Resolution approach for multi-objective problems with uncertain demands

The job-shop scheduling problem (JSP) is one of the hardest problems (NP-complete problem). In lots of cases, the combination of goals and resources has exponentially increasing search space. The objective of resolution of such a problem is generally, to maximize the production with a lower cost and makespan. In this paper, we explain how to modify the objective function of genetic algorithms to treat the multiobjective problem and to generate a set of diversified optimal solutions in order to help decision maker. The solutions proposed by our approach are compared to the lower bound of the cost and makespan in order to prove the qualities and robustness of our proposed approach.

A new multi-objective scheduling method based on the GA is proposed to the job-shop scheduling problem (JSP) constrained by machines, workers. Function objectives of the proposed method are to minimize the completion time, the maximum load of machines and the total expense of machines and workers. Firstly, the mathematical model is constructed. Then, on the basis of the mathematical model, the genetic algorithm (GA) based on Pareto is applied, and an optimal or suboptimal scheduling plan can be obtained. The optimal solutions are not unique due to the multi-objective of JSP. Finally, a scheduling example is employed to illustrate that the proposed method could solve multi-objective job shop scheduling problem effectively.

The job-shop scheduling problem is one of the hardest problems (NP-complete problem) {Garey and Johnson 1979, Computer and Intractability: A Guide to the Theory of NP-completeness (San Francisco: Freeman)}. In lots of cases, the combination of goals and resources exponentially increases the search space, and the generation of consistent and satisfying schedules is more and more difficult. This article shows the coupling of three approaches in order to contribute to the solving of the job-shop scheduling problem: genetic algorithms (GAs); constraint logic programming (CLP); and multi-criteria decision-making (MCDM). The GAs are searching algorithms based on the mechanics of natural selection. They employ a probabilistic search for locating the globally optimal solution. They start with an initial population often randomly generated. The difficulty holds in the creation of this initial population which is considered an important parameter of GAs. CLP is a concept based on operation research (OR) and artificial intelligence (AI). It tends to rid itself of their drawbacks and to regroup their advantages. It aims at providing a set of solutions to a problem expressed in term of constraints. A MCDM approach aims at providing an analysis of a set of possible alternatives according to a set of conflicting criteria in order to help the user. This article explains first how to use the CLP to generate a first population. Second it describes the application of GAs to provide a set of job-shop scheduling minimizing the global makespan. Among the set of job-shop scheduling minimizing the global makespan, it is then possible for the decision-maker to select the most satisfying scheduling according to other criteria, e.g. balance of workload or makespan of each manufacturing order. A large-sized example illustrates clearly the advantages of our hybrid method.

This paper presents a two-stage genetic algorithm (2S-GA) for multi-objective Job Shop scheduling problems. The 2S-GA is proposed with three criteria: Minimize makespan, Minimize total weighted earliness, and Minimize total weighted tardiness. The proposed algorithm is composed of two Stages: Stage 1 applies parallel GA to find the best solution of each individual objective function with migration among populations. In Stage 2 the populations are combined. The evolution process of Stage 2 is based on Steady-State GA using the weighted aggregating objective function. The algorithm developed can be used with one or two objectives without modification. The genetic algorithm is designed and implemented with the GALIB object library. The random keys representation is applied to the problem. The schedules are constructed using a permutation with m-repetitions of job numbers. Performance of the proposed algorithm is tested on published benchmark instances and compared with results from other published approaches for both the single objective and multi-objective cases. The experimental results show that 2S-GA is effective and efficient to solve job shop scheduling problem in term of solution quality.

A global optimization method for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the global topology optimization method in flow problems, this research works on two single-objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and the multi-objective optimization problem, which combines these two problems. The shape of flow channels is represented by the level set function, and the pressure loss and the temperature of the channels are evaluated by the Building-Cube Method (BCM), which is a Cartesian-mesh CFD approach. The proposed method resulted in an agreement with previous study in the single-objective problems in its topology, and achieved global exploration of non-dominated solutions in the multi-objective problem.

