly desired in some real-world applications. In this paper, we study the joint optimization of SER and LTR for real-time MPSoCs. We propose a novel static task scheduling algorithm to simultaneously maximize SER and LTR for real-time homogeneous MPSoC systems under the constraints of deadline, energy budget, and task precedence. Specifically, we develop a new solution representation scheme and two evolutionary operators that are closely integrated with two popular multiobjective evolutionary optimization frameworks, namely NSGAII and SPEA2. Extensive experimental results on standard benchmarks and synthetic applications show the efficacy of our scheme. More specifically, our scheme can achieve significantly better solutions (i.e., LTR-SER tradeoff fronts) with remarkably higher hypervolume and can be dozens or even hundreds of times faster than the state-of-the-art algorithms. The results also demonstrate that our scheme can be applied to heterogeneous MPSoC systems and is effective in improving reliability for heterogeneous MPSoC systems.

Integrating scheduling with optimal sublot for parallel machine with job splitting and dependent setup times

This paper addresses a novel problem of the parallel capacitated machines with job splitting and dependent setup times (PCMS), Pmc|split, pj, sjp|Cmax. A mixed integer programming (MIP) model is developed to find an optimal schedule with minimum makespan. Since the problem is NP-hard, metaheuristics are required to find a near optimal solution for larger, more practical problems. Therefore, this paper presents the first applications of two effective metaheuristics, Particle Swarm Optimization (PSO) and Differential Evolution (DE) with a solution representation scheme for solving the problem. To evaluate the metaheuristics’ performances, the lower bound is also firstly developed. Experimental results reveal that, in the small-size problems, there are no distinctive differences between the two algorithms’ performances, since both algorithms are able to find the optimal solutions. However, for medium to large size problems, the DE outperforms the PSO by providing significantly superior results of makespan for 22 out of 27 instances.

Hybrid bi-objective gray wolf optimization algorithm for a truck scheduling problem in the automotive industry

This paper investigates a bi-objective truck scheduling problem (BTSP) in the automotive industry, where a set of containers are transported in batches from a cross-dock to an assembly manufacturer. Each container is characterized by an arbitrary size, an unequal release time and a due date. The problem is to assign containers into batches and schedule these batches on identical trucks so as to minimize the makespan and the total weighted earliness and tardiness cost. A mixed integer linear programming (MILP) model is developed for solving BTSP to optimality via an epsilon-constraint method. Due to NP-hardness of the considered problem, a hybrid bi-objective gray wolf optimization (HBGWO) algorithm is proposed by combining the decomposition framework and the gray wolf optimizer (GWO) metaheuristic. A new solution representation scheme is developed to accommodate the problem characteristic. In addition, the Gaussian mutation (GM) and a tailored local search are introduced to enhance the algorithm’s convergence ability and exploitation performance, respectively. Computational results indicate that the proposed hybrid algorithm is effective and efficient in solving BTSP with different scales.

Optimal scheduling for location geosynchronous satellites refueling problem

This paper addresses the scheduling problem arising from refueling multiple geosynchronous (GEO) satellites with multiple servicing vehicles [many-to-many (M2M) refueling]. The problem is defined by a set of potential fuel tanker locations, a homogeneous fleet of servicing vehicles with limited capacities, and a set of fuel-deficient GEO satellites with known fuel demands. The objective is to open a subset of fuel tankers, to assign GEO satellites to these tankers and to design vehicle servicing sequences, in order to minimize the total mission costs. To achieve such an economical refueling strategy, the fuel tanker location and routing decision are required to be determined simultaneously. It is shown that this problem can be formulated as a location-routing problem (LRP) which is obviously NP-hard. In order to solve it, an ant colony optimization (ACO) metaheuristic that features a special solution representation scheme is proposed. The proposed algorithm is then tested on two types of instances depending on whether the cost for opening a fuel tanker is considered or not. Numerical experiments show that both the consideration of the fuel tanker opening costs and their locations do affect the refueling schedule. Furthermore, the proposed algorithm outperforms the existing approaches in the M2M refueling mission design, and it is able to detect the optimal refueling strategy on all instances containing 85 GEO targets with 15 potential fuel tankers while previous works stopped at 15 satellites and 2 fuel tankers.

Improved discrete cuckoo search for the resource-constrained project scheduling problem

An Improved Discrete Cuckoo Search (IDCS) is proposed in this paper to solve resource-constrained project scheduling problems (RCPSPs). The original Cuckoo Search (CS) was inspired by the breeding behaviour of some cuckoo species and was designed specifically for application in continuous optimisation problems, in which the algorithm had been demonstrated to be effective. The proposed IDCS aims to improve the original CS for solving discrete scheduling problems by reinterpreting its key elements: solution representation scheme, Lévy flight and solution improvement operators. An event list solution representation scheme has been used to present projects and a novel event movement and an event recombination operator has been developed to ensure better quality of received results and improve the efficiency of the algorithm. Numerical results have demonstrated that the proposed IDCS can achieve a competitive level of performance compared to other state-of-the-art metaheuristics in solving a set of benchmark instances from a well-known PSPLIB library, especially in solving complex benchmark instances.

