The evolution of gene regulatory networks in variable environments poses Multi-objective Optimization Problem (MOP), where the expression levels of genes must be tuned to meet the demands of each environment. When for...
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The evolution of gene regulatory networks in variable environments poses Multi-objective Optimization Problem (MOP), where the expression levels of genes must be tuned to meet the demands of each environment. When formalized in the context of monotone systems, this problem falls into a sub-class of linear MOPs. Here, the constraints are partial orders and the objectives consist of either the minimization or maximization of single variables, but their number can be very large. To efficiently and exhaustively find Pareto optimal solutions, we introduce a mapping between colored Hasse diagrams and polytopes associated with an ideal point. A dynamic program based on edge contractions yields an exact closed form description of the Pareto optimal set, in polynomial time of the number of objectives relative to the number of faces of the Pareto front. We additionally discuss the special case of series-parallel graphs with monochromatic connected components of bounded size, for which the running time and the representation of solutions can in principle be linear in the number of objectives. (C) 2018 Elsevier B.V. All rights reserved.
We develop a multi-objective model for the resource allocation problem in a dynamic PERT network, where the activity durations are exponentially distributed random variables and the new projects are generated accordin...
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We develop a multi-objective model for the resource allocation problem in a dynamic PERT network, where the activity durations are exponentially distributed random variables and the new projects are generated according to a Poisson process. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a Poisson process with the generation rate of new projects. It is assumed that the mean time spent in each service station is a non-increasing function and the direct cost of each activity is a non-decreasing function of the amount of resource allocated to it. The decision variables of the model are the allocated resource. quantities. To evaluate the distribution function of total duration for any particular project, we apply a longest path technique in networks of queues. Then, the problem is formulated as a multi-objective optimal control problem that involves three conflicting objective functions. The objective functions are the project direct cost (to be minimized), the mean of the project completion time (min) and the variance of the project completion time (min). Finally, the goal attainment method is applied to solve a discrete-time approximation of the original optimal control problem. We also computationally investigate the trade-off between accuracy and the computational time of the discrete-time approximation technique. (c) 2006 Elsevier Inc. All rights reserved.
Industrial hazardous waste management involves the collection, transportation, treatment, recycling and disposal of industrial hazardous materials that pose risk to their surroundings. In this paper, a new multiobject...
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Industrial hazardous waste management involves the collection, transportation, treatment, recycling and disposal of industrial hazardous materials that pose risk to their surroundings. In this paper, a new multiobjective location-routing model is developed, and implemented in the Marmara region of Turkey. The aim of the model is to help decision makers decide on locations of treatment centers utilizing different technologies, routing different types of industrial hazardous wastes to compatible treatment centers, locations of recycling centers and routing hazardous waste and waste residues to those centers, and locations of disposal centers and routing waste residues there. In the mathematical model, three criteria are considered: minimizing total cost, which includes total transportation cost of hazardous materials and waste residues and fixed cost of establishing treatment, disposal and recycling centers;minimizing total transportation risk related to the population exposure along transportation routes of hazardous materials and waste residues;and minimizing total risk for the population around treatment and disposal centers, also called site risk. A lexicographic weighted Tchebycheff formulation is developed and computed with CPLEX software to find representative efficient solutions to the problem. Data related to the Marmara region is obtained by utilizing Arcview 9.3 GIS software and Marmara region geographical database. (C) 2012 Elsevier B.V. All rights reserved.
Energy planning for individual large energy consumers becomes increasingly important due to several supply options competing and/or complementing each other and the high uncertainty associated with fuel prices. Hotel ...
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Energy planning for individual large energy consumers becomes increasingly important due to several supply options competing and/or complementing each other and the high uncertainty associated with fuel prices. Hotel units are among the largest energy consumers in the building sector, where energy planning may greatly facilitate investment decisions for efficiently meeting energy demand. The present paper presents a linear programming model, including both continuous and integer variables, which represent energy flows and discrete energy technologies, respectively. Furthermore, the model comprises fuzzy parameters in order to handle adequately the uncertainties regarding energy costs. The obtained fuzzy linear programming model is then translated into the equivalent multipleobjective linear programming model, which provides a set of efficient solutions, each one characterized by quantification of the risk associated with the uncertain energy costs. The proposed methodology is illustrated with a case study referring to a large hotel unit located nearby Athens. (C) 2002 Elsevier Science Ltd. All rights reserved.
This paper studies the performance of two stochastic local search algorithms for the biobjective Quadratic Assignment Problem with different degrees of correlation between the flow matrices. The two algorithms follow ...
