Multi-objective Mathematical Programming Research Articles

A hybrid grey-based C5 and firefly algorithm for stock selection

Portfolio optimisation is a major issue in the investment theory. The main issue in portfolio optimisation is selecting an optimal combination of securities according to risk and return. Due to diversity of stocks traded on the stock exchange as well as various criteria, decision problem is considered as a complex and hard problem. Thus, it is necessary to employ a combination of optimisation models, multiple attribute decision-making (MADM) and data mining for dealing with the complexity and difficulty of the problem. Accordingly, the present study aims to form a final portfolio in Tehran Stock Exchange using the hybrid approach of data mining and multiple-criteria decision-making (MCDM). According to this approach, the candidate stocks are first classified using C5 data mining algorithm based on the risk target. Then, the classes are ranked using the grey relation analysis. The final portfolio is formed through a multi-objective mathematical programming model based on the firefly algorithm which minimises the risk coefficient while maximising the rank.

Performance Study of a Multi-Objective Mathematical Programming Modeling Approach for Energy Optimization in Building Envelopes

Architecture is very responsive to the environmental and climatic factors which affect the built environment with unsteady state. Technology can be used to keep these factors under control by optimizing building design to fit with the surrounding environment and the energy needs. In addition, building envelopes play a major role in achieving thermal comfort for occupants and reducing energy consumption. Building envelopes energy optimization became a leading approach in the architectural research and implementation. This study hypothesizes that using solar shading devices with suitable design decisions of the fenestration affects the daylight level, solar heat gain, visual comfort, and thermal comfort for users. The main objective of this study is to examine the relationships between building envelope design and building energy efficiency through research and simulations. In addition, it explores which combinations of the design elements are the most efficient in terms of lighting and HVAC loads which gives the designers a variety of optimum design solutions to choose the architectural from. This research focuses on the implementation and effectiveness of shading devices, glass type, and window-wall ratio (WWR) in energy optimization through building envelope. The study used MATLAB software for the mathematical model simulation while Revit software was used for the model validation. The study found that south orientation for buildings associated with horizontal shading elements is the best solution in terms of cooling loads in summer. In winter, however, the optimal solution was south orientation with vertical shading elements in terms of heating loads and illuminance levels.

A Decision Support Methodology for Locating Bank Branches: A Case Study in Turkey

This paper presents an integrated decision support methodology for locating bank branches. The methodology is composed of two stages: problem structuring, and modeling. In the first stage, initially, a number of criteria are selected with the help of a detailed literature review and expert opinions. Subsequently, importance weights of these criteria for different types of bank branches are identified based on judgments of experts for pairwise comparison questions. At the modeling stage, considering the characteristics and importance of the criteria, a novel multi-objective mathematical programming model is proposed to find specific locations of bank branches. The proposed methodology is applied in locating branches of a Turkish bank. In order to test the validity of the results and robustness, a sensitivity analysis is conducted and the solutions are found to be robust.

Directed Bee Colony Optimization Algorithm to Solve the Nurse Rostering Problem.

The Nurse Rostering Problem is an NP-hard combinatorial optimization, scheduling problem for assigning a set of nurses to shifts per day by considering both hard and soft constraints. A novel metaheuristic technique is required for solving Nurse Rostering Problem (NRP). This work proposes a metaheuristic technique called Directed Bee Colony Optimization Algorithm using the Modified Nelder-Mead Method for solving the NRP. To solve the NRP, the authors used a multiobjective mathematical programming model and proposed a methodology for the adaptation of a Multiobjective Directed Bee Colony Optimization (MODBCO). MODBCO is used successfully for solving the multiobjective problem of optimizing the scheduling problems. This MODBCO is an integration of deterministic local search, multiagent particle system environment, and honey bee decision-making process. The performance of the algorithm is assessed using the standard dataset INRC2010, and it reflects many real-world cases which vary in size and complexity. The experimental analysis uses statistical tools to show the uniqueness of the algorithm on assessment criteria.

Separated vehicle scheduling optimisation for container trucking transportation based on hybrid quantum evolutionary algorithm

To optimise the trucking problem with time windows, a multi-objective mathematical programming model was established for separated vehicle scheduling. To compute Pareto solutions, a phased optimal algorithm based on hybrid quantum evolution was put forward. To enhance the convergence rate, a greedy repair operator was designed. To avoid premature convergence, a neighbourhood search based on node switching was performed. To maintain the dispersion of the Pareto solutions, an adaptive grid operator was designed. The effectiveness of the proposed method compared to previous scheduling modes and other algorithms was verified experimentally. For the same transport capacity, the vehicle scheduling method based on a quantum evolutionary algorithm can greatly reduce both the number of vehicles and cost.

