The Radiotherapy Optimisation Test Set (TROTS) is an extensive set of problems originating from radiotherapy (radiation therapy) treatment planning. This dataset is created for 2 purposes: (1) to supply a large-scale ...
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The Radiotherapy Optimisation Test Set (TROTS) is an extensive set of problems originating from radiotherapy (radiation therapy) treatment planning. This dataset is created for 2 purposes: (1) to supply a large-scale dense dataset to measure performance and quality of mathematical solvers, and (2) to supply a dataset to investigate the multi-criteria optimisation and decision-making nature of the radiotherapy problem. The dataset contains 120 problems (patients), divided over 6 different treatment protocols/tumour types. Each problem contains numerical data, a configuration for the optimisation problem, and data required to visualise and interpret the results. The data is stored as HDF5 compatible Matlab files, and includes scripts to work with the dataset. (C) 2017 The Authors. Published by Elsevier Inc.
A new Pareto front approximation method is proposed for multiobjective optimization problems (MOPs) with bound constraints. The method employs a hybrid optimization approach using two derivative-free direct search tec...
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A new Pareto front approximation method is proposed for multiobjective optimization problems (MOPs) with bound constraints. The method employs a hybrid optimization approach using two derivative-free direct search techniques, and intends to solve black box simulation-based MOPs where the analytical form of the objectives is not known and/or the evaluation of the objective function(s) is very expensive. A new adaptive weighting scheme is proposed to convert a multiobjective optimization problem to a single objective optimization problem. Another contribution of this paper is the generalization of the star discrepancy-based performance measure for problems with more than two objectives. The method is evaluated using five test problems from the literature, and a realistic engineering problem. Results show that the method achieves an arbitrarily close approximation to the Pareto front with a good collection of well-distributed nondominated points for all six test problems.
This paper proposes a goal programming methodology to ensure that a mix of balance and optimisation is achieved across a hierarchical decision network. The extended goal programming principle is used for this purpose....
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This paper proposes a goal programming methodology to ensure that a mix of balance and optimisation is achieved across a hierarchical decision network. The extended goal programming principle is used for this purpose. A model is constructed that provides consideration of balance and efficiency of multipleobjectives and stakeholders at each network node level. A goal programming formulation to provide the decision that best meets the goals of the network is given. The proposed model is controlled by three key parameters that represent the level of non-compensation between objectives, level of non-compensation between stakeholders, and level of centralisation in the network. The methodology is demonstrated on an example pertaining to regional renewable energy generation and the results are discussed. Conclusions are drawn as to the effect of different attitudes towards compensatory behaviour between objectives and stakeholders in the network. (C) 2016 Elsevier B.V. All rights reserved.
The logistic model is adopted in order to fit growth trends of innovative products for a single growth process. In the current competitive environment, we are incapable of predicting a product's life cycle such th...
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The logistic model is adopted in order to fit growth trends of innovative products for a single growth process. In the current competitive environment, we are incapable of predicting a product's life cycle such that it can be described as a smooth S curve. Given this, we propose the use of a fuzzy piecewise regression model as a revision of the traditional logistic model. While no proper probability distribution for market share data currently exists, the proposed method is not only able to detect change-points, but can also identify predicted intervals when the growth trend of an analyzed generation is affected by other product generations. The market shares of four television technologies are used in order to demonstrate the performance of the proposed model. The results show that the proposed model outperforms the logistic model, providing both the best and worst possible market shares for the corresponding generation, and highlighting the time of impact of external influences by identifying change-points.
In this paper we address the computation of indifference regions in the weight space for multiobjective integer and mixed-integer linear programming problems and the graphical exploration of this type of information f...
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In this paper we address the computation of indifference regions in the weight space for multiobjective integer and mixed-integer linear programming problems and the graphical exploration of this type of information for three-objective problems. We present a procedure to compute a subset of the indifference region associated with a supported nondominated solution obtained by the weighted-sum scalarization. Based on the properties of these regions and their graphical representation for problems with up to three objective functions, we propose an algorithm to compute all extreme supported nondominated solutions adjacent to a given solution and another one to compute all extreme supported nondominated solutions to a three-objective problem. The latter is suitable to characterize solutions in delimited nondominated areas or to be used as a final exploration phase. A computer implementation is also presented. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
This paper presents a biobjective robust optimization formulation for identifying robust solutions from a given Pareto set. The objectives consider both solution and model robustness when the exact values of the selec...