An Improved Firefly Algorithm for the Unrelated Parallel Machines Scheduling Problem With Sequence-Dependent Setup Times

Research in the area of unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup times has received little attention from the research community. However, this problem is NP-hard even without considering the setup times, and when sequence-dependent setup times are included, finding optimal solutions becomes very difficult, especially for the problems with large dimension. In this paper, a firefly algorithm (FA) which is refined with a local search solution improvement mechanism is presented to solve this problem, with the objective of reaching a near-optimum solution. Since the classical FA was originally designed for continuous optimization problems, a new solution representation scheme is designed to make the FA suitable for a combinatorial optimization problem such as the UPMSP. Three different popular metaheuristic algorithms are developed in parallel to verify and measure the effectiveness of the proposed algorithm. More so, the success of the novel firefly scheduling method is measured by comparing the quality of its solutions against the best-known methods from the literature. An exhaustive computational and statistical analysis is carried out to show an excellent performance of the new method on a large set of problem instances. The numerical results show that the improved FA is competitive, fast, and efficient and provide good quality solutions for both small and large problem instances.

Computational Intelligence Approaches for Energy Optimization in Wireless Sensor Networks

Wireless sensor networking is a promising technology that can lead to automatic, intelligent, easier and more secure systems. A wireless sensor network (WSN) consists of small battery powered devices with limited energy resources. One of the major challenges in WSN lies in the energy constraint and computation resources available at the sensor nodes. One way to achieve energy efficiency would be through the use of a clustering technique. In this paper, we propose computational intelligence (CI) approaches to deal with the problem of sensor nodes clustering in a WSN with the ultimate goal to reduce energy expenditures and thus to extend the lifetime of the network. The main motivation is that CI brings about flexibility, autonomous behavior, and robustness against topology changes, communication failures, and scenario changes. The main features of the proposed work span over two aspects. First, four metaheuristics have been adapted to deal with the tackled problem namely genetic algorithms, evolution strategies, particle swarm optimization and artificial bees colony. In this context, a suitable solution representation scheme has been developed and accordingly the algorithms operators, and overall dynamics have been defined. Second, the four developed algorithms are combined with an exhaustive search that is triggered whenever the number of alive sensor nodes drops below a given threshold. The performance of the proposed algorithms has been assessed and compared to the most known state of the art clustering based method namely low energy adaptive clustering hierarchy algorithm (LEACH). The obtained results show that the proposed approaches optimize in an efficient manner the lifetime of WSNs. They also show that the proposed algorithms compete and even outperform LEACH algorithm.

Developing a Decision Support System for University Course Timetabling: A Real World Problem

There are several characteristics that make timetabling problems particularly difficult to solve. Even the small instances of university course timetabling problem have huge search spaces, they are often highly constrained, they require sophisticated solution representation schemes, and they usually require very time-consuming fitness evaluation routines. Thus standard evolutionary algorithms lack of efficiency to deal with them. In this paper we have proposed a Genetic Algorithm (GA) with biased selection strategy for decoding chromosomes. Using this type of decoding strategy improves the feasibility ratio of the population. Since the resulted GA incorporates GA with problem specific knowledge for decoding and solution construction, we can call it a Memetic Algorithm (MA). Our developed MA incorporates the problem specific knowledge for decoding chromosomes in evaluation step such that most of the generated chromosomes are decoded into feasible timetables. This knowledge is used for selecting all five elements (i.e. course, professor, day, time-block, room) of each single event when decoding and evaluating a chromosome. Generating vast amount of feasible chromosomes makes the progress of search process possible in a time efficient manner. Developed solver package is coded in MATLAB and its data entry interface is coded in a spreadsheet to facilitate the application of the Decision Support System for a user without programming skills. Experimental results show the capability of the developed algorithm for generating feasible solutions.