A hybrid grey-based C5 and firefly algorithm for stock selection

Portfolio optimisation is a major issue in the investment theory. The main issue in portfolio optimisation is selecting an optimal combination of securities according to risk and return. Due to diversity of stocks traded on the stock exchange as well as various criteria, decision problem is considered as a complex and hard problem. Thus, it is necessary to employ a combination of optimisation models, multiple attribute decision-making (MADM) and data mining for dealing with the complexity and difficulty of the problem. Accordingly, the present study aims to form a final portfolio in Tehran Stock Exchange using the hybrid approach of data mining and multiple-criteria decision-making (MCDM). According to this approach, the candidate stocks are first classified using C5 data mining algorithm based on the risk target. Then, the classes are ranked using the grey relation analysis. The final portfolio is formed through a multi-objective mathematical programming model based on the firefly algorithm which minimises the risk coefficient while maximising the rank.

Multiobjective portfolio optimization: bridging mathematical theory with asset management practice

We attempt to establish an integrated portfolio optimization business framework, in order to bridge the underlying gap between the complex mathematical theory of multiobjective mathematical programming and asset management practice. Our aim is to assist practitioners and portfolio managers in formulating successful investment strategies, by providing them with an effective decision support tool. In particular, we propose a multiobjective portfolio model, able to support the simultaneous optimization of multiple investment objectives. We also manage to integrate a set of sophisticated real-world non-convex investment policy limitations, such as the cardinality constraints, the buy-in thresholds, the transaction costs, along with particular normative rules. The underlying investment management rationale of the proposed managerial protocol is displayed through an illustrative business flowchart, while we also provide an analytical step-by-step portfolio management business routine. The validity of the model is verified through an extended empirical testing application on the Eurostoxx 50. According to the results, a sufficient number of efficient or Pareto optimal portfolios produced by the model, appear to possess superior out-of-sample returns with respect to the underlying benchmark.

Multi-objective optimization to evaluate tradeoffs among forest ecosystem services following fire hazard reduction in the Deschutes National Forest, USA

Forest owners worldwide are increasingly interested in managing forests to provide a broad suite of ecosystem services, balancing multiple objectives and evaluating management activities in terms of potential tradeoffs. We describe a multi-objective mathematical programming model to quantify tradeoffs in expected sediment delivery and the preservation of Northern spotted owl (NSO) habitat following fuel treatments to reduce fire hazard in the Deschutes National forest in Central Oregon, USA. Our model integrates the management objective of fire hazard reduction and the provision of ecosystem services (water quality and NSO habitat protection) and helps evaluate tradeoffs among them. Our results suggest significant reductions in fire hazard can be achieved without compromising any NSO habitat by strategically placing the treatments; however, the treatments will lead to a short term increase in sediment delivery. An analysis of environmental risks showed that over the longer term, the increase in sediment delivery and NSO habitat loss caused by wildfires would be 30–50% greater in areas without fuel treatments. The use of the multi-objective optimization model described in this study can help managers quantify and assess potential tradeoffs among ecosystem services and provide data for more informed decision making.

Possibilistic Linear Programming Problems involving Normal Random Variables

A new solution procedure of possibilistic linear programming problem is developed involving the right hand side parameters of the constraints as normal random variables with known means and variances and the objective function coefficients are considered as triangular possibility distribution. In order to solve the proposed problem, convert the problem into a crisp equivalent deterministic multi-objective mathematical programming problem and then solved by using fuzzy programming method. A numerical example is presented to illustrate the solution procedure and developed methodology.

A multilevel and multistage efficiency evaluation of innovation systems: A multiobjective DEA approach

