MILP method for objective reduction in multi-objective optimization

Vázquez, Daniel; Fernández‐Torres, María J.; Ruiz‐Femenia, Rubén; Jiménez, Laureano

doi:10.1016/j.compchemeng.2017.10.021

Cited by 15 publications

(17 citation statements)

References 27 publications

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“…In this technique, a weight is assigned to each objective function. Then, the objective functions are combined to build a single objective function [39][40][41][42][43][44][45]. Suppose that the weight of objective function w is W w .…”

Section: Weighted-sums Methodsmentioning

confidence: 99%

Selection of Food Items for Diet Problem Using a Multi-objective Approach under Uncertainty

Amin¹,

Mulligan-Gow²,

Zhang³

2020

Application of Decision Science in Business and Management

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It is a problem that concerns us all: what should we eat on a day-to-day basis to meet our health goals? Scientists have been utilizing mathematical programming to answer this question. Through the use of operations research techniques, it is possible to find a list of foods that, in a certain quantity, can provide all nutrient recommendations in a day. In this research, a multi-objective programming model is provided to determine the selected food items for a diet problem. Two solution approaches are developed to solve this problem including weighted-sums and ε-constraint methods. Two sources of uncertainty have been considered in the model. To handle these sources, a scenario-based approach is utilized. The application of this model is shown using a case study in Canada. Using the proposed model and the solution approaches, the best food items can be selected and purchased to minimize the total cost and maximize health.

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Section: Weighted-sums Methodsmentioning

confidence: 99%

Selection of Food Items for Diet Problem Using a Multi-objective Approach under Uncertainty

Amin¹,

Mulligan-Gow²,

Zhang³

2020

Application of Decision Science in Business and Management

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“…Compared with the single objective optimization, it is difficult to evaluate the advantage of acceptable solutions in multi-objective optimization [26]- [28]. Thus, there is no unique optimal solution, but a set of optimal solutions.…”

Section: ) Multi-objective Optimizationmentioning

confidence: 99%

Energy-Efficient Trajectory Planning Algorithm Based on Multi-Objective PSO for the Mobile Sink in Wireless Sensor Networks

Yang

2019

IEEE Access

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In wireless sensor networks (WSNs), collecting data with mobile sinks is an effective way to solve the ''energy hole problem''. However, most of existing algorithms of mobile sinks ignore the load balance of rendezvous nodes, which will significantly shorten the network lifetime. Moreover, most mobile sinks are usually required to visit locations of sensor nodes without taking advantage of their communication ranges. Therefore, this paper proposes an energy-efficient trajectory planning algorithm (EETP) based on multi-objective particle swarm optimization (MOPSO) to shorten the trajectory length of the mobile sink and balance the load of rendezvous nodes. EETP aims to reduce the delay in data delivery and prolong the network lifetime. To shorten the trajectory length of the mobile sink, we design a mechanism to select potential visiting points within communication overlapping ranges of sensor nodes, rather than locations of sensor nodes. Additionally, according to trajectory characteristics of the mobile sink, we design an effective trajectory encoding method that can generate a trajectory containing an unfixed number of visiting points. The simulation results show that the proposed EETP is superior to existing WRP, CB and the MOPSO-based algorithm, in terms of delay in data delivery, network lifetime and energy consumption. INDEX TERMS Mobile sink, MOPSO, load balance of rendezvous nodes, trajectory planning.

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“…In a previous work (Vázquez et al, 2018), we proposed three models which allowed the user to minimize the number of objectives by maintaining the dominance structure of the system to a certain degree, given some inputs. It is based upon the concept of δ-error, introduced by Brockhoff & Zitzler (2006a, 2006b, 2006c and on the work performed by Guillén-Gosálbez (2011), increasing its efficiency and its modifiability in order to obtain different models which allow the user to perform different studies.…”

Section: A C C E P T E D Mmentioning

confidence: 99%

“…A brief overview of the theoretical foundations is presented. A comprehensive review of the theoretical foundations is out of the scope of this paper, but the interested reader is referred to our previous work (Vázquez et al, 2018) and references therein.…”

Section: Theoretical Foundationsmentioning

confidence: 99%

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MILP models for objective reduction in multi-objective optimization: Error measurement considerations and non-redundancy ratio

Vázquez

Ruiz‐Femenia

Jiménez

2018

Computers & Chemical Engineering

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A common approach in multi-objective optimization (MOO) consists of removing redundant objectives or reducing the set of objectives minimizing some metrics related with the loss of the dominance structure. In this paper, we comment some weakness related to the usual minimization of the maximum error (infinity norm or δ-error) and the convenience of using a norm 1 instead. Besides, a new model accounting for the minimum number of Pareto solutions that are lost when reducing objectives is provided, which helps to further describe the effects of the objective reduction in the system. A comparison of the performance of these algorithms and its usefulness in objective reduction against principal component analysis + Deb & Saxena's algorithm (Deb & Saxena Kumar, 2005) is provided, and the ability of combining it with a principal component analysis in order to reduce the dimensionality of a system is also studied and commented.

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MILP method for objective reduction in multi-objective optimization

Cited by 15 publications

References 27 publications

Selection of Food Items for Diet Problem Using a Multi-objective Approach under Uncertainty

Selection of Food Items for Diet Problem Using a Multi-objective Approach under Uncertainty

Energy-Efficient Trajectory Planning Algorithm Based on Multi-Objective PSO for the Mobile Sink in Wireless Sensor Networks

MILP models for objective reduction in multi-objective optimization: Error measurement considerations and non-redundancy ratio

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