Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment

In designing phase of systems, design parameters such as component reliabilities and cost are normally under uncertainties. This paper presents a methodology for solving the multi-objective reliability optimization model in which parameters are considered as imprecise in terms of triangular interval data. The uncertain multi-objective optimization model is converted into deterministic multi-objective model including left, center and right interval functions. A conflicting nature between the objectives is resolved with the help of intuitionistic fuzzy programming technique by considering linear as well as the nonlinear degree of membership and non-membership functions. The resultants max–min problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Finally, a numerical instance is presented to show the performance of the proposed approach.     

A goal programming model for joint decision making of inventory lot-size,supplier selection and carrier selection

In this paper, we address a problem in which a storage space constrained buyer procures a single product in multiple periods from multiple suppliers. The production capacity constrained suppliers offer all-unit quantity discounts. The late deliveries and rejections are also incorporated in sourcing. In addition, we consider transportation cost explicitly in decision making which may vary because of freight quantity and distance of shipment between the buyer and a supplier. We propose a multi-objective integer linear programming model for joint decision making of inventory lot-sizing, supplier selection and carrier selection problem. In the multi-objective formulation, net rejected items, net costs and net late delivered items are considered as three objectives that have to be minimized simultaneously over the decision horizon. The intent of the model is to determine the timings, lot-size to be procured, and supplier and carrier to be chosen in each replenishment period. We solve the multi-objective optimization problem using three variants of goal programming (GP) approaches: preemptive GP, non-preemptive GP and weighted max–min fuzzy GP. The solution of these models is compared at different service-level requirements using value path approach.     

Multi-objective optimization of the maritime cargo routing and scheduling problem

This paper addresses the multi-objective maritime cargo routing and scheduling problem, in which the delivery of bulk products from pickup to delivery ports is served by a heterogeneous fleet of vessels. A mixed integer linear programming (MILP) model is formulated to simultaneously minimize total operation costs, the scheduling makespan, and delays in selected deliveries. The model accounts for several real features, such as time windows, capacity of the vessel's compartments, and ports requirements. A fuzzy weighted max–min method was applied to solve the problem. Two heuristics were developed to effectively handle the complex generated MILP models during the solution process. Experiments were conducted to evaluate the optimization approach using real-life instances provided by a fertilizer company. Finally, a case study shows that the developed model and algorithmic framework are flexible and effective in coping with real problems, incorporating specific business rules from different companies.     

Multi-objective list scheduling of workflow applications in distributed computing infrastructures

Executing large-scale applications in distributed computing infrastructures (DCI), for example modern Cloud environments, involves optimization of several conflicting objectives such as makespan, reliability, energy, or economic cost. Despite this trend, scheduling in heterogeneous DCIs has been traditionally approached as a single or bi-criteria optimization problem. In this paper, we propose a generic multi-objective optimization framework supported by a list scheduling heuristic for scientific workflows in heterogeneous DCIs. The algorithm approximates the optimal solution by considering user-specified constraints on objectives in a dual strategy: maximizing the distance to the user’s constraints for dominant solutions and minimizing it otherwise. We instantiate the framework and algorithm for a four-objective case study comprising makespan, economic cost, energy consumption, and reliability as optimization goals. We implemented our method as part of the ASKALON environment (Fahringer et al., 2007) for Grid and Cloud computing and demonstrate through extensive real and synthetic simulation experiments that our algorithm outperforms related bi-criteria heuristics while meeting the user constraints most of the time.     

Vendor selection in outsourcing

In any large organization, millions of dollars are spent on outsourcing. Most large organizations are outsourcing those activities that are either not cost efficient if done in-house or not core to their businesses. One of the most critical steps in outsourcing is vendor selection, which is a strategic decision. We model the vendor selection problem as a multi-objective optimization problem, where one or more buyers order multiple products from different vendors in a multiple sourcing network. Price, lead-time and rejects (quality) are explicitly considered as three conflicting criteria that have to be minimized simultaneously. A pricing model under quantity discounts is used to represent the purchasing cost. We present and compare several multi-objective optimization methods for solving the vendor selection problem. The methods include weighted objective, goal programming and compromise programming. The multicriteria models and the methods are illustrated using a realistic example. Value path approach is used to compare the results of different models.     

