Multi-objective simulation-based evolutionary algorithm for an aircraft spare parts allocation problem

Simulation optimization has received considerable attention from both simulation researchers and practitioners. In this study, we develop a solution framework which integrates multi-objective evolutionary algorithm (MOEA) with multi-objective computing budget allocation (MOCBA) method for the multi-objective simulation optimization problem. We apply it on a multi-objective aircraft spare parts allocation problem to find a set of non-dominated solutions. The problem has three features: huge search space, multi-objective, and high variability. To address these difficulties, the solution framework employs simulation to estimate the performance, MOEA to search for the more promising designs, and MOCBA algorithm to identify the non-dominated designs and efficiently allocate the simulation budget. Some computational experiments are carried out to test the effectiveness and performance of the proposed solution framework.     

A three-phase matheuristic for capacitated multi-commodity fixed-cost network design with design-balance constraints

This paper proposes a three-phase matheuristic solution strategy for the capacitated multi-commodity fixed-cost network design problem with design-balance constraints. The proposed matheuristic combines exact and neighbourhood-based methods. Tabu search and restricted path relinking meta-heuristics cooperate to generate as many feasible solutions as possible. The two meta-heuristics incorporate new neighbourhoods, and computationally efficient exploration procedures. The feasible solutions generated by the two procedures are then used to identify an appropriate part of the solution space where an exact solver intensifies the search. Computational experiments on benchmark instances show that the proposed algorithm finds good solutions to large-scale problems in a reasonable amount of time.     

An efficient evolutionary multi-objective framework for MEMS design optimisation: validation, comparison and analysis

The application of multi objective evolutionary algorithms (MOEA) in the design optimisation of microelectromechanical systems (MEMS) is of particular interest in this research. MOEA is a class of soft computing techniques of biologically inspired stochastic algorithms, which have proved to outperform their conventional counterparts in many design optimisation tasks. MEMS designers can utilise a variety of multi-disciplinary design tools that explore a complex design search space, however, still follow the traditional trial and error approaches. The paper proposes a novel framework, which couples both modelling and analysis tools to the most referenced MOEAs (NSGA-II and MOGA-II). The framework is validated and evaluated through a number of case studies of increasing complexity. The research presented in this paper unprecedentedly attempts to compare the performances of the mentioned algorithms in the application domain. The comparative study shows significant insights into the behaviour of both of the algorithms in the design optimisation of MEMS. The paper provides extended discussions and analysis of the results showing, overall, that MOGA-II outperforms NSGA-II, for the selected case studies.     

A continuation approach to mode-finding of multivariate Gaussian mixtures and kernel density estimates

This paper presents a novel method of multi-objective optimization by learning automata (MOLA) to solve complex multi-objective optimization problems. MOLA consists of multiple automata which perform sequential search in the solution domain. Each automaton undertakes dimensional search in the selected dimension of the solution domain, and each dimension is divided into a certain number of cells. Each automaton performs a continuous search action, instead of discrete actions, within cells. The merits of MOLA have been demonstrated, in comparison with a multi-objective evolutionary algorithm based on decomposition (MOEA/D) and non-dominated sorting genetic algorithm II (NSGA-II), on eleven multi-objective benchmark functions and an optimal problem in the midwestern American electric power system which is integrated with wind power, respectively. The simulation results have shown that MOLA can obtain more accurate and evenly distributed Pareto fronts, in comparison with MOEA/D and NSGA-II.     

A hybrid genetic algorithm–neural network strategy for simulation optimization

Simulation optimization aims at determining the best values of input parameters, while the analytical objective function and constraints are not explicitly known in terms of design variables and their values only can be estimated by complicated analysis or time-consuming simulation. In this paper, a hybrid genetic algorithm–neural network strategy (GA–NN) is proposed for such kind of optimization problems. The good approximation performance of neural network (NN) and the effective and robust evolutionary searching ability of genetic algorithm (GA) are applied in hybrid sense, where NNs are employed in predicting the objective value, and GA is adopted in searching optimal designs based on the predicted fitness values. Numerical simulation results and comparisons based on a well-known pressure vessel design problem demonstrate the feasibility and effectiveness of the framework, and much better results are achieved than some existed literature results.     

