A novel decomposition method for MILP and its application to optimal operation of a thermal storage system

Yokoyama, Ryohei; Ito, Koichi

doi:10.1016/s0196-8904(00)00002-9

Cited by 9 publications

(4 citation statements)

References 11 publications

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“…For each subproblem, if the optimality criterion is satisfied, the current feasible solution is judged to be the optimal solution of the original MILP problem. If the optimality criterion is not satisfied, other values for the variable in the subproblems are assumed, and the procedure is repeated ( Yokoyama & Ito, 2000 ).…”

Section: Milp-based Decompositionmentioning

confidence: 99%

A hyper-matheuristic approach for solving mixed integer linear optimization models in the context of data envelopment analysis

González

López-Espín

Aparicio

et al. 2022

PeerJ Computer Science

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Mixed Integer Linear Programs (MILPs) are usually NP-hard mathematical programming problems, which present difficulties to obtain optimal solutions in a reasonable time for large scale models. Nowadays, metaheuristics are one of the potential tools for solving this type of problems in any context. In this paper, we focus our attention on MILPs in the specific framework of Data Envelopment Analysis (DEA), where the determination of a score of technical efficiency of a set of Decision Making Units (DMUs) is one of the main objectives. In particular, we propose a new hyper-matheuristic grounded on a MILP-based decomposition in which the optimization problem is divided into two hierarchical subproblems. The new approach decomposes the model into discrete and continuous variables, treating each subproblem through different optimization methods. In particular, metaheuristics are used for dealing with the discrete variables, whereas exact methods are used for the set of continuous variables. The metaheuristics use an indirect representation that encodes an incomplete solution for the problem, whereas the exact method is applied to decode the solution and generate a complete solution. The experimental results, based on simulated data in the context of Data Envelopment Analysis, show that the solutions obtained through the new approach outperform those found by solving the problem globally using a metaheuristic method. Finally, regarding the new hyper-matheuristic scheme, the best algorithm selection is found for a set of cooperative metaheuristics ans exact optimization algorithms.

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Section: Milp-based Decompositionmentioning

confidence: 99%

A hyper-matheuristic approach for solving mixed integer linear optimization models in the context of data envelopment analysis

González

López-Espín

Aparicio

et al. 2022

PeerJ Computer Science

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“…Problems closer to reality could of course also be solved. Two examples can be found in [5] and [6]. It is not possible, or even worthwhile, to go into deeper theoretic discussions on how these methods work but some details are perhaps of interest.…”

Section: Optimisation Basicsmentioning

confidence: 99%

Optimal heating of large block of flats

Gustafsson

Rönnqvist

2008

Energy and Buildings

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“…Models that were impossible to solve just a few years ago can now be dealt with in just a few minutes. Examples of recent studies in the field of energy science and MILP can be found in (Gustafsson, 2000;Yokoyama and Ito, 2000;Bojic and Stojanovic, 1998), while a study on load management can be found in (Banerjee, 1998).…”

Section: Optimization Basicsmentioning

confidence: 99%

Optimization models and solution methods for load management

Gustafsson¹,

Rönnqvist

Claesson

2004

Int. J. Energy Res.

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SUMMARYThe electricity market in Sweden has changed during recent years. Electricity for industrial use can now be purchased from a number of competing electricity suppliers. Hence, the price for each kilowatt-hour is significantly lower than it was just two years ago and interest in electricity conservation measures has declined. However, part of the electricity tariff, i.e. the demand cost expressed in Swedish Kronor (SEK) for each kilowatt, is almost the same as before. Attention has thereby been drawn to load management measures in order to reduce this specific cost. Saving one kWh might lead to a monetary saving of between SEK 0.22 and SEK 914; this paper demonstrates how to eliminate only those kWh that actually save a significant amount of money. A load management system has been installed in a small carpentry factory that can turn off equipment based on a pre-set priority and number of minutes each hour. The question now is what level of the electricity load is optimal in a strictly mathematical sense, i.e. how many kW should be set in the load management computer in order to maximise profitability? In this paper, we develop a mathematical model that can be used as a tool both to find the most profitable subscription level and to control the choices to be made. Numerical results from a case study are presented.

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A novel decomposition method for MILP and its application to optimal operation of a thermal storage system

Cited by 9 publications

References 11 publications

A hyper-matheuristic approach for solving mixed integer linear optimization models in the context of data envelopment analysis

A hyper-matheuristic approach for solving mixed integer linear optimization models in the context of data envelopment analysis

Optimal heating of large block of flats

Optimization models and solution methods for load management

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