A parallel competitive colonial algorithm for JIT flowshop scheduling

This paper proposes two parallel algorithms which are improved by heuristics for a bi-objective flowshop scheduling problem with sequence-dependent setup times in a just-in-time environment. In the proposed algorithms, the population will be decomposed into the several sub-populations in parallel. Multiple objectives are combined with min–max method then each sub-population evolves separately in order to obtain a good approximation of the Pareto-front. After unifying the obtained results, we propose a variable neighborhood algorithm and a hybrid variable neighborhood search/tabu search algorithm to improve the Pareto-front. The non-dominated sets obtained from our proposed algorithms, a genetic local search and restarted iterated Pareto greedy algorithm are compared. It is found that most of the solutions in the net non-dominated front are yielded by our proposed algorithms.     

Multiple-objective heuristics for scheduling unrelated parallel machines

This research proposes two heuristics and a Genetic Algorithm (GA) to find non-dominated solutions to multiple-objective unrelated parallel machine scheduling problems. Three criteria are of interest, namely: makespan, total weighted completion time, and total weighted tardiness. Each heuristic seeks to simultaneously minimize a pair of these criteria; the GA seeks to simultaneously minimize all three. The computational results show that the proposed heuristics are computationally efficient and provide solutions of reasonable quality. The proposed GA outperforms other algorithms in terms of the number of non-dominated solutions and the quality of its solutions.     

Scheduling interfering job sets on parallel machines

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT–LPT–SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy – based on the properties of a non-dominated solution – to ensure that all parts of the non-dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs.     

A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs

In this paper, we consider the problem of permutation flowshop scheduling with the objectives of minimizing the makespan and total flowtime of jobs, and present a Multi-Objective Simulated-annealing Algorithm (MOSA). Two initial sequences are obtained by using simple and fast existing heuristics, supplemented by the implementation of three improvement schemes. Each of the two resultant sequences corresponds to a possible non-dominated solution containing the minimum value of one objective function. These sequences, taken one at a time, are given as the starting sequences to the MOSA. The MOSA seeks to obtain non-dominated solutions through the implementation of a simple probability function that attempts to generate solutions on the Pareto-optimal front. The probability function selects probabilistically a particular objective function, considering which the algorithm uncovers non-dominated solutions. Moreover, the probability function is varied in such a way that the entire objective-function space is covered uniformly so as to obtain as many non-dominated and well-dispersed solutions as possible. The parameters in the proposed MOSA are determined after conducting a pilot study. Two variants of the proposed algorithm, called MOSA-I and MOSA-II, with different parameter settings with respect to the temperature and epoch length, are considered in the performance evaluation of algorithms. In order to evaluate MOSA-I and MOSA-II, we have made use of 90 benchmark problems provided by Taillard [Eur. J. Operation. Res. 64 (1993) 278]. After an extensive literature survey, the following flowshop multi-objective scheduling algorithms have been identified as benchmark procedures: (a) MOGLS (Multi-Objective Genetic Local Search) by Ishibuchi and Murata [IEEE Trans. Syst., Man, Cybernet. C: Appl. Rev. 28 (1998) 392]; (b) Elitist Non-dominated sorting Genetic Algorithm (ENGA) by Bagchi [Multi-Objective Scheduling by Genetic Algorithms, Kluwer Academic Publishers, 1999]; (c) GPW (Gradual Priority Weighting) approach by Chang, Hsieh and Lin [Int. J. Prod. Econ. 79 (2002) 171]; and (d) a posteriori approach based heuristic by Framinan, Leisten and Ruiz-Usano [Eur. J. Operation. Res. 141 (2002) 559]. The non-dominated sets obtained from each of the existing benchmark algorithms and the proposed MOSA-I and MOSA-II are compared, and subsequently combined to obtain a net non-dominated front. It is found that most of the solutions in the net non-dominated front are yielded by MOSA-I and MOSA-II. In addition, it is noteworthy that both MOSA-I and MOSA-II require less computational effort than the MOGLS, ENGA and GPW.     