A comparison of two chromosome representation schemes used in solving a family-based scheduling problem

Meta-heuristic algorithms have been widely used in solving scheduling problems; previous studies focused on enhancing existing algorithmic mechanisms. This study advocates a new perspective-developing new chromosome (solution) representation schemes may improve the performance of existing meta-heuristic algorithms. In the context of a scheduling problem, known as permutation manufacturing-cell flow shop (PMFS), we compare the effectiveness of two chromosome representation schemes (Sold and Snew) while they are embedded in a meta-heuristic algorithm to solve the PMFS scheduling problem. Two existing meta-heuristic algorithms, genetic algorithm (GA) and ant colony optimization (ACO), are tested. Denote a tested meta-heuristic algorithm by X_Y, where X represents an algorithmic mechanism and Y represents a chromosome representation. Experiment results indicate that GA_ Snew outperforms GA_Sold, and ACO_Snew also outperforms ACO_Sold. These findings reveal the importance of developing new chromosome representations in the application of meta-heuristic algorithms.

A Memetic Algorithm for Periodic Capacitated Arc Routing Problem

This paper investigates the Periodic Capacitated Arc Routing Problem (PCARP), which is often encountered in the waste collection application. PCARP is an extension of the well-known Capacitated Arc Routing Problem (CARP) from a single period to a multi-period horizon. PCARP is a hierarchical optimization problem which has a primary objective (minimizing the number of vehicles ) and a secondary objective (minimizing the total cost ). An important factor that makes PCARP challenging is that its primary objective is little affected by existing operators and thus difficult to improve. We propose a new Memetic Algorithm (MA) for solving PCARP. The MA adopts a new solution representation scheme and a novel crossover operator. Most importantly, a Route-Merging (RM) procedure is devised and embedded in the algorithm to tackle the insensitive objective . The MA with RM (MARM) has been compared with existing meta-heuristic approaches on two PCARP benchmark sets and a real-world data set. The experimental results show that MARM obtained better solutions than the compared algorithms in much less time, and even updated the best known solutions of all the benchmark instances. Further study reveals that the RM procedure plays a key role in the superior performance of MARM.

A hybrid particle swarm based method for process planning optimisation

A process planning (PP) problem is defined as to determine a set of operation-methods (machine, tool, and set-up configuration) that can convert the given stock to the designed part. Essentially, the PP problem involves the simultaneous decision making of two tasks: operation-method selection and sequencing. This is a combinatorial optimisation problem and it is difficult to find the best solution in a reasonable amount of time. In this article, an optimisation approach based on particle swarm optimisation (PSO) is proposed to solve the PP problem. Due to the characteristic of discrete process planning solution space and the continuous nature of the original PSO, a novel solution representation scheme is introduced for the application of PSO in solving the PP problem. Moreover, two kinds of local search algorithms are incorporated and interweaved with PSO evolution to improve the best solution in each generation. The numerical experiments and analysis have demonstrated that the proposed algorithm is capable of gaining a good quality solution in an efficient way.

A simultaneous bus route design and frequency setting problem for Tin Shui Wai, Hong Kong

A bus network design problem for Tin Shui Wai, a suburban residential area in Hong Kong, is investigated, which considers the bus services from the origins inside this suburban area to the destinations in the urban areas. The problem aims to improve the existing bus services by reducing the number of transfers and the total travel time of the users. This has been achieved by the proposed integrated solution method which can solve the route design and frequency setting problems simultaneously. In the proposed solution method, a genetic algorithm, which tackles the route design problem, is hybridized with a neighborhood search heuristic, which tackles the frequency setting problem. A new solution representation scheme and specific genetic operators are developed so that the genetic algorithm can search all possible route structures, rather than selecting routes from the predefined set. To avoid premature convergence, a diversity control mechanism is incorporated in the solution method based on a new definition of hamming distance. To illustrate the robustness and quality of solutions obtained, computational experiments are performed based on 1000 perturbed demand matrices. The t-test results show that the design obtained by the proposed solution method is robust under demand uncertainty, and the design is better than both the current design and the design obtained by solving the route design problem and the frequency setting problem sequentially. Compared with the current bus network design, the proposed method can generate a design which can simultaneously reduce the number of transfers and total travel time at least by 20.9% and 22.7% respectively. Numerical studies are also performed to illustrate the effectiveness of the diversity control mechanism introduced and the effects of weights on the two objective values.

Genetic algorithms with different representation schemes for complex hybrid flexible flow line problems

This paper introduces some advanced genetic algorithms for a complex hybrid flexible flow line problem with a makespan objective that was recently formulated. General precedence constraints among jobs are taken into account, as are machine release dates, time lags and sequence dependent set-up times; both anticipatory and non-anticipatory. This combination of constraints captures many real world industrial problems; among those is the ceramic tile production that served as our inspiration. The introduced algorithms employ solution representation schemes with different degrees of directness. Several new machine assignment rules are introduced and implemented in some proposed genetic algorithms. The different genetic algorithms are compared among each other and to some heuristics as well. The results indicate that simple solution representation schemes result in the best performance, even for complex scheduling problems and that the genetic algorithms lead to a better solution quality than all tested heuristics.