Waste-to-energy (WTE) facilities have begun to play an increasingly important role in the management of municipal solid waste (MSW) worldwide. However, due to the environmental and economic impacts they impose on urba...
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Waste-to-energy (WTE) facilities have begun to play an increasingly important role in the management of municipal solid waste (MSW) worldwide. However, due to the environmental and economic impacts they impose on urban sustainability, the location of WTE facilities is always a sensitive issue. With the frequent involvement of private investors in WTE projects in recent years, the uncertainties associated with MSW generation often impose a huge financial risk on both the private investors involved and the government. Therefore, decision support for the location planning of WTE facilities is necessary and critical. A bi-objective two-stage robust model has been developed to help governments identify cost-effective and environmental friendly WTE facility location strategies under uncertainty, in which one objective is to minimize worst-case annual government spending, while the other minimizes environmental disutility. To efficiently solve the model, a novel solution method has been developed based on a combination of the c-constraint method and the column-and-constraint generation algorithm. The proposed model is demonstrated via a case study in the city of Shanghai where the government plans to locate incinerators to release pressure on sanitary land-fills. The computational results show that the proposed model and solution method can effectively support decision-makers. A further sensitivity analysis reveals several useful MSW management insights. (C) 2017 Elsevier B.V. All rights reserved.
. In radiation therapy treatment planning, generating a treatment plan is a multi-objective optimisation problem. The decision-making strategy is uniform for each group of cancer patients, e.g. prostate cancer, and ca...
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. In radiation therapy treatment planning, generating a treatment plan is a multi-objective optimisation problem. The decision-making strategy is uniform for each group of cancer patients, e.g. prostate cancer, and can thus be automated. Predefined priorities and aspiration levels are assigned to each objective, and the strategy is to attain these levels in order of priority. Therefore, a straightforward lexicographic approach is sequential epsilon-constraint programming where objectives are sequentially optimised and constrained according to predefined rules, mimicking human decision-making. The clinically applied 2-phase epsilon-constraint (2p epsilon c) method captures this approach and generates clinically acceptable treatment plans. However, the number of optimisation problems to be solved for the 2p epsilon c method, and hence the computation time, scales linearly with the number of objectives. To improve the daily planning workload and to further enhance radiation therapy, it is extremely important to reduce this time. Therefore, we developed the lexicographic reference point method (LRPM), a lexicographic extension of the reference point method, for generating a treatment plan by solving a single optimisation problem. The LRPM processes multiple a priori defined reference points into modified partial achievement functions. In addition, a priori bounds on a subset of the partial trade-offs can be imposed using a weighted sum component. The LRPM was validated for 30 randomly selected prostate cancer patients. While the treatment plans generated using the LRPM were of similar clinical quality to those generated using the 2p epsilon c method, the LRPM decreased the average computation time from 12.4 to 1.2 minutes, a speed-up factor of 10. (C) 2017 Elsevier B.V. All rights reserved.
An efficient frontier in the typical portfolio selection problem provides an illustrative way to express the tradeoffs between return and risk. Following the basic ideas of modern portfolio theory as introduced by Mar...
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An efficient frontier in the typical portfolio selection problem provides an illustrative way to express the tradeoffs between return and risk. Following the basic ideas of modern portfolio theory as introduced by Markowitz, security returns are usually extracted from past data. Our purpose in this paper is to incorporate future returns scenarios in the investment decision process. For representative points on the efficient frontier, the minimax regret portfolio is calculated, on the basis of the aforementioned scenarios. These points correspond to specific weight combinations. In this way, the areas of the efficient frontier that are more robust than others are identified. The underlying key-contribution is related to the extension of the conventional minimax regret criterion formulation, in multiobjectiveprogramming problems. The validity of the approach is verified through an illustrative empirical testing application on the Eurostoxx 50. (C) 2017 Elsevier B.V. All rights reserved.
In this paper, we propose an algorithm for solving multiobjective minimization problems on nonempty closed convex subsets of the Euclidean space. The proposed method combines a reflection technique for obtaining a fea...
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In this paper, we propose an algorithm for solving multiobjective minimization problems on nonempty closed convex subsets of the Euclidean space. The proposed method combines a reflection technique for obtaining a feasible point with a projected subgradient method. Under suitable assumptions, we show that the sequence generated using this method converges to a Pareto optimal point of the problem. We also present some numerical results. (C) 2016 Elsevier B.V. All rights reserved.
Coal-mining companies should clearly be investing in energy savings and treatment technologies aimed at reducing both their energy consumption and their pollution levels in order to meet the requirements of government...
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Coal-mining companies should clearly be investing in energy savings and treatment technologies aimed at reducing both their energy consumption and their pollution levels in order to meet the requirements of government regulations relating to environmental protection;however, when considering the types of technical equipment to use and the timing of their investment, these companies also need to consider their profits and the costs of such investment. We therefore propose a "multi-objective mixed integer non-linear programming" (MMINLP) model of investment in energy savings and emission reductions designed to handle this type of decision-making problem. Given three objectives (maximum profits, minimal energy consumption and minimal pollution), we develop a hybrid mixed-coding "particle swarm optimization and multi-objective non-dominated sorting genetic algorithm-II" (PSO-NSGA-II) to optimize the continuous and discrete decision variables as a means of helping companies to reach the optimum decision. We also integrate the subtractive clustering-multi-criteria tournament decision-gain analysis method (SC-MTD-GAM) to select the best trade-off solutions on the optimal Pareto fronts. Finally, we carry out a case study of investment decisions on energy savings and emission reductions in the Zhenzhou Coal Industry (Group) Co., Ltd., China, with the results revealing that the proposed model can support decision making for energy savings and emission reductions in coal mining areas. As compared with the NSGA-II and "non-dominated sorting particle swarm optimization" (NSPSO) algorithms, the proposed PSO-NSGA-II is found to have better convergence, coverage and uniformity. (C) 2016 Elsevier B.V. All rights reserved.