The job-shop scheduling problem (JSP) is a hard combinatorial optimization problem. In this paper, the mixed programming of MATLAB and VC is considered to solve the JSP. Firstly, MATLAB is used to implement an improved genetic algorithm (GA), and then the program is packaged into a dynamic link library (DLL). Secondly, VC is used to realize the input/output interface and call the GA DLL to schedule and store the scheduling results into the ORACLE database. Finally, the simulation results show that the improved GA has good optimization performance in solving JSP and the mixed programming design is effective.

The design of Renewable Energy Power Plants (REPPs) is crucial not only for the investments' performance and attractiveness measures, but also for the maximization of resource (source) usage (e.g. sun, water, and wind) and the minimization of raw materials (e.g. aluminum: Al, cadmium: Cd, iron: Fe, silicon: Si, and tellurium: Te) consumption. Hence, several appropriate and satisfactory Multi-Objective Problems (MOPs) are mandatory during the REPPs' design phases. MOPs related tasks can only be managed by very well organized knowledge acquisition on all REPPs' design equations and models. The proposed MOPs need to be solved with one or more multi-objective algorithm, such as Multi-Objective Evolutionary Algorithms (MOEAs). In this respect, the first aim of this research study is to start gathering knowledge on the REPPs' MOPs. The second aim of this study is to gather detailed information about all MOEAs and available free software tools for their development. The main contribution of this research is the initialization of a proposed multi-objective evolutionary algorithm knowledge acquisition system for renewable energy power plants (MOEAs-KAS-F-REPPs) (research and development loopwise process: develop, train, validate, improve, test, improve, operate, and improve). As a simple representative example of this knowledge acquisition system research with two selective and elective proposed standard objectives (as test objectives) and eight selective and elective proposed standard constraints (as test constraints) are generated and applied as a standardized MOP for a virtual small hydropower plant design and investment. The maximization of energy generation (MWh) and the minimization of initial investment cost (million €) are achieved by the Multi-Objective Genetic Algorithm (MOGA), the Niched Sharing Genetic Algorithm/Non-dominated Sorting Genetic Algorithm (NSGA-I), and the NSGA-II algorithms in the Scilab 6.0.0 as only three standardized MOEAs amongst all proposed standardized MOEAs on two desktop computer configurations (Windows 10 Home 1709 64 bits, Intel i5-7200 CPU @ 2.7 GHz, 8.00 GB RAM with internet connection and Windows 10 Pro, Intel(R) Core(TM) i5 CPU 650 @ 3.20 GHz, 6,00 GB RAM with internet connection). The algorithm run-times (computation time) of the current applications vary between 20.64 and 59.98 seconds.

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

This paper presents a multi-objective mathematical model for a flexible job shop scheduling problem (FJSSP) with fuzzy processing times, which is solved by a hybrid intelligent algorithm (HIA). This problem contains a combination of a classical job shop problem with parallel machines (JSPM) to provide flexibility in the production route. Despite the previous studies, the number of parallel machines is not pre-specified in this paper. This constraint with other ones (e.g., sequence-dependent setup times, reentrant workflows, and fuzzy variables) makes the given problem more complex. To solve such a multi-objective JSPM, Pareto-based optimization algorithms based on multi-objective meta-heuristics and multi-criteria decision making (MCDM) methods are utilized. Then, different comparison metrics (e.g., quality, mean ideal distance, and rate of achievement simultaneously) are used. Also, this paper includes two major phases to provide a new model of the FJSSP and introduce a new proposed HIA for solving the presented model, respectively. This algorithm is a hybrid genetic algorithm with the SAW/TOPSIS method, namely HGASAW/HGATOPSIS. The comparative results indicate that HGASAW and HGATOPSIS outperform the non-dominated sorting genetic algorithm (NSGA-II) to tackle the fuzzy multi-objective JSPM.

Classification is important task of data mining used to extract knowledge from huge volume of data. By nature, classification is multi-objective problem, as it required optimization of multiple objectives simultaneously like accuracy, sensitivity, squared error, precision etc. Traditionally, evolutionary algorithms were used to solve multi-objective classification problem by considering it as single-objective problem, but this approach gives single solution to problem. Therefore, multi-objective evolutionary algorithms are used to solve classification problem. In this paper, we have used Pareto approach to optimize neural network to solve classification problem. Non-dominated sorting genetic algorithm is used to simultaneously optimize accuracy and mean squared error objectives of neural network along with local search. As slow convergence to optimal solutions is major disadvantage of evolutionary algorithm. To speed up convergence to optimal solutions hybrid technique is adopted by augmenting evolutionary technique with local search algorithm. This proposed approach gives set of Pareto optimal solutions which represent different solutions for given classification problem.