Total completion time with makespan constraint in no-wait flowshops with setup times

The m-machine no-wait flowshop scheduling problem with the objective of minimizing total completion time subject to the constraint that the makespan value is not greater than a certain value is addressed in this paper. Setup times are considered non-zero values, and thus, setup times are treated as separate from processing times. Several recent algorithms, an insertion algorithm, two genetic algorithms, three simulated annealing algorithms, two cloud theory-based simulated annealing algorithms, and a differential evolution algorithm are adapted and proposed for the problem. An extensive computational analysis has been conducted for the evaluation of the proposed algorithms. The computational analysis indicates that one of the nine proposed algorithms, one of the simulated annealing algorithms (ISA-2), performs much better than the others under the same computational time. Moreover, the analysis indicates that the algorithm ISA-2 performs significantly better than the earlier existing best algorithm. Specifically, the best performing algorithm, ISA-2, proposed in this paper reduces the error of the existing best algorithm in the literature by at least 90% under the same computational time. All the results have been statistically tested.     

Bicriteria train scheduling for high-speed passenger railroad planning applications

This paper is concerned with a double-track train scheduling problem for planning applications with multiple objectives. Focusing on a high-speed passenger rail line in an existing network, the problem is to minimize both (1) the expected waiting times for high-speed trains and (2) the total travel times of high-speed and medium-speed trains. By applying two practical priority rules, the problem with the second criterion is decomposed and formulated as a series of multi-mode resource constrained project scheduling problems in order to explicitly model acceleration and deceleration times. A branch-and-bound algorithm with effective dominance rules is developed to generate Pareto solutions for the bicriteria scheduling problem, and a beam search algorithm with utility evaluation rules is used to construct a representative set of non-dominated solutions. A case study based on Beijing–Shanghai high-speed railroad in China illustrates the methodology and compares the performance of the proposed algorithms.     

A New Hybrid Evolutionary Multiobjective Algorithm Guided by Descent Directions

Hybridization of local search based algorithms with evolutionary algorithms is still an under-explored research area in multiobjective optimization. In this paper, we propose a new multiobjective algorithm based on a local search method. The main idea is to generate new non-dominated solutions by adding a linear combination of descent directions of the objective functions to a parent solution. Additionally, a strategy based on subpopulations is implemented to avoid the direct computation of descent directions for the entire population. The evaluation of the proposed algorithm is performed on a set of benchmark test problems allowing a comparison with the most representative state-of-the-art multiobjective algorithms. The results show that the proposed approach is highly competitive in terms of the quality of non-dominated solutions and robustness.     

The influence of the fitness evaluation method on the performance of multiobjective search algorithms

In this paper we are concerned with finding the Pareto optimal front or a good approximation to it. Since non-dominated solutions represent the goal in multiobjective optimisation, the dominance relation is frequently used to establish preference between solutions during the search. Recently, relaxed forms of the dominance relation have been proposed in the literature for improving the performance of multiobjective search methods. This paper investigates the influence of different fitness evaluation methods on the performance of two multiobjective methodologies when applied to a highly constrained two-objective optimisation problem. The two algorithms are: the Pareto archive evolutionary strategy and a population-based annealing algorithm. We demonstrate here, on a highly constrained problem, that the method used to evaluate the fitness of candidate solutions during the search affects the performance of both algorithms and it appears that the dominance relation is not always the best method to use.     

Finding representative systems for discrete bicriterion optimization problems

Given a discrete bicriterion optimization problem, we propose two box algorithms to compute a finite representative system for the non-dominated set satisfying a number of quality features. Its cardinality N and the accuracy Δ satisfy the relation O(A/Δ), where A is the area of a starting box defined by the ideal and the nadir point.     

