Bi-objective Function Research Articles

Reconfigurable DC/DC Converter for Efficiency and Reliability Optimization

In order to efficiently design power conditioning systems, operating conditions have to be considered. For instance, power converter design should take into account the intermittency of the renewable energy sources and the relatively low efficiency of some of their subsystems such as photovoltaic modules. This paper deals with dc–dc power converter design and aims to improve both reliability and efficiency. The approach adopted is based on a boost-based topology equipped with three MOSFETs in parallel. It uses a novel biobjective algorithm based on a biobjective function that optimizes the power converter efficiency and reliability. The proposed algorithm defines the number of MOSFETs to commutate in order to guarantee the best compromise between the converter efficiency and its reliability, depending on the available input power. The converter efficiency is determined by the power converter losses, calculated using the power device parameters and their junction temperature measurement as inputs. The converter reliability is calculated using its mean time between failures as assessed in the military handbook for reliability prediction of electronic equipment (MIL-HDBK-217F). Experimental results carried out on a 2.5 kW prototype demonstrate the effectiveness of the proposed system and the details from one day’s photovoltaic power production are presented and discussed.

Integrating drivers’ differences in optimizing green supply chain management at tactical and operational levels

Green Supply Chain Management (GSCM) has attained a huge attention by researchers in the last few decades. However, the effect of human aspects (e.g. drivers’ differences) in designing and managing green supply chains (GSCs) has been ignored despite the fact of their crucial importance in adopting and achieving optimal green strategies. In this paper, a novel approach is developed for integrating drivers’ differences to examine their effect on fuel consumption and CO2 emissions, denoted by a Green Driving Index (GDI), in optimizing green supply chain at the tactical and operational management levels. More specifically, a more realistic mixed integer nonlinear programming model is proposed to deal with multi-site, multi-product, and multi-period Aggregate Production Planning (APP) setting with different levels of drivers and different types of vehicles. The proposed model aims to minimize the total cost and CO2 emissions across the supply chain. Also, it aims to derive optimal assignments between vehicles, drivers, and the destinations as well as an optimal selection and training of the selected drivers. Two formulations of the problem are developed. Specifically, the first formulation minimizes a single objective function of total costs across the supply chain while considering the greenhouse gas (GHG) limits in the constraints whereas the second formulation minimizes a bi-objective function (total costs and GHG). A numerical study and sensitivity analyses are conducted to confirm the verification of the two proposed formulations. The results demonstrate that as CO2 emissions allowable limits become stricter, the model selects drivers having higher GDIs. The results indicate that the drivers’ differences should be considered in GSCM to generate realistic plans with minimum costs and minimal CO2 emissions.

A flexible job shop cell scheduling with sequence‐dependent family setup times and intercellular transportation times using conic scalarization method

AbstractIn this paper, we propose novel mathematical models involving both single‐ and biobjective functions that deal with a flexible job shop scheduling problem in cellular manufacturing environment by taking into consideration exceptional parts, intercellular moves, intercellular transportation times, sequence‐dependent family setup times, and recirculation. The problem has been known as NP‐hard. The proposed models have been tested and solved using Lingo 11.0 with minimization of makespan for the problems involving about 4 cells, 4 part families, 15 parts, and 12 machines. The most suitable model among the proposed single‐objective models is determined using the test results. Then, another objective function as total tardiness is added to this model. The obtained biobjective model is solved using the scalarization methods, the weighted sum method, ɛ‐constraint method, and conic scalarization method (CSM), in order to convert the mathematical model's objectives into a single‐objective function. By utilizing these scalarization methods, the Pareto effective solutions are generated for a specific test problem. The advantages of the CSM are demonstrated by considering the Pareto effective solutions.