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This paper studies the performance of two stochastic local search algorithms for the biobjective Quadratic Assignment Problem with different degrees of correlation between the flow matrices. The two algorithms follow two fundamentally different ways of tackling multiobjective combinatorial optimization problems. The first is based on the component-wise ordering of the objective value vectors of neighboring solutions, while the second is based on different scalarizations of the objective function vector. Our experimental results suggest that the performance of the algorithms with respect to solution quality and computation time depends strongly on the correlation between the flow matrices. In addition, some variants of these stochastic local search algorithms obtain very good solutions in short computation time. (c) 2004 Elsevier B.V. All rights reserved.
Given an input solution that may not be Pareto optimal, we present a new inverse optimization methodology for multi-objective convex optimization that determines a weight vector producing a weakly Pareto optimal solut...
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Given an input solution that may not be Pareto optimal, we present a new inverse optimization methodology for multi-objective convex optimization that determines a weight vector producing a weakly Pareto optimal solution that preserves the decision maker's trade-off intention encoded in the input solution. We introduce a notion of trade-off preservation, which we use as a measure of similarity for approximating the input solution, and show its connection with minimizing an optimality gap. We propose a linear approximation to the inverse model and a successive linear programming algorithm that balance between trade-off preservation and computational efficiency, and show that our model encompasses many of the existing inverse optimization models from the literature. We demonstrate the proposed method using clinical data from prostate cancer radiation therapy. (C) 2018 Elsevier B.V. All rights reserved.
This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent rand...
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This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent random variables with exponential distributions, and the new projects are generated according to a Poisson process. The system is represented as a queuing network with finite concurrent projects, where each activity of a project is performed at a devoted service station with one server located in a node of the network. For modeling dynamic PERT networks with CONPIP, we first convert the network of queues into a stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to solve and find the completion time distribution for any particular project. Finally, we propose a multi-objective model with three conflict objectives to optimally control the resources allocated to the servers, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem. (C) 2011 Elsevier B.V. All rights reserved.
We present an algorithm for generating a subset of non-dominated vectors of multipleobjective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a n...
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We present an algorithm for generating a subset of non-dominated vectors of multipleobjective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors. (c) 2006 Elsevier B.V. All rights reserved.
Many engineering problems have multiple conflicting objectives, and they are also stochastic due to inherent uncertainties. One way to represent the multi-objective nature of problems is to use the Pareto optimality t...
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Many engineering problems have multiple conflicting objectives, and they are also stochastic due to inherent uncertainties. One way to represent the multi-objective nature of problems is to use the Pareto optimality to show the trade-off between objectives. Pareto optimality involves the identification of solutions that are not dominated by other solutions based on their respective objective functions. However, the Pareto optimality concept does not contain any information about the uncertainty of solutions. Evaluation and comparison of solutions becomes difficult when the objective functions are subjected to uncertainty. A new metric, the Pareto Uncertainty Index (PUI), is presented. This metric includes uncertainty due to the stochastic coefficients in the objective functions as part of the Pareto optimality concept to form an extended probabilistic Pareto set, we define as the p-Pareto set. The decision maker can observe and assess the randomness of solutions and compare the promising solutions according to their performance of satisfying objectives and any undesirable uncertainty. The PUI is an effective and convenient decision-making tool to compare promising solutions with multiple uncertain objectives. (C) 2020 Elsevier B.V. All rights reserved.
Transmission congestion management is a vital task in electricity markets. Series FACTS devices can be used as effective tools to relieve congestion mostly employing Optimal Power Flow based methods, in which total co...
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Transmission congestion management is a vital task in electricity markets. Series FACTS devices can be used as effective tools to relieve congestion mostly employing Optimal Power Flow based methods, in which total cost as the objective function is minimized. However, power system stability may be deteriorated after relieving congestion using traditional methods leading to a vulnerable power system against disturbances. In this paper, a multi-objective framework is proposed for congestion management where three competing objective functions including total operating cost, voltage and transient stability margins are simultaneously optimized. This leads to an economical and robust operating point where enough levels of voltage and transient security are included. The proposed method optimally locates and sizes series FACTS devices on the most congested branches determined by a priority list based on Locational Marginal Prices. Individual sets of Pareto solutions, resulted from solving multi-objective congestion management for each location of FACTS devices, are merged together to create the comprehensive Pareto set. Results of testing the proposed method on the well-known New-England test system are discussed in details and confirm efficiency of the proposed method. (C) 2014 Elsevier B.V. All rights reserved.
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