Multi-objective colonial competitive algorithm for hybrid flowshop problem

This study analyses the multi-objective optimization in hybrid flowshop problem, in which two conflicting objectives, makespan and total weighted tardiness, are considered to be minimized simultaneously. The multi-objective version of Colonial Competitive Algorithm (CCA) for real world optimization problem is introduced and investigated. In contrast to multi-objective problems solved by CCA, presented in the literature, which used the combination of the objectives as single objective, the proposed algorithm is established on Pareto solutions concepts. Another novelty of this paper is estimating the power of each imperialist by a probabilistic criterion for this multi objective algorithm. Besides that, the variable neighborhood search is implemented as an assimilation strategy. Performance of the algorithm is finally compared with a famous algorithm for scheduling problem, NSGA-II, and the multi-objective form of CCA [28].     

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

In this paper, we study the multiobjective co-design problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model.     

The use of a fuzzy multi-objective linear programming for solving a multi-objective single-machine scheduling problem

This paper develops a fuzzy multi-objective linear programming (FMOLP) model for solving a multi-objective single-machine scheduling problem. The proposed model attempts to minimize the total weighted tardiness and makespan simultaneously. In this problem, a proposed FMOLP method is applied with respect to the overall acceptable degree of the decision maker (DM) satisfaction. A number of numerical examples are solved to show the effectiveness of the proposed approach. The related results are compared with the Wang and Liang's approach. These computational results show that the proposed FMOLP model achieves lower objective functions and higher satisfaction degrees.     

An effective ant colony optimization algorithm for multi-objective job-shop scheduling with equal-size lot-splitting

This paper proposes several novel hybrid ant colony optimization (ACO)-based algorithms to resolve multi-objective job-shop scheduling problem with equal-size lot splitting. The main issue discussed in this paper is lot-splitting of jobs and tradeoff between lot-splitting costs and makespan. One of the disadvantages of ACO is its uncertainty on time of convergence. In order to enrich search patterns of ACO and improve its performance, five enhancements are made in the proposed algorithms including: A new type of pheromone and greedy heuristic function; Three new functions of state transition rules; A nimble local search algorithm for the improvements of solution quality; Mutation mechanism for divisive searching; A particle swarm optimization (PSO)-based algorithm for adaptive tuning of parameters. The objectives that are used to measure the quality of the generated schedules are weighted-sum of makespan, tardiness of jobs and lot-splitting cost. The developed algorithms are analyzed extensively on real-world data obtained from a printing company and simulated data. A mathematical programming model is developed and paired-samples t-tests are performed between obtained solutions of mathematical programming model and proposed algorithms in order to verify effectiveness of proposed algorithms.     

MTO 管理模式下钢铁企业生产合同计划建模与优化

基于对钢铁企业MTO管理模式下合同计划的编制策略、约束条件和优化目标的研究，建立了合同计划优化模型，模型综合考虑了拖期惩罚费用、设备能力均衡利用和库存成本等优化目标，并采用加权法将多目标优化模型转换为单目标优化模型，针对模型的特点设计了求解模型的特殊PSO算法，以某钢铁企业的实际合同计划问题作为实例，在算法不同参数组合下进行了系统的测试，实验结果表明模型和算法是令人满意的。     

Scheduling jobs with deterioration effect and controllable processing time

This article considered the single machine scheduling with controllable processing time (resource allocation) and deterioration effect concurrently. It discussed the minimization of three objectives, which involve the weighted sum of the makespan and the total resource consumption cost, the total resource consumption cost under the condition that the makespan (total flow time) is restricted to a fixed constant and the optimal resource allocation and the optimal job sequence is what we need to make decision. Considering the makespan constraint, it proved that these problems can be solved in polynomial time. A special case of the last problem can be solved in polynomial time with respect to the total flow time constraint.