Heuristic approaches to determine base-stock levels in a serial supply chain with a single objective and with multiple objectives

This paper deals with the problem of determination of installation base-stock levels in a serial supply chain. The problem is treated first as a single-objective inventory-cost optimization problem, and subsequently as a multi-objective optimization problem by considering two cost components, namely, holding costs and shortage costs. Variants of genetic algorithms are proposed to determine the best base-stock levels in the single-objective case. All variants, especially random-key gene-wise genetic algorithm (RKGGA), show an excellent performance, in terms of convergence to the best base-stock levels across a variety of supply chain settings, with minimum computational effort. Heuristics to obtain base-stock levels are proposed, and heuristic solutions are introduced in the initial population of the RKGGA to expedite the convergence of the genetic search process. To deal with the multi-objective supply-chain inventory optimization problem, a simple multi-objective genetic algorithm is proposed to obtain a set of non-dominated solutions.     

A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems

A simple augmented ?-constraint (SAUGMECON) method is put forward to generate all non-dominated solutions of multi-objective integer programming (MOIP) problems. The SAUGMECON method is a variant of the augmented ?-constraint (AUGMECON) method proposed in 2009 and improved in 2013 by Mavrotas et al. However, with the SAUGMECON method, all non-dominated solutions can be found much more efficiently thanks to our innovations to algorithm acceleration. These innovative acceleration mechanisms include: (1) an extension to the acceleration algorithm with early exit and (2) an addition of an acceleration algorithm with bouncing steps. The same numerical example in Lokman and Köksalan (2012) is used to illustrate workings of the method. Then comparisons of computational performance among the method proposed by  and , the method developed by Lokman and Köksalan (2012) and the SAUGMECON method are made by solving randomly generated general MOIP problem instances as well as special MOIP problem instances such as the MOKP and MOSP problem instances presented in Table 4 in Lokman and Köksalan (2012). The experimental results show that the SAUGMECON method performs the best among these methods. More importantly, the advantage of the SAUGMECON method over the method proposed by Lokman and Köksalan (2012) turns out to be increasingly more prominent as the number of objectives increases.     

Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems

The structure-control design approach of mechatronic systems requires a different design formulation where the mechanical structure and control system are simultaneously designed. Optimization problems are commonly stated to confront the structure-control design formulation. Nevertheless, these problems are often very complex with a highly nonlinear dependence between the design variables and performance functions. This fact has made the use of evolutionary algorithms, a feasible alternative to solve the highly nonlinear optimization problem; the method to find the best solution is an open issue in the structure-control design approach. Hence, this paper presents a mechanism to exhaustively exploit the solutions in the differential evolution (DE) algorithm in order to find more non-dominated solutions with uniformly distributed Pareto front and better trade-offs in the structure-control design framework. The proposed approach adopts an external population to retain the non-dominated solutions found during the evolutionary process and includes a mechanism to mutate the individuals in their corresponding external population region. As a study case, the structure-control design of a serial-parallel manipulator with its control system is stated as a dynamic optimization problem and is solved by using the proposed approach. A comparative analysis shows that the multi-objective exhaustive exploitation differential evolution obtained a superior performance in the structure-control design framework than a DE algorithm which did not consider the proposal. Hence, the resulting designs provide better trade-offs between the structure-control performance functions.     

Finding preferred subsets of Pareto optimal solutions

Multi-objective optimization algorithms can generate large sets of Pareto optimal (non-dominated) solutions. Identifying the best solutions across a very large number of Pareto optimal solutions can be a challenge. Therefore it is useful for the decision-maker to be able to obtain a small set of preferred Pareto optimal solutions. This paper analyzes a discrete optimization problem introduced to obtain optimal subsets of solutions from large sets of Pareto optimal solutions. This discrete optimization problem is proven to be NP-hard. Two exact algorithms and five heuristics are presented to address this problem. Five test problems are used to compare the performances of these algorithms and heuristics. The results suggest that preferred subset of Pareto optimal solutions can be efficiently obtained using the heuristics, while for smaller problems, exact algorithms can be applied.     

Determining the Pareto set in a bicriteria two-echelon inventory/distribution system

This article concerns two-echelon inventory/distribution system, consisting of a warehouse and a retailer. We assume that the demand is deterministic and stockouts are not permitted. Two criteria are considered: to minimize the annual inventory cost and the annual total number of damaged items by improper shipment handling. The problem consists of determining the non-dominated inventory policies in such a way that the trade-off between both criteria is achieved. We present the characterization of the non-dominated optimal solution set and we use this result to correct the solution method previously proposed by other authors for a problem with identical cost structure. An efficient algorithm to calculate the non-dominated solution set is introduced. Computational results on several randomly generated problems are reported.     