Preface: Special issue on the VeRoLog 2015 conference

VeRoLog is the annual conference sponsored by the EURO Working Group on Vehicle Routing and Logistics Optimization within EURO, the Association of the European Operational Research Societies. It brings together the large community of researchers and practitioners interested in vehicle routing optimization and its relations with logistics. The conference is open to high-quality methodological contributions as well as relevant real-world applications and case studies from the industry and service sectors. VeRoLog 2015, which forms the basis of the current special issue, was organized in Vienna. The former conferences were located in Bologna (2012), Southampton (2013), and Oslo (2014). Researchers in the field of Vehicle Routing and Logistics from many parts of Europe and beyond met at the University of Vienna from June 8th to June 10th, 2015. There were 181 participants from 29 countries (). The conference was organized into two plenaries (given by Martin Savelsbergh and Tolga Bektas) and 37 sessions including 123 presentations. strong focus was on rich and real-world routing, especially in the field of green and electric vehicle routing problems, city logistics and bike sharing, and safe and secure routing. In total 28 presentations focused on one of these topics. VeRoLog now also has a solver challenge on rich vehicle routing. The paper of the winner is also included in the special issue. The following seven papers are a selection of the best papers presented during the conference. The paper by Belloso, Juan, Faulin, and Martinez, entitled A Biased-Randomized Metaheuristic for the Vehicle Routing Problem with Clustered and Mixed analyzes the Vehicle Routing Problem with Backhauls, where delivery and pickup customers are served from a central depot. Initially, it focusses on the version with clustered backhauls (VRPCB), where all delivery customers on a route have to be served before the first pickup customer can be visited. This is motivated by the fact that vehicles are often rear loaded. The paper presents a relatively simple to implement yet efficient metaheuristic algorithm that employs a biased randomized version of the popular savings heuristic within a metaheuristic framework. skewed probability distribution is used to induce a biased (oriented) randomization effect on the savings list of routing edges, and the sequencing constraints are considered via penalty costs. On some classical benchmark instances for the VRPCB, competitive results are obtained and a new best-known solution is found. In order to show the robustness of the proposed approach, it is also applied-after a minor adaptation-to the Vehicle Routing Problem with Mixed Backhauls, where line-haul and backhaul customers might appear in any order during a route. The second paper, entitled An Adaptive and Diversified Vehicle Routing Approach to Reducing the Security Risk of Cash-in-Transit Operations and authored by Bozkaya, Salman, and Telciler, considers the new problem class of inconsistent vehicle routing problems. The authors consider the transportation of valuables (e.g., cash). Due to the high-risk nature of this operation (e.g., robberies), they consider a bi-objective function where they

A two-level method of production planning and scheduling for bi-objective reentrant hybrid flow shops

This research deals with a two-level method of production planning and scheduling problems of the reentrant hybrid flow shops. The hybrid flow shop has serial stages where each stage consists of identical parallel machines. Products can be processed at any one of the parallel machines at a stage in the hybrid flow shop. Also a product may have reentrant operations which require revisits of some stages several times. We consider a two-level hierarchical process on production planning and scheduling of the reentrant hybrid flow shop with the bi-objective function to improve productivity and customer satisfaction. Computational experiments show that the combination of preemptive goal programming based production planning algorithms and Pareto genetic based scheduling algorithms outperforms other two-level algorithms. Also we provide results of the application of the proposed method to both randomly generated problems and a real world Thin Film Transistor and Liquid Crystal Display (TFT-LCD) industry.

Lateral Penumbra Modelling Based Leaf End Shape Optimization for Multileaf Collimator in Radiotherapy.

Lateral penumbra of multileaf collimator plays an important role in radiotherapy treatment planning. Growing evidence has revealed that, for a single-focused multileaf collimator, lateral penumbra width is leaf position dependent and largely attributed to the leaf end shape. In our study, an analytical method for leaf end induced lateral penumbra modelling is formulated using Tangent Secant Theory. Compared with Monte Carlo simulation and ray tracing algorithm, our model serves well the purpose of cost-efficient penumbra evaluation. Leaf ends represented in parametric forms of circular arc, elliptical arc, Bézier curve, and B-spline are implemented. With biobjective function of penumbra mean and variance introduced, genetic algorithm is carried out for approximating the Pareto frontier. Results show that for circular arc leaf end objective function is convex and convergence to optimal solution is guaranteed using gradient based iterative method. It is found that optimal leaf end in the shape of Bézier curve achieves minimal standard deviation, while using B-spline minimum of penumbra mean is obtained. For treatment modalities in clinical application, optimized leaf ends are in close agreement with actual shapes. Taken together, the method that we propose can provide insight into leaf end shape design of multileaf collimator.

MLPNN Training via a Multiobjective Optimization of Training Error and Stochastic Sensitivity.

The training of a multilayer perceptron neural network (MLPNN) concerns the selection of its architecture and the connection weights via the minimization of both the training error and a penalty term. Different penalty terms have been proposed to control the smoothness of the MLPNN for better generalization capability. However, controlling its smoothness using, for instance, the norm of weights or the Vapnik-Chervonenkis dimension cannot distinguish individual MLPNNs with the same number of free parameters or the same norm. In this paper, to enhance generalization capabilities, we propose a stochastic sensitivity measure (ST-SM) to realize a new penalty term for MLPNN training. The ST-SM determines the expectation of the squared output differences between the training samples and the unseen samples located within their Q -neighborhoods for a given MLPNN. It provides a direct measurement of the MLPNNs output fluctuations, i.e., smoothness. We adopt a two-phase Pareto-based multiobjective training algorithm for minimizing both the training error and the ST-SM as biobjective functions. Experiments on 20 UCI data sets show that the MLPNNs trained by the proposed algorithm yield better accuracies on testing data than several recent and classical MLPNN training methods.