     

Multi-objective genetic algorithm and its applications to flowshop scheduling

In this paper, we propose a multi-objective genetic algorithm and apply it to flowshop scheduling. The characteristic features of our algorithm are its selection procedure and elite preserve strategy. The selection procedure in our multi-objective genetic algorithm selects individuals for a crossover operation based on a weighted sum of multiple objective functions with variable weights. The elite preserve strategy in our algorithm uses multiple elite solutions instead of a single elite solution. That is, a certain number of individuals are selected from a tentative set of Pareto optimal solutions and inherited to the next generation as elite individuals. In order to show that our approach can handle multi-objective optimization problems with concave Pareto fronts, we apply the proposed genetic algorithm to a two-objective function optimization problem with a concave Pareto front. Last, the performance of our multi-objective genetic algorithm is examined by applying it to the flowshop scheduling problem with two objectives: to minimize the makespan and to minimize the total tardiness. We also apply our algorithm to the flowshop scheduling problem with three objectives: to minimize the makespan, to minimize the total tardiness, and to minimize the total flowtime.     

Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm

The traditional production scheduling problem considers performance indicators such as processing time, cost, and quality as optimization objectives in manufacturing systems; however, it does not take energy consumption or environmental impacts completely into account. Therefore, this paper proposes an energy-efficient model for flexible flow shop scheduling (FFS). First, a mathematical model for a FFS problem, which is based on an energy-efficient mechanism, is described to solve multi-objective optimization. Since FFS is well known as a NP-hard problem, an improved, genetic-simulated annealing algorithm is adopted to make a significant trade-off between the makespan and the total energy consumption to implement a feasible scheduling. Finally, a case study of a production scheduling problem for a metalworking workshop in a plant is simulated. The experimental results show that the relationship between the makespan and the energy consumption may be apparently conflicting. In addition, an energy-saving decision is performed in a feasible scheduling. Using the decision method, there could be significant potential for minimizing energy consumption.     

面向能耗机制的多目标柔性作业车间调度*

针对面向绿色制造的车间调度问题,考虑能源消耗、最大完工时间、生产成本等调度目标,建立了多目标柔性作业车间调度问题模型,并提出一种改进离散蝙蝠算法来求解。针对这个模型的特点,为了有效地表达出工序与粒子种群之间的关系,提出一种整数编码策略。为了避免粒子早熟收敛、求解精度低等问题,设计了一种具有记忆能力的粒子变异操作。为了克服基本蝙蝠算法固定参数不足的缺点,重新调整惯性权重的值,提出一种线性递减的惯性权重策略。针对具体生产实例进行验证,实验数据表明,该改进算法在求解多目标柔性作业车间调度问题上具有良好的性能,是一种有效的调度算法。     

A multi-objective optimization approach for health-care facility location-allocation problems in highly developed cities such as Hong Kong

Public health-care facilities are essential to all communities, and their location/allocation has long been an important issue in urban planning. Given the steady growth of Hong Kong's population, new health-care facilities will need to be built over the next few years. This research examines the problem of where such health-care facilities should be located to improve the equity of accessibility, raise the total accessibility for the entire population, reduce the population that falls outside the coverage range, and decrease the cost of building new facilities. However, because urban areas such as Hong Kong are complex socio-ecological systems, the aforementioned conflicting objectives make it impossible to find one ‘best’ solution that meets all of the objectives. Therefore, this research uses a genetic algorithm based multi-objective optimization (MOO) approach to yield a set of Pareto solutions that can be used to find the most practical tradeoffs between the conflicting objectives. The MOO approach is used to optimize the location of new health-care facilities in Hong Kong for 2020. Because the MOO approach provides a set of diverse plans, planners can compare the value of each objective and the spatial distribution of facilities to analyze or select the solution that best supports their further decisions. Comparing the Pareto solutions with other solutions, it indicates that the MOO approach is a sensible choice for solving multi-objective problems of health-care facility location-allocation in Hong Kong.     

A multi-objective approach to facility layout problem by genetic search algorithm and Electre method

Classical approaches to layout design problem tend to maximise the efficiency of layout, measured by the handling cost related to the interdepartmental flow and to the distance among the departments. However, the actual problem involves several conflicting objectives hence requiring a multi-objective formulation. Multi-objective approaches, recently proposed, in most cases lead to the maximisation of a weighted sum of score functions. The poor practicability of such an approach is due to the difficulty of normalising these functions and of quantifying the weights. In this paper, this difficulty is overcome by approaching the problem in two subsequent steps: in the first step, the Pareto-optimal solutions are determined by employing a multi-objective constrained genetic algorithm and the subsequent selection of the optimal solution is carried out by means of the multi-criteria decision-making procedure Electre. This procedure allows the decision maker to express his preferences on the basis of the knowledge of candidate solution set. Quantitative (handling cost) and qualitative (adjacency and distance requests between departments) objectives are considered referring to a bay structure-based layout model, that allows to take into account also practical constraints such as the aspect ratio of departments. Results obtained confirm the effectiveness of the proposed procedure as a practicable support tool for layout designers.     