Branch and bound is a well-known generic method for computing an optimal solution of a single objective optimization problem. Based on the idea "divide to conquer", it consists in an implicit enumeration pri...
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Branch and bound is a well-known generic method for computing an optimal solution of a single objective optimization problem. Based on the idea "divide to conquer", it consists in an implicit enumeration principle viewed as a tree search. Although the branch and bound was first suggested by Land and Doig (1960), the first complete algorithm introduced as a multi-objective branch and bound that we identified was proposed by Kiziltan and Yucaoglu (1983). Rather few multi-objective branch and bound algorithms have been proposed. This situation is not surprising as the contributions on the extensions of the components of branch and bound for multi-objective optimization are recent. For example, the concept of bound sets, which extends the classic notion of bounds, has been mentioned by Villarreal and Karwan (1981). But it was only developed for the first time in 2001 by Ehrgott and Gandibleux, and fully defined in 2007. This paper describes a state-of-the-art of multi-objective branch and bound, which reviews concepts, components and published algorithms. It mainly focuses on the contributions belonging to the class of optimization problems who has received the most of attention in this context from 1983 until 2015: the linear optimization problems with zero-one variables and mixed 0-1/continuous variables. Only papers aiming to compute a complete set of efficient solutions are discussed. (C) 2017 Elsevier B.V. All rights reserved.
In real-world applications, there are many fields involving dynamic multi-objective optimization problems (DMOPs), in which objectives are in conflict with each other and change over time or environments. In this pape...
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In real-world applications, there are many fields involving dynamic multi-objective optimization problems (DMOPs), in which objectives are in conflict with each other and change over time or environments. In this paper, a modified coevolutionary multi-swarm particle swarm optimizer is proposed to solve DMOPs in the rapidly changing environments (denoted as CMPSODMO). A frame of multi-swarm based particle swarm optimization is adopted to optimize the problem in dynamic environments. In CMPSODMO, the number of swarms (PSO) is determined by the number of the objective functions, and all of these swarms utilize an information sharing strategy to evolve cooperatively. Moreover, a new velocity update equation and an effective boundary constraint technique are developed during evolution of each swarm. Then, a similarity detection operator is used to detect whether a change has occurred, followed by a memory based dynamic mechanism to response to the change. The proposed CMPSODMO has been extensively compared with five state-of-the-art algorithms over a test suit of benchmark problems. Experimental results indicate that the proposed algorithm is promising for dealing with the DMOPs in the rapidly changing environments. (C) 2017 Elsevier B.V. All rights reserved.
In this paper, we are interested in producing discrete and tractable representations of the set of non dominated points for multi-objective optimization problems, both in the continuous and discrete cases. These repre...
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In this paper, we are interested in producing discrete and tractable representations of the set of non dominated points for multi-objective optimization problems, both in the continuous and discrete cases. These representations must satisfy some conditions of coverage, i.e. providing a good approximation of the non-dominated set, spacing, i.e. without redundancies, and cardinality, i.e. with the smallest possible number of points. This leads us to introduce the new concept of (epsilon, epsilon')-kernels, or epsilon-kernels when epsilon' = epsilon is possible, which correspond to epsilon=Pareto sets satisfying an additional. condition, of epsilon'-stability. Among these, the kernels of small, or possibly optimal, cardinality are claimed to be good representations of the non-dominated set. We first establish some general properties on epsilon-kernels. Then, for the bi-objective case, we propose some generic algorithms computing in polynomial time either an epsilon-kernel of small size or, for a fixed size k, an epsilon-kernel with a nearly optimal approximation ratio 1 + epsilon. For more than two objectives, we show that epsilon-kernels do not necessarily exist but that (epsilon, epsilon' )-kernels with epsilon' <= root 1 + epsilon-1 always exist. Nevertheless, we show that the size of a smallest (epsilon, epsilon')-kernel can be very far from the size of a smallest epsilon-Pareto set. (C) 2016 Published by Elsevier B.V.
The lack of discrimination power and the inappropriate multipliers schemes remain major issues in data envelopment analysis (DEA). To overcome these problems, the multiple criteria DEA (MCDEA) model was introduced in ...
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The lack of discrimination power and the inappropriate multipliers schemes remain major issues in data envelopment analysis (DEA). To overcome these problems, the multiple criteria DEA (MCDEA) model was introduced in the late 1990s, drawing from a multipleobjective perspective. However, because the objectives of the MCDEA model are generally conflicting, an optimal solution satisfying all objectives simultaneously often does not exist. Within this context, goal programming (GP) approaches were proposed to solve the MCDEA model. This paper focuses specifically on the GP formulation, known as GPDEA. However, recently, the GPDEA models were found to be invalid, and no alternative formulation, under a GP framework, was proposed. Therefore, the aim here is to develop a formulation for adequately solving the MCDEA model using weighted GP. In order to do so, we point out inconsistencies in the existing GPDEA models, and we present the WGP-MCDEA model. (C) 2016 Elsevier B.V. All rights reserved.
This work presents a sufficient criteria for partial efficient solutions of the cutting stock problem with two objectives. We consider two important objectives for an industry: number of processed objects (cost of raw...
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This work presents a sufficient criteria for partial efficient solutions of the cutting stock problem with two objectives. We consider two important objectives for an industry: number of processed objects (cost of raw materials) and number of different patterns (cost of setup). These optimality results are established through a new approach based on connections between discrete optimization and continuous vector optimization.
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