This paper proposes an integrated approach for dynamic facility layout problem considering the material handling equipment (MHE). The objectives of this problem are minimization of the fixed costs of MHE, minimization of material handling cost (MHC) and minimization of machine rearrangement costs (MRC). To be more realistic, MHE fixed costs, MRC and MHC, which might be of different importance to decision maker, are considered separately in three objective functions. An integrated model is proposed which is able to simultaneously select the MHE along with the arranging and re-arranging facilities. The model belongs to the class of multi-objective nonlinear mathematical programming models. Considering the NP-hard nature of the model and inspiring the existing water flow like algorithm, a novel Pareto-based meta-heuristic algorithm called multi-objective water flow like algorithm (MOWFA)is developed to solve the problem. We comprehensively discuss the parameter tuning of the algorithms utilizing Taguchi method. Finally, the performance of the proposed MOWFA is evaluated against two well-known meta-heuristic algorithms called non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA). Computational results indicate the greater efficiency of the algorithm compared to the two addressed algorithms for solving the given multi-objective problem.

An effective job shop scheduling (JSS) in the manufacturing industry is helpful to meet the production demand and reduce the production cost, and to improve the ability to compete in the ever increasing volatile market demanding multiple products.In so many combinatorial optimization problems, job shop scheduling problems have earned a reputation for being difficult to solve. Job-shop scheduling is essentially an ordering problem. A new encoding scheme for a classic job-shop scheduling problem is presented. The aim is to find an allocation for each job and to define the sequence of jobs on each machine so that the resulting schedule has a minimal completion time.Genetic algorithm that has demonstrated considerable success in providing efficient solutions to many non polynomial-hard optimization problems is used to solve job-shop scheduling problem. The schedules given by genetic algorithms are constructed using a priority rule and under several constraints. After a schedule is obtained a checking operation is applied to ensure that the solution is feasible. The approach is tested on a set of instances. The results validate the effectiveness of the algorithm.

Parameters optimization of selected casting processes using teaching–learning-based optimization algorithm

The two primary goals of a multi-objective evolutionary algorithm (MOEA) for solving multi-objective optimization problems are to search as much non-dominated solutions as possible towards the true Pareto front and to maintain diversity of Pareto optimal solutions along tradeoff curves. This study presents a new hybrid MOEA, the niched Pareto tabu search combined with genetic algorithm (NPTSGA), to find Pareto-optimal solutions to multi-objective optimization problems. The NPTSGA is developed on the thoughts of integrating genetic algorithm (GA) with the improved tabu search (TS) based MOEA, niched Pareto tabu search (NPTS). The proposed NPTSGA is then tested through a simple test example and compared with other two techniques, NPTS and niched Pareto genetic algorithm (NPGA). Computational results indicate that the proposed NPTSGA is an efficient and effective method for solving multi-objective problems, while keeping the balance between the intensification of non-domination to the true Pareto-optimal solutions (TPS) and the diversification of the near Pareto-optimal solutions (NPS) along the tradeoff curves.

In the process of multi-objective problems, traditional algorithms have certain defects, especially because of the increasing number of conflicts and the increasingly complex application environment. This paper proposes a practical method to solve the multi-objective optimization problem for the duration and cost requirements in the construction project management, in order to reduce the error probability that the optimized project will produce in the actual project. Different from the existing optimization methods, this design modifies the curve of the time cost, and improves the parameters of the traditional genetic algorithm design and operation process design, which greatly increases the degree of fitness between the algorithm and the actual project. The model is based on genetic algorithms and combines different algorithms, so a simple and excellent Pareto solution can be quickly obtained. At the same time, optimization and simulation are carried out in an orderly way during the construction period. This new method is reasonable and effective in the very complicated multi-objective optimization problem of managing construction period and cost through an engineering example.