Optimization of manufacturing systems using a neural network metamodel with a new training approach

In this study, two manufacturing systems, a kanban-controlled system and a multi-stage, multi-server production line in a diamond tool production system, are optimized utilizing neural network metamodels (tst_NNM) trained via tabu search (TS) which was developed previously by the authors. The most widely used training algorithm for neural networks has been back propagation which is based on a gradient technique that requires significant computational effort. To deal with the major shortcomings of back propagation (BP) such as the tendency to converge to a local optimal and a slow convergence rate, the TS metaheuristic method is used for the training of artificial neural networks to improve the performance of the metamodelling approach. The metamodels are analysed based on their ability to predict simulation results versus traditional neural network metamodels that have been trained by BP algorithm (bp_NNM). Computational results show that tst_NNM is superior to bp_NNM for both of the manufacturing systems.     

Portfolio optimization with an envelope-based multi-objective evolutionary algorithm

The problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades. Classical mean–variance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance. In the case of linear constraints, the problem can be solved efficiently by parametric quadratic programming (i.e., variants of Markowitz’ critical line algorithm). However, there are many real-world constraints that lead to a non-convex search space, e.g., cardinality constraints which limit the number of different assets in a portfolio, or minimum buy-in thresholds. As a consequence, the efficient approaches for the convex problem can no longer be applied, and new solutions are needed.In this paper, we propose to integrate an active set algorithm optimized for portfolio selection into a multi-objective evolutionary algorithm (MOEA). The idea is to let the MOEA come up with some convex subsets of the set of all feasible portfolios, solve a critical line algorithm for each subset, and then merge the partial solutions to form the solution of the original non-convex problem. We show that the resulting envelope-based MOEA significantly outperforms existing MOEAs.     

Ordinal Optimization of G/G/1/K Polling Systems with <Emphasis Type="Italic">k</Emphasis>-Limited Service Discipline

In this paper, we propose an ordinal optimization theory based algorithm to solve the optimization problem of G/G/1/K polling system with k-limited service discipline for a good enough solution using limited computation time. We assume that the arrival rates do not deteriorate visibly within a very short period. Our approach consists of two stages. In the first stage, we employ a typical genetic algorithm to select N=1024 roughly good solutions from the huge discrete solution space Ω using an offline trained artificial neural network as a surrogate model for fitness evaluation. The second stage consists of several substages to select estimated good enough solutions from the previous N, and the solution obtained in the last substage is the good enough solution that we seek. Using numerous tests, we demonstrate: (i) the computational efficiency of our algorithm in the aspect that we can apply our algorithm in real-time based on the arrival rate assumption; (ii) the superiority of the good enough solution, which achieves drastic objective value reduction in comparison with other existing service disciplines. We provide a performance analysis for our algorithm based on the derived models. The results show that the good enough solution that we obtained is among the best 3.31×10⁻⁶% in the solution space with probability 0.99. This research work was supported in part by the National Science Council of Taiwan, ROC, Grant NSC95-2221-E-009-099-MY2.     

Neural network as a simulation metamodel in economic analysis of risky projects

An artificial neural network (ANN) model for economic analysis of risky projects is presented in this paper. Outputs of conventional simulation models are used as neural network training inputs. The neural network model is then used to predict the potential returns from an investment project having stochastic parameters. The nondeterministic aspects of the project include the initial investment, the magnitude of the rate of return, and the investment period. Backpropagation method is used in the neural network modeling. Sigmoid and hyperbolic tangent functions are used in the learning aspect of the system. Analysis of the outputs of the neural network model indicates that more predictive capability can be achieved by coupling conventional simulation with neural network approaches. The trained network was able to predict simulation output based on the input values with very good accuracy for conditions not in its training set. This allowed an analysis of the future performance of the investment project without having to run additional expensive and time-consuming simulation experiments.     

Incorporating the threat of terrorist attacks in the design of public service facility networks