Hybridizing a multi-objective simulated annealing algorithm with a multi-objective evolutionary algorithm to solve a multi-objective project scheduling problem

In this paper, a multi-objective project scheduling problem is addressed. This problem considers two conflicting, priority optimization objectives for project managers. One of these objectives is to minimize the project makespan. The other objective is to assign the most effective set of human resources to each project activity. To solve the problem, a multi-objective hybrid search and optimization algorithm is proposed. This algorithm is composed by a multi-objective simulated annealing algorithm and a multi-objective evolutionary algorithm. The multi-objective simulated annealing algorithm is integrated into the multi-objective evolutionary algorithm to improve the performance of the evolutionary-based search. To achieve this, the behavior of the multi-objective simulated annealing algorithm is self-adaptive to either an exploitation process or an exploration process depending on the state of the evolutionary-based search. The multi-objective hybrid algorithm generates a number of near non-dominated solutions so as to provide solutions with different trade-offs between the optimization objectives to project managers. The performance of the multi-objective hybrid algorithm is evaluated on nine different instance sets, and is compared with that of the only multi-objective algorithm previously proposed in the literature for solving the addressed problem. The performance comparison shows that the multi-objective hybrid algorithm significantly outperforms the previous multi-objective algorithm.     

Multi-objective optimization of water distribution systems based on a real options approach

This paper describes a multi-objective optimization model including Real Options concepts for the design and operation of water distribution networks. This approach is explained through a case study with some possible expansion areas defined to fit different future scenarios. A multi-objective decision model with conflicting objectives is detailed. Also, environmental impacts are considered that take into account not only the life cycle carbon emissions of the different materials used during the construction of the networks but also the emissions related to energy consumption during operation. These impacts are translated by giving a cost to each tonne of carbon dioxide emitted. This work presents a new multi-objective simulated annealing algorithm linked to a hydraulic simulator to verify the hydraulic constraints, and the results are represented as points on the Pareto front. The results show that the approach can deal explicitly with conflicting objectives, with environmental impacts and with future uncertainty.     

基于灰色综合关联分析的多目标优化方法

针对现有多目标优化方法存在的搜索性能弱、效率低等问题,提出一种基于灰色综合关联分析的多目标优化方法.该多目标优化方法采用单目标优化算法构建高质量的参考序列,计算参考序列与优化解的目标函数值序列之间的灰色综合关联度,定义基于灰色综合关联度的解支配关系准则,将灰色综合关联度作为多目标优化算法的适应度值.以带顺序相关调整时间的多目标流水车间调度问题作为应用对象,建立总生产成本、最大完工时间、平均流程时间及机器平均闲置时间的多目标函数优化模型.提出基于灰色关联分析的多目标烟花算法,对所建立的多目标优化模型进行优化求解.仿真实验表明,所提出多目标烟花算法的性能优于3种基于不同多目标优化方法的烟花算法及两种经典多目标算法,验证了所提出的多目标优化方法及多目标算法的可行性和有效性.     

Constrained multi-objective optimization algorithms: Review and comparison with application in reinforced concrete structures

Engineering design problems are often multi-objective in nature, which means trade-offs are required between conflicting objectives. In this study, we examine the multi-objective algorithms for the optimal design of reinforced concrete structures. We begin with a review of multi-objective optimization approaches in general and then present a more focused review on multi-objective optimization of reinforced concrete structures. We note that the existing literature uses metaheuristic algorithms as the most common approaches to solve the multi-objective optimization problems. Other efficient approaches, such as derivative-free optimization and gradient-based methods, are often ignored in structural engineering discipline. This paper presents a multi-objective model for the optimal design of reinforced concrete beams where the optimal solution is interested in trade-off between cost and deflection. We then examine the efficiency of six established multi-objective optimization algorithms, including one method based on purely random point selection, on the design problem. Ranking and consistency of the result reveals a derivative-free optimization algorithm as the most efficient one.