Design methodology for optimising a high insulation voltage insulated gate bipolar transistor gate driver signal transmission function

In this study, a design methodology for optimising a signal transmission function for high galvanic insulation (up to 30 kV) insulated gate bipolar transistor gate driver is proposed. The technology is based on a printed circuit board magnetic planar transformer with electronic circuits for excitation and reception. The objective of this study is to optimise the geometric elements of the transformer and its associated electronics devices with the help of a virtual prototyping tool. A bi-objective problem of the overall system that leads to a Pareto front is presented. Several Pareto fronts’ results are obtained assuming different insulation layers thickness. The chosen transformer solution is justified and depends on the bi-objective functions and the galvanic insulation level of the system. Moreover, the experimental results are compared with the simulation results. Finally, the comparisons between experimental and simulation results are proposed to lead to a conclusion of this methodology.

Computing molecular signatures as optima of a bi-objective function: method and application to prediction in oncogenomics.

BACKGROUNDFilter feature selection methods compute molecular signatures by selecting subsets of genes in the ranking of a valuation function. The motivations of the valuation functions choice are almost always clearly stated, but those for selecting the genes according to their ranking are hardly ever explicit.METHODWe addressed the computation of molecular signatures by searching the optima of a bi-objective function whose solution space was the set of all possible molecular signatures, ie, the set of subsets of genes. The two objectives were the size of the signature–to be minimized–and the interclass distance induced by the signature–to be maximized–.RESULTSWe showed that: 1) the convex combination of the two objectives had exactly n optimal non empty signatures where n was the number of genes, 2) the n optimal signatures were nested, and 3) the optimal signature of size k was the subset of k top ranked genes that contributed the most to the interclass distance. We applied our feature selection method on five public datasets in oncology, and assessed the prediction performances of the optimal signatures as input to the diagonal linear discriminant analysis (DLDA) classifier. They were at the same level or better than the best-reported ones. The predictions were robust, and the signatures were almost always significantly smaller. We studied in more details the performances of our predictive modeling on two breast cancer datasets to predict the response to a preoperative chemotherapy: the performances were higher than the previously reported ones, the signatures were three times smaller (11 versus 30 gene signatures), and the genes member of the signature were known to be involved in the response to chemotherapy.CONCLUSIONSDefining molecular signatures as the optima of a bi-objective function that combined the signature size and the interclass distance was well founded and efficient for prediction in oncogenomics. The complexity of the computation was very low because the optimal signatures were the sets of genes in the ranking of their valuation. Software can be freely downloaded from http://gardeux-vincent.eu/DeltaRanking.php

An order-based estimation of distribution algorithm for stochastic hybrid flow-shop scheduling problem

In view of the stochastic nature of the data in real-world manufacturing systems, it is crucial to develop effective algorithms to solve the scheduling problems with uncertainty. In this paper, an order-based estimation of distribution algorithm (OEDA) is proposed to solve the hybrid flow-shop scheduling problem (HFSP) with stochastic processing times. Considering the effectiveness and robustness of a schedule, it aims to minimise the makespan of the initial scenario as well as the deviation of all results of the stochastic scenarios and the initial one. To be specific, a bi-objective function is used to evaluate the individuals of the population, and a probability model is designed to describe the probability distribution of the solution space. Meanwhile, optimal computing budget allocation (OCBA) technique is employed to provide a reliable identification to the good solutions among the population. A mechanism is also presented to update the probability model with the superior individuals that are identified by the OCBA. The new individuals are generated by sampling the probability model to track the area with promising solutions. In addition, the influence of parameter setting is investigated based on Taguchi method of design-of-experiment (DOE), and a suitable parameter setting is suggested. Extensive numerical testing results and comparisons with the existing algorithm are provided, which demonstrate the effectiveness of the proposed OEDA.