In this paper, we consider the design problem of a public service facility network with existing facilities when there is a threat of possible terrorist attacks. The aim of the system planner, who is responsible for the operation of the network, is to open new facilities, relocate existing ones if necessary, and protect some of the facilities to ensure a maximum coverage of the demand that is assumed to be aggregated at customer zones. By doing so, the system planner anticipates that a number of unprotected facilities will be rendered out-of-service by terrorist attacks. It is assumed that the sum of the fixed cost of opening new facilities, the relocation costs, and the protection costs cannot exceed a predetermined budget level. Adopting the approach of gradual (or partial) coverage, we formulate a bilevel programming model where the system planner is the leader and the attacker is the follower. The objective of the former is the maximization of the total service coverage, whereas the latter wants to minimize it. We propose a heuristic solution procedure based on tabu search where the search space consists of the decisions of the system planner, and the corresponding objective value is computed by optimally solving the attacker??s problem using CPLEX. To assess the quality of the solutions produced by the tabu search (TS) heuristic, we also develop an exhaustive enumeration method, which explores all the possible combinations of opening new facilities, relocating existing ones, and protecting them. Since its time complexity is exponential, it can only be used for relatively small instances. Therefore, to be used as a benchmark method, we also implement a hill climbing procedure employed with the same type of moves as the TS heuristic. Besides, we carry out a sensitivity analysis on some of the problem parameters to investigate their effect on the solution characteristics.     

RAMP for the capacitated minimum spanning tree problem

This paper introduces dual and primal-dual RAMP algorithms for the solution of the capacitated minimum spanning tree problem (CMST). A surrogate constraint relaxation incorporating cutting planes is proposed to explore the dual solution space. In the dual RAMP approach, primal-feasible solutions are obtained by simple tabu searches that project dual solutions onto primal feasible space. A primal-dual approach is achieved by including a scatter search procedure that further exploits the adaptive memory framework. Computational results from applying the methods to a standard set of benchmark problems disclose that the dual RAMP algorithm finds high quality solutions very efficiently and that its primal-dual enhancement is still more effective.     

Scatter search for the vehicle routing problem with time windows

In this paper we use a scatter search framework to solve the vehicle routing problem with time windows (VRPTW). Our objective is to achieve effective solutions and to investigate the effects of reference set design parameters pertaining to size, quality and diversity. Both a common arc method and an optimization-based set covering model are used to combine vehicle routing solutions. A reactive tabu search metaheuristic and a tabu search with an advanced recovery feature, together with a set covering procedure are used for solution improvement. Our approach led to a robust solution method, generating solution quality that is competitive with the current best metaheuristics.     

An example of simulation optimisation using a neural network metamodel: finding the optimum number of kanbans in a manufacturing system

A method of finding the optimum solution for a stochastic discrete-event system is described. A simulation model of the system is first built and then used to train a neural network metamodel. The optimisation process consists of using the metamodel to find an approximate optimum solution. This solution is then used by the simulation as the starting point in a more precise search for an optimum. The approach is demonstrated with an example that finds the optimum number of kanbans needed to control a manufacturing system.     

A robustness approach to uncapacitated network design problems

In this paper, we address uncapacitated network design problems characterised by uncertainty in the input data. Network design choices have a determinant impact on the effectiveness of the system. Design decisions are frequently made with a great degree of uncertainty about the conditions under which the system will be required to operate. Instead of finding optimal designs for a given future scenario, designers often search for network configurations that are “good” for a variety of likely future scenarios. This approach is referred to as the “robustness” approach to system design. We present a formal definition of “robustness” for the uncapacitated network design problem, and develop algorithms aimed at finding robust network designs. These algorithms are adaptations of the Benders decomposition methodology that are tailored so they can efficiently identify robust network designs. We tested the proposed algorithms on a set of randomly generated problems. Our computational experiments showed two important properties. First, robust solutions are abundant in uncapacitated network design problems, and second, the proposed algorithms performance is satisfactory in terms of cost and number of robust network designs obtained.     

Evolutionary multiobjective optimization in noisy problem environments

This paper presents a multiobjective evolutionary algorithm (MOEA) capable of handling stochastic objective functions. We extend a previously developed approach to solve multiple objective optimization problems in deterministic environments by incorporating a stochastic nondomination-based solution ranking procedure. In this study, concepts of stochastic dominance and significant dominance are introduced in order to better discriminate among competing solutions. The MOEA is applied to a number of published test problems to assess its robustness and to evaluate its performance relative to NSGA-II. Moreover, a new stopping criterion is proposed, which is based on the convergence velocity of any MOEA to the true Pareto optimal front, even if the exact location of the true front is unknown. This stopping criterion is especially useful in real-world problems, where finding an appropriate point to terminate the search is crucial.     