Evaluating the efficiency of innovation systems can serve as a substantial enabling tool for policymaking serving to identify best practices and develop potential improvements of actions and strategies. It also serves to provide valuable insight in understanding the nature and dynamics of innovation process at its different stages and levels. The main aim of the paper is to present an integrated assessment and classification framework for national and regional innovation efficiency. The proposed model is based on Data Envelopment Analysis and is formulated as a multiobjective mathematical program in order to consider the objectives and constraints of the different stages and levels of the innovation process. Additionally, the model copes with DEA inconsistencies when ratio measures are employed. In the second part of the study, a multicriteria decision aid approach, based on an ordinal regression model, is applied in order to study how environmental factors on innovation and entrepreneurship affect the estimated efficiency scores. The proposed approach is applied to a set of 23 European countries and their 185 corresponding regions. The results show that there are large differences regarding the efficiency scores of the different stages and levels, implying the existence of significant divergences from the expected norm concerning innovation efficiency. The contribution of the paper lies (i) in the proposed multiobjective model, which is able to model the multiple stages and levels of the innovation process and handle ratio measures without requiring the same set of inputs and outputs at different levels and (ii) in the presented application of the model in the efficiency evaluation of innovation systems, including a meta-analysis of the results based on the framework of the Quadruple Innovation Helix. Such an approach may provide a valuable tool for country/region comparison and policy formulation.

Forming the stock optimized portfolio using model Grey based on C5 and the Shuffled frog leap algorithm

The classic approach of the portfolio optimization is solvable by the classic models of mathematic planning when the number of assets able to investment and the available constraints in the market are limited. However, when considering the terms and constraints of real world, the classic approach of portfolio optimization is not easily solvable using the classical methods of mathematical optimization. It is why, using the methods Meta-heuristic and the evolutionary algorithms in portfolio optimization has been of the most Important issues recently. The main objective of present research is to present an appropriate practical approach to select the optimal stock portfolio. On this regard, a multi-objective mathematical programming model has been designed based on Grey Relational Analysis and C5 algorithm, and then to solve this model and in order to achieve the optimized combination of the rank and risk, the Shuffled Frog-Leaping Algorithm was used. The presented methodology was used in Tehran Stock Exchange.

Industrial Waste Reuse and By‐product Synergy Optimization

SummaryBy‐product synergy is a growing practice worldwide. It consists in the maximization of resources utilization with the replacement of raw materials by by‐products as inputs for industrial processes. In order to support decision making in such strategic projects, appropriate tools must be developed. This article presents the results of a research project, which includes the development of a multiobjective mathematical programming model for the optimization of by‐product flows, synergy configurations, and investment decisions in eco‐industrial networks. This model is evaluated using data related to the Kalundborg industrial symbiosis (IS) in order to illustrate its utilization, as well as to assess, in a retrospective manner, the behavior of the companies involved with respect to both economic and environmental benefits of synergies. The experiments also illustrate the influence of the municipality on synergy implementation and how a scenario‐based approach can be used to anticipate raw material price increase. The results are generally coherent with the actual timing of synergy initializations. Further, the considerable effect of water price on the length of investments’ payback period illustrates the impact of policies and regulations on IS.

A Multi-objective Mathematical Programming For Sustainable Reverse Logistics Network Design. Part I: Model Formulation

Green OA (SR). Author can archive publisher's version/PDF. Link to publisher's version: http://doi.org/10.2495/IWAMA150331

A new multi-objective solution approach to solve transmission congestion management problem of energy markets

Transmission congestion management plays a key role in deregulated energy markets. To correctly model and solve this problem, power system voltage and transient stability limits should be considered to avoid obtaining a vulnerable power system with low stability margins. Congestion management is modeled as a multi-objective optimization problem in this paper. The proposed scheme includes the cost of congestion management, voltage stability margin and transient stability margin as its multiple competing objectives. Moreover, a new effective Multi-objective Mathematical Programming (MMP) solution approach based on normalized normal constraint (NNC) method is presented to solve the multi-objective optimization problem of the congestion management, which can generate a well-distributed and efficient Pareto frontier. The proposed congestion management model and MMP solution approach are implemented on the New-England’s test system and the obtained results are compared with the results of several other congestion management methods. These comparisons verify the superiority of the proposed approach.

The design of an activity buffer that minimises project delay

The theory of constraint (TOC) has long been applied to planning project schedules, and critical chain and buffer management are both developed to reduce the impact of future project uncertainties. Several models are proposed for the project activity buffers, including: 1) the cut and paste method proposed by Goldratt, in 1997; 2) the square root error method proposed by Newbold, in 1998; 3) the adaptive procedure with density proposed by Tukel in 2005. This study proposes a multi-objective mathematical programming model that enables project managers to concurrently maximise the on time delivery of project activities. The multi-objective model is consolidated into a single-objective programming model using a fuzzy membership function. Maximising the value of this membership function leads to the maximisation of the probability of on time completion for all project activities. The model is applied to a real case and the result shows that the proposed fuzzy model determines the duration of activities, which ensures that a project can be completed with the highest probability compared to other methods.