Filter-based optimization techniques for selection of feature subsets in ensemble systems

Feature selection methods select a subset of attributes (features) of a dataset and it is done based on a defined measure, eliminating the redundant and irrelevant ones. When a feature selection method is applied in a dataset, we aim to improve the quality of the dataset representation. For ensemble systems, feature selection techniques can supply different feature subsets for the individual components, reducing the redundancy that can exist among the features of an input pattern and to increase the diversity level of these systems. This paper proposes the application of three well-known optimization techniques (particle swarm optimization, ant-colony optimization and genetic algorithms), in both mono and bi-objective versions, to choose subsets of features for the individual components of ensembles. The feature selection process was based on two filter-based evaluation criteria that tried to capture the idea of diversity of individual classifiers and group diversity of an ensemble system. In this case, these optimization techniques try to maximize these diversities measures, either individually (mono-objective) or together (bi-objective). An empirical analysis was performed, where all ensemble systems were applied to 11 datasets and we compared both mono and bi-objective versions among each other and with a random subset procedure. Based on the empirical analysis, we will observe that PSO with a bi-objective function will be the most promising direction, when selecting attributes for individual components of ensemble systems.

Robust-based interactive portfolio selection problems with an uncertainty set of returns

This paper considers a robust portfolio selection problem with an uncertainty set of future returns and satisfaction levels in terms of the total return and robustness parameter. Since the proposed model is formulated as an ill-defined problem due to uncertainty and is bi-objective, that is, to maximize both the abovementioned satisfaction levels, it is difficult to solve the model directly without introducing some criterion of optimality for the bi-objective functions. Therefore, by introducing fuzzy goals and an interactive fuzzy satisficing method, the proposed model is transformed into a deterministic equivalent problem. Furthermore, to obtain the exact optimal portfolio analytically, a solution method is developed by introducing the auxiliary problem and performing equivalent transformations. In order to compare the proposed model with previous useful models, numerical examples are provided, and the results show that it is important to maximize the robustness parameter and total return using the interactive process for adjusting investor's satisfaction levels.

Optimising safety stock placement and lead time in an assembly supply chain using bi-objective MAX–MIN ant system

The problem of placing safety inventory over a network, which assembles a product, is a challenging issue in supply chain design (SCD) because manufacturers always want to reduce inventory all over the supply chain (SC). Moreover, the process of designing a SC and then placing inventory, to offer high service level at the lowest possible cost, across a complex SC, is not an easy task for decision makers. In this paper we use the SC representation proposed by Graves and Willems (2000), Manufacturing & Service Operations Management 2 (1), 68–83, where a SC is divided into many supplying, manufacturing, and delivering stages. Our problem is to select one resource option to perform each stage, and based on the selected options to place an amount of inventory (in-progress and on-hand) at each stage, in order to offer a satisfactory customer service level with as low as possible total supply chain cost. A resource option here represents a supplier, a manufacturing plant (production line), or a transport mode in a supplying, manufacturing, or delivering stage, respectively. We developed an approach based on ant colony optimisation (ACO) to minimise simultaneously the total supply chain cost and the products’ lead time to ensure product deliveries without delays. What are new in our approach are the bi-objective function and the computational efficiency of our ACO-based approach. In addition, ACO has not been applied to solve the inventory placement problem. As a validation of the model, we: (a) describe a successful application at CIFUNSA, one of the largest iron foundry in the world, and (b) compare different CPU time instances and metrics about multi-objective optimisation.

SFLA approach to solve PBUC problem with emission limitation

In this paper, the Shuffled Frog Leaping Algorithm is proposed to solve the Profit Based Unit Commitment problem under deregulated environment with emission limitation. The bi-objective function optimization problem is formulated as a maximization of the Generation Companies profit and a minimization of the emission output of the thermal units, while all of the constrains should be satisfied. This work, considers the new softer demand constraint to allocate fixed and transitional cost to the scheduled hours. The IEEE 10 unit 39 bus test system with 24h data is taken as the input for simulation using MATLAB 7.10 version. From the results obtained, it is observed the proposed algorithm achieves maximum profit and minimum emission level with less computational time compared to traditional unit commitment.

A Multiobjective Approach for the Heuristic Optimization of Compactness and Homogeneity in the Optimal Zoning

This paper presents a multiobjective methodology for optimal zoning design (OZ), based on the grouping of geographic data with characteristics of territorial aggregation. The two objectives considered are the minimization of the geometric compactness on the geographical location of the data and the homogeneity of any of the descriptive variables. Since this problem is NP hard [1], our proposal provides an approximate solution taking into account properties of partitioning algorithms and design restrictions for territorial space. Approximate solutions are generated through the set of optimum values (Maxima) and the corresponding minimals (dual Minima) [2] of the bi-objective function using Variable Neighborhood Search (VNS) [3] and the Pareto order defined over this set of values. The results obtained by our proposed approach constitute good solutions and are generated in a reasonably low computational time.