Level Crossing Prediction with Neural Networks

A level crossing predictor or alarm system with prediction horizon k is said to be optimal if it, at time t detects that an upcrossing will occur at time t + k, with a certain high probability and simultaneously gives a minimum number of false alarms. For a Gaussian stationary process, the optimal level crossing predictor can be explicitly specified in terms of the predicted value of the process itself and of its derivative. To the authors knowledge this simple optimal solution has not been used to any substantial degree. In this paper it is shown how a neural network can be trained to approximate an optimal alarm system arbitrarily well. As in other methods of parametrization, the choice of model structure, as well as an appropriate representation of data, are crucial for a good result. Comparative studies are presented for two Gaussian ARMA-processes, for which the optimal predictor can be derived theoretically. These studies confirm that a properly trained neural network can indeed approximate an optimal alarm system quite well – with due attention paid to the problems of model structure and representation of data. The technique is also tested on a strongly non-Gaussian Duffing process with satisfactory results.     

A new orthogonal evolutionary algorithm based on decomposition for multi-objective optimization

The diversity of solutions is very important for multi-objective evolutionary algorithms to deal with multi-objective optimization problems (MOPs). In order to achieve the goal, a new orthogonal evolutionary algorithm based on objective space decomposition (OEA/D) is proposed in this paper. To be specific, the objective space of an MOP is firstly decomposed into a set of sub-regions via a set of direction vectors, and OEA/D maintains the diversity of solutions by making each sub-region have a solution to the maximum extent. Also, the quantization orthogonal crossover (QOX) is used to enhance the search ability of OEA/D. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D, NSGAII, NICA and D2MOPSO. Simulation results on six multi-objective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto fronts than other four algorithms.     

A sequential method for the development of visual interactive meta-simulation models using neural networks

This paper proposes a practical and efficient method for the development of visual interactive meta-simulation models using neural networks. The method first uses a randomised simulation experimental design to obtain a set of results from a previously validated simulation model. The bootstrap technique is used on these results to generate a series of neural network models that are then trained using back propagation. The visual interactive meta-simulation model consists of the collective response from the trained neural network models. The accuracy of the meta-simulation model is assessed using the bootstrap technique and improved accuracy obtained by increasing the size of the randomised simulation experimental design set and re-training. This paper describes the approach, gives results for five example problems and suggests that the method is a practical extension to visual interactive simulation.     

Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand

We examine neighborhood structures for heuristic search applicable to a general class of vehicle routing problems (VRPs). Our methodology utilizes a cyclic-order solution encoding, which maps a permutation of the customer set to a collection of many possible VRP solutions. We identify the best VRP solution in this collection via a polynomial-time algorithm from the literature. We design neighborhoods to search the space of cyclic orders. Utilizing a simulated annealing framework, we demonstrate the potential of cyclic-order neighborhoods to facilitate the discovery of high quality a priori solutions for the vehicle routing problem with stochastic demand (VRPSD). Without tailoring our solution procedure to this specific routing problem, we are able to match 16 of 19 known optimal VRPSD solutions. We also propose an updating procedure to evaluate the neighbors of a current solution and demonstrate its ability to reduce the computational expense of our approach.     

New simulation-based frameworks for multi-objective reliability-based design optimization of structures

In the present study, two new simulation-based frameworks are proposed for multi-objective reliability-based design optimization (MORBDO). The first is based on hybrid non-dominated sorting weighted simulation method (NSWSM) in conjunction with iterative local searches that is efficient for continuous MORBDO problems. According to NSWSM, uniform samples are generated within the design space and, then, the set of feasible samples are separated. Thereafter, the non-dominated sorting operator is employed to extract the approximated Pareto front. The iterative local sample generation is then performed in order to enhance the accuracy, diversity, and increase the extent of non-dominated solutions. In the second framework, a pseudo-double loop algorithm is presented based on hybrid weighted simulation method (WSM) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) that is efficient for problems including both discrete and continuous variables. According to hybrid WSM-NSGA-II, proper non-dominated solutions are produced in each generation of NSGA-II and, subsequently, WSM evaluates the reliability level of each candidate solution until the algorithm converges to the true Pareto solutions. The valuable characteristic of presented approaches is that only one simulation run is required for WSM during entire optimization process, even if solutions for different levels of reliability be desired. Illustrative examples indicate that NSWSM with the proposed local search strategy is more efficient for small dimension continuous problems. However, WSM-NSGA-II outperforms NSWSM in terms of solutions quality and computational efficiency, specifically for discrete MORBDOs. Employing global optimizer in WSM-NSGA-II provided more accurate results with lower samples than NSWSM.