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This paper presents a biobjective robust optimization formulation for identifying robust solutions from a given Pareto set. The objectives consider both solution and model robustness when the exact values of the selected solution are affected by uncertainty. The problem is formulated equivalently as a model with uncertainty on the constraint parameters and objective function coefficients. Structural properties and a solution algorithm are developed for the case of multiobjective linear programs. The algorithm is based on facial decomposition;each subproblem is a biobjective linear program and is related to an efficient face of the multiobjective program. The resulting Pareto set reduction methodology allows the handling of continuous and discrete Pareto sets, and can be generalized to consider criteria other than robustness. The use of secondary criteria to further break ties among the many efficient solutions provides opportunities for additional trade-off analysis in the space of the secondary criteria. Examples illustrate the algorithm and characteristics of solutions obtained. (C) 2016 Elsevier B.V. All rights reserved.
It is important, in practice, to find robust solutions to optimisation problems. This issue has been the subject of extensive research focusing on single-objective problems. Recently, researchers also acknowledged the...
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It is important, in practice, to find robust solutions to optimisation problems. This issue has been the subject of extensive research focusing on single-objective problems. Recently, researchers also acknowledged the need to find robust solutions to multi-objective problems and presented some first results on this topic. In this paper, we deal with bi-objective optimisation problems in which only one objective function is uncertain. The contribution of our paper is three-fold. Firstly, we introduce and analyse four different robustness concepts for bi-objective optimisation problems with one uncertain objective function, and we propose an approach for defining a meaningful robust Pareto front for these types of problems. Secondly, we develop an algorithm for computing robust solutions with respect to these four concepts for the case of discrete optimisation problems. This algorithm works for finite and for polyhedral uncertainty sets using a transformation to a multi-objective (deterministic) optimisation problem and the recently published concept of Pareto robust optimal solutions (lancu & Trichakis, 2014). Finally, we apply our algorithm to two real-world examples, namely aircraft route guidance and the shipping of hazardous materials, illustrating the four robustness concepts and their solutions in practical applications. (C) 2016 Elsevier B.V. All rights reserved.
In this paper, we introduce vector variational-like inequality with its weak formulation for multitime multiobjective variational problem. Moreover, we establish the relationships between the solutions of introduced i...
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In this paper, we introduce vector variational-like inequality with its weak formulation for multitime multiobjective variational problem. Moreover, we establish the relationships between the solutions of introduced inequalities and (properly) efficient solutions of multitime multiobjective variational problem, involving the invexities of multitime functionals. Some examples are provided to illustrate our results. (C) 2016 Elsevier B.V. All rights reserved.
This paper deals with project portfolio selection evaluated by multiple experts. The problem consists of selecting a subset of projects that satisfies a set of constraints and represents a compromise among the group o...
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This paper deals with project portfolio selection evaluated by multiple experts. The problem consists of selecting a subset of projects that satisfies a set of constraints and represents a compromise among the group of experts. It can be modeled as a multi-objective combinatorial optimization problem and solved by two procedures based on inverse optimization. It requires to find a minimal adjustment of the expert's evaluations such that a portfolio becomes ideal in the objective space. Several distance functions are considered to define a measure of the adjustment. The two procedures are applied to randomly generated instances of the knapsack problem and computational results are reported. Finally, two illustrative examples are analyzed and several theoretical properties are proved. (c) 2015 Elsevier Ltd. All rights reserved.
This paper presents an application of extended goal programming in the field of offshore wind farm site selection. The strategic importance of offshore shore wind farms is outlined, drawing on the case of the United K...
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This paper presents an application of extended goal programming in the field of offshore wind farm site selection. The strategic importance of offshore shore wind farms is outlined, drawing on the case of the United Kingdom proposed round three sites as an example. The use of multi-objective modelling methodologies for the offshore wind farm sector is reviewed. The technique of extended goal programming is outlined and its flexibility in combining different decision maker philosophies described. An extended goal programming model for site selection based on the United Kingdom future sites is then developed and a parametric analysis undertaken at the meta-objective level. The results are discussed and conclusions are drawn.
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