Multi-objective integer programming: An improved recursive algorithm

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.Comment: 11 pages, 6 tables; v2: added more details and a computational stud

Uncertainty management in multiobjective hydro-thermal self-scheduling under emission considerations

In this paper, a stochastic multiobjective framework is proposed for a day-ahead short-term Hydro Thermal Self-Scheduling (HTSS) problem for joint energy and reserve markets. An efficient linear formulations are introduced in this paper to deal with the nonlinearity of original problem due to the dynamic ramp rate limits, prohibited operating zones, operating services of thermal plants, multi-head power discharge characteristics of hydro generating units and spillage of reservoirs. Besides, system uncertainties including the generating units\u27 contingencies and price uncertainty are explicitly considered in the stochastic market clearing scheme. For the stochastic modeling of probable multiobjective optimization scenarios, a lattice Monte Carlo simulation has been adopted to have a better coverage of the system uncertainty spectrum. Consequently, the resulting multiobjective optimization scenarios should concurrently optimize competing objective functions including GENeration COmpany\u27s (GENCO\u27s) profit maximization and thermal units\u27 emission minimization. Accordingly, the ε-constraint method is used to solve the multiobjective optimization problem and generate the Pareto set. Then, a fuzzy satisfying method is employed to choose the most preferred solution among all Pareto optimal solutions. The performance of the presented method is verified in different case studies. The results obtained from ε-constraint method is compared with those reported by weighted sum method, evolutionary programming-based interactive Fuzzy satisfying method, differential evolution, quantum-behaved particle swarm optimization and hybrid multi-objective cultural algorithm, verifying the superiority of the proposed approach

Domination and Decomposition in Multiobjective Programming

During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

Quality Representation in Multiobjective Programming

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective programming problems. This manuscript presents two methods for generating discrete representations with equidistant points for multiobjective programs with solution sets determined by convex cones. The Bilevel Controlled Spacing (BCS) method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing. The Constraint Controlled Spacing (CCS) method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. Both methods (under certain assumptions) are proven to produce (weakly) nondominated points. Along the way, several interesting results about obtuse, simplicial cones are also proved. Both the BCS and CCS methods are tested and show promise on a variety of problems: linear, convex, nonconvex (CCS only), two-dimensional, and three-dimensional. Sample Matlab code for two of these examples can be found in the appendices as well as tables containing the generated solution points. The manuscript closes with conclusions and ideas for further research in this field

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

Petroleum Refinery Planning Under Uncertainty: A Multiobjective Optimization Approach with Economic and Operational Risk Management

In the current modernized globalization era, crude oil prices have reached a record high of USD 147 per barrel according to the NYMEX exchange on June 2008. It is forecast to spiral upwards (with the current graph trend) to a much higher price level. The current situation of fluctuating high petroleum crude oil prices is affecting the markets and industries worldwide by the uncertainty and volatility of the petroleum industry. As oil refining is the downstream of the petroleum industry, it is increasingly important for refineries to operate at an optimal level in the presence of volatility of crude oil prices. Downstream refineries must assess the potential impact that may affect its optimal profit margin by considering the costs of purchasing the raw material of crude oils and prices of saleable intermediates and products as well as production yields. With optimization, refinery will be able to operate at optimal condition. In this work, we have attempted to solve model formulation concerning the petroleum refinery planning under uncertainty. We use stochastic programming optimization incorporating the weighted sum method as well as the epsilon constraint method to solve the model formulation of the petroleum refinery planning under uncertainty. The objective of this research project is to formulate a deterministic model followed by a two stage stochastic programming model with recourse problem for a petroleum refinery planning. The two stage stochastic risk model is then reformulated using Mean Absolute Deviation as the risk measure. After formulating the stochastic model using Mean Absolute Deviation, the problem is then investigated using the Pareto front solution of efficient frontier of the resulting multiobjective optimization problem by using the Weighted Sum Method as well as the ε-constraint method in order to obtain the Pareto Optimal Curve which generates a wide selection of optimization solutions for our problem. The implementation of the multiobjective optimization problem is then automated to report the model solution by capturing the solution values using the GAMS looping system. Note that some of the major parameters used throughout the formulated stochastic programming model include prices of the raw material crude oil and saleable products, market demands for products, and production yields. The main contribution on this work in the first part is to conduct a further study/research on the implementation of the model formulation in Khor et al. (2008) where the model formulated by Khor et al. (2008) uses variance as the risk measure. The results obtain in the previous paper will be compared with the method in this paper that incorporates Mean Absolute Deviation as the risk measure. To further study the model formulated, the solution obtain is further enhanced using the Weighted Sum Method as well as the Epsilon constraint method to obtain the Pareto Optimal Curve generation. Hence, most of the exposition on the model formulation and solution algorithms are taken directly from the original paper so as to provide the readers with the most accurate information possible

Performance Analysis of Turbocharger in Diesel Engine

This report explains the project entitled 'Performance Analysis of Turbocharger in Diesel Engine' where the performance of the turbocharger that operated on diesel engine is studied, Each possible aspect of the engine performance will be investigated thoroughly and the feature that enhanced the operating system of the engine with turbocharger will be determined. The goal is to find out the best pressure ratio and the best efficiency for the selected turbocharger with the selected diesel engine. The pressure ratio and the efficiency will be determined using calculation based on Turbocharger Equation Calculation Model. All calculation results will be characterized in the turbocharger performance graph evaluation for the selected turbocharger in term of best pressure ratio and efficiency. During the study, it was discovered that there best efficiency achieved at the pressure rationof 1.7. Priorto that, during the data gathering process, because of the cost factor, the real time test with the engine was not conducted. Recommendations were given to close the gaps that were found in this study

Multi-objective, multi-year dynamic generation and transmission expansion planning- renewable energy sources integration for Iran's National Power Grid

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Multicriteria Optimization Techniques for Understanding the Case Mix Landscape of a Hospital

Various medical and surgical units operate in a typical hospital and to treat their patients these units compete for infrastructure like operating rooms (OR) and ward beds. How that competition is regulated affects the capacity and output of a hospital. This article considers the impact of treating different patient case mix (PCM) in a hospital. As each case mix has an economic consequence and a unique profile of hospital resource usage, this consideration is important. To better understand the case mix landscape and to identify those which are optimal from a capacity utilisation perspective, an improved multicriteria optimization (MCO) approach is proposed. As there are many patient types in a typical hospital, the task of generating an archive of non-dominated (i.e., Pareto optimal) case mix is computationally challenging. To generate a better archive, an improved parallelised epsilon constraint method (ECM) is introduced. Our parallel random corrective approach is significantly faster than prior methods and is not restricted to evaluating points on a structured uniform mesh. As such we can generate more solutions. The application of KD-Trees is another new contribution. We use them to perform proximity testing and to store the high dimensional Pareto frontier (PF). For generating, viewing, navigating, and querying an archive, the development of a suitable decision support tool (DST) is proposed and demonstrated.Comment: 38 pages, 17 figures, 11 table