Parallel multiobjective evolutionary algorithms for batch scheduling in heterogeneous computing and grid systems

This article presents six parallel multiobjective evolutionary algorithms applied to solve the scheduling problem in distributed heterogeneous computing and grid systems. The studied evolutionary algorithms follow an explicit multiobjective approach to tackle the simultaneous optimization of a system-related (i.e. makespan) and a user-related (i.e. flowtime) objectives. Parallel models of the proposed methods are developed in order to efficiently solve the problem. The experimental analysis demonstrates that the proposed evolutionary algorithms are able to efficiently compute accurate results when solving standard and new large problem instances. The best of the proposed methods outperforms both deterministic scheduling heuristics and single-objective evolutionary methods previously applied to the problem.     

A mapping technique for better solution exploration: NSGA-II adaptation

A mapping method (MaM) for a better solution space exploration adapted to NSGA-II method is presented. The Mapping technique divides the solution space into several zones using a Hamming distance to a reference solution. We present a bijective mapping function from the search space to the binary representation space of solutions. For each zone, a mapping metric is used to evaluate the solution space exploration. According to this evaluation, a local search is performed. The mapping is adapted to the well known non-dominated sorting genetic algorithm-II (NSGA-II) method applied to solve the flexible job shop problem (FJSP) case. We present the comparison between the hybridization using the local search for the non-dominated solutions and the hybridization using the mapping metrics. The multi-objective metrics show the efficiency of mapping adaptation in terms of convergence and diversity.     

Unique NSGA-II and MOPSO algorithms for improved dynamic cellular manufacturing systems considering human factors

In this study, we present a new mathematical model of a multi-objective dynamic cellular manufacturing system (MDCMS) that considers human factors. Human factors are incorporated into the proposed model in terms of human reliability and decision-making processes. Three objective functions are considered simultaneously. The first objective minimizes the total cost of the MDCMS. The second objective function minimizes inconsistency in the decision-making style of operators in the common manufacturing cells. The third objective function balances the workload of cells with respect to the efficiency of operators, which is calculated based on human reliability analysis. Various studies have been conducted in the field of MDCMS, but human factors have not received sufficient attention as important elements. Due to the NP-hardness of the MDCMS problem, two innovative meta-heuristic algorithms are developed, i.e., a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective particle swarm optimization method. The results obtained by the algorithms were compared and analyzed using different criteria. Several test problems were considered to verify and validate the proposed model and solution methods. To the best of our knowledge, this is the first study to consider human reliability and decision-making styles in a large MDCMS in an actual production setting.     

Helper-objectives: Using multi-objective evolutionary algorithms for single-objective optimisation

This paper investigates the use of multi-objective methods to guide the search when solving single-objective optimisation problems with genetic algorithms. Using the job shop scheduling and travelling salesman problems as examples, experiments demonstrate that the use of helper-objectives (additional objectives guiding the search) significantly improves the average performance of a standard GA. The helper-objectives guide the search towards solutions containing good building blocks and help the algorithm escape local optima. The experiments reveal that the approach works if the number of simultaneously used helper-objectives is low. However, a high number of helper-objectives can be used in the same run by changing the helper-objectives dynamically. The experiments reveal that for the majority of problem instances studied, the proposed approach significantly outperforms a traditional GA.The experiments also demonstrate that controlling the proportion of non-dominated solutions in the population is very important when using helper-objectives, since the presence of too many non-dominated solutions removes the selection pressure in the algorithm.     

Fast and fine quickest path algorithm

We address the quickest path problem proposing a new algorithm based on the fact that its optimal solution corresponds to a supported non-dominated point in the objective space of the minsum–maxmin bicriteria path problem. This result allows us to design a label setting algorithm which improves all existing algorithms in the state-of-the-art, as it is shown in the extensive experiments carried out considering synthetic and real networks.