Valuing crop diversity in biodiesel production plans

The problem of defining efficient and environmentally compatible short-term agricultural plans for biodiesel exploitation is dealt with in this paper with a multi-objective modelling framework. To optimally use local resources, the first phase of the plan consists in the analysis of land and climate features in order to evaluate which energy crop can be successfully grown. This phase is performed at local scale using GIS (geographic information system) data and software. The second phase consists in the formulation of a multi-objective mathematical programming problem. Using the land to be cultivated in each parcel with each crop as decision variables, we solve a three objectives problem: the maximization of the net energy produced, of the greenhouse gases avoided with respect to conventional fossil fuels and of the diversity of the energy crop mix. The last is quantitatively measured using a well-known biodiversity index, which allows to study the trade-off between a more varied crop mix and the other two objectives along the frontier of Pareto efficient solutions. The proposed methodology is applied to a region of Mato Grosso, Brazil, where biodiesel is produced from oleaginous crops.

Eco-efficient supply chain networks: development of a design framework and application to a real case study

This paper presents a supply chain network design framework that is based on multi-objective mathematical programming and that can identify ‘eco-efficient’ configuration alternatives that are both efficient and ecologically sound. This work is original in that it encompasses the environmental impact of both transportation and warehousing activities. We apply the proposed framework to a real-life case study (i.e. Lindt & Sprüngli) for the distribution of chocolate products. The results show that cost-driven network optimisation may lead to beneficial effects for the environment and that a minor increase in distribution costs can be offset by a major improvement in environmental performance. This paper contributes to the body of knowledge on eco-efficient supply chain design and closes the missing link between model-based methods and empirical applied research. It also generates insights into the growing debate on the trade-off between the economic and environmental performance of supply chains, supporting organisations in the eco-efficient configuration of their supply chains.

Trademark colours: Cadbury vs Nestlé & Beiersdorf vs Unilever

The field of economics associates capacity planning with economic scale size and finds the characteristics of the production function whereas the operations management community focuses on demand fulfillment to reduce the loss of sales or inventory for profit maximization. However, there is a troublesome capacity trade-off for firms that need to achieve economic scale size and demand fulfillment simultaneously; in particular, a firm's demand is variable and some of the variation is random. This study proposes a multi-objective mathematical program with data envelopment analysis (DEA) constraints to set an efficient target which shows a trade-off between the most-productive-scale-size (MPSS) benchmark and a potential demand fulfillment benchmark. The study also employs the minimax regret (MMR) approach and the stochastic programming (SP) technique to address target variations caused by demand fluctuations. The result shows how capacity planning via the proposed models can help managers address the capacity dilemma.

Multi-objective Phasor Measurement Unit Placement in Electric Power Networks: Integer Linear Programming Formulation

A multi-objective optimal phasor measurement unit placement model using integer linear programming is presented in this article. The proposed model simultaneously optimizes two objectives, i.e., minimization of phasor measurement unit numbers and maximization of measurement redundancy. To calculate the redundancy criteria, the single-line outage and the phasor measurement unit loss are considered simultaneously. A linear formulation is presented for both objective functions. Also herein, to address conflicting attributes and identify Pareto optimal solutions of the multi-objective optimal phasor measurement unit placement problem, a new multi-objective mathematical programming method is proposed. Finally, a new index, i.e., minimum distance to utopia point, is implemented to select the most preferred solution among the available Pareto front based options on the goal to achieve judicious decision makers. Two test systems, i.e., a modified 9-bus and an IEEE 118-bus test systems, are used to illustrate the effectiveness of the proposed framework.

Most productive scale size versus demand fulfillment: A solution to the capacity dilemma

The field of economics associates capacity planning with economic scale size and finds the characteristics of the production function whereas the operations management community focuses on demand fulfillment to reduce the loss of sales or inventory for profit maximization. However, there is a troublesome capacity trade-off for firms that need to achieve economic scale size and demand fulfillment simultaneously; in particular, a firm's demand is variable and some of the variation is random. This study proposes a multi-objective mathematical program with data envelopment analysis (DEA) constraints to set an efficient target which shows a trade-off between the most-productive-scale-size (MPSS) benchmark and a potential demand fulfillment benchmark. The study also employs the minimax regret (MMR) approach and the stochastic programming (SP) technique to address target variations caused by demand fluctuations. The result shows how capacity planning via the proposed models can help managers address the capacity dilemma.