Research on Atmospheric Environmental Capacity Model of Urban Agglomeration

The urban agglomeration is the area with industrial centralization, dense population and vehicles collecting, which is the heavily air polluted place but also the place with demand of hi-quality atmosphere. The only condition to assure the city clusters in sustainable development is that the economy and the environment shall be advanced in coordination, i.e. the economy shall be kept fast developing while the air quality shall satisfy the citizen’s healthy existence and the biologic balance. The basic measure to realize such condition is to control the total amount of pollutants discharged not exceed the atmospheric environmental capacity(AEC) ,in short, implementing the capacity total quantity control(CTQC).so calculate the value of atmospheric environmental capacity is very important. On account that this thesis has considered comprehensively the relations among ambient air quality to come up to national ambient air quality standard(NAAQS), the investment for controlling the pollution and the loss by contamination hazard, an optimized atmospheric environmental capacity model is established with the bi-objective functions of least investment for controlling the pollution and loss by contamination hazard as well as the restricting condition is atmospheric environmental quality meet the NAAQS. Taking the northern urban agglomeration in Leshan City as an example we have calculated the actual SO2 atmospheric environmental capacity and provided an instance for the model’s promotion of application.

Bilevel Biobjective Pseudo Boolean Programming Problems

In the present paper a kind of bilevel programming problem in 0---1 variables, based on the mathematical model attached by us to a concrete portfolio optimization problem, is analyzed. The upper level function is to be maximized, while the lower level function (which is a biobjective function) is to be maximized-minimized in the lexicographic sense. The core idea of this paper is to present a way for solving the proposed bilevel problem by reducing it to a finite number of couples of linear pseudo boolean programming problems. One of these last types of problems is an assignment problem. Also, in this paper the notion of a max ???p min ??? max point is introduced and several necessary and sufficient optimal conditions (useful for solving the problems gained after applying the splitting technique) are proved. Furthermore, an algorithm for solving the initial problem is proposed and an example is given.

Optimization MRI Cylindrical Coils Using Discretized Stream Function With High Order Smoothness

The design of coil for magnetic resonance image (MRI) application is an optimization problem, in which a specified distribution of the magnetic field inside a region of interest is generated by choosing the optimal distribution of current density on a specified non-intersecting design surface. This paper proposes an iterative optimization method for designing MRI coils on a cylindrical surface by using a piecewise discretized scalar stream function as design variable. The surface current density is accurately calculated using piecewise interpolation with smoothness based on the developable property for a cylindrical surface. MRI coils are designed by choosing bi-objective functions and pseudo-Newton sensitivity analysis. The smoothness of the coil are maintained by adjusting the value of derivative degrees of freedom of design variables which are used to interpolate the stream function. Pareto points provide more flexible choices between the two complementary objectives.

A genetic algorithm for robust hybrid flow shop scheduling

Most of scheduling methods consider a deterministic environment for which the data of the problem are known. Nevertheless, in reality, several kinds of uncertainties should be considered, and robust scheduling allows uncertainty to be taken into account. In this article, we consider a scheduling problem under uncertainty. Our case study is a hybrid flow shop scheduling problem, and the processing time of each job for each machine at each stage is the source of uncertainty. To solve this problem, we developed a genetic algorithm. A robust bi-objective evaluation function was defined to obtain a robust, effective solution that is only slightly sensitive to data uncertainty. This bi-objective function minimises simultaneously the makespan of the initial scenario, and the deviation between the makespan of all the disrupted scenarios and the makespan of the initial scenario. We validated our approach with a simulation in order to evaluate the quality of the robustness faced with uncertainty. The computational results show that our algorithm can generate a trade off for effectiveness and robustness for various degrees of uncertainty.

Robust and stable flexible job shop scheduling with random machine breakdowns using a hybrid genetic algorithm

This paper addresses the problem of finding robust and stable solutions for the flexible job shop scheduling problem with random machine breakdowns. A number of bi-objective measures combining the robustness and stability of the predicted schedule are defined and compared while using the same rescheduling method. Consequently, a two-stage Hybrid Genetic Algorithm (HGA) is proposed to generate the predictive schedule. The first stage optimizes the primary objective, minimizing makespan in this work, where all the data is considered to be deterministic with no expected disruptions. The second stage optimizes the bi-objective function and integrates machines assignments and operations sequencing with the expected machine breakdown in the decoding space. An experimental study and Analysis of Variance (ANOVA) is conducted to study the effect of different proposed measures on the performance of the obtained results. Results indicate that different measures have different significant effects on the relative performance of the proposed method. Furthermore, the effectiveness of the current proposed method is compared against three other methods; two are taken from literature and the third is a combination of the former two methods.