Enhanced directed search: a continuation method for mixed-integer multi-objective optimization problems

Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect that the solution set forms at least locally a manifold. Recently, the Pareto Tracer (PT) has been proposed, which is such a multi-objective continuation method. While the method works reliably for MOPs with box and equality constraints, no strategy has been proposed yet to adequately treat general inequalities, which we address in this work. We formulate the extension of the PT and present numerical results on some selected benchmark problems. The results indicate that the new method can indeed handle general MOPs, which greatly enhances its applicability.

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The Directed Search Method for Unconstrained Parameter Dependent Multi-objective Optimization Problems

Studies in Computational Intelligence - NEO 2015 ◽

10.1007/978-3-319-44003-3_12 ◽

2016 ◽

pp. 281-330

Author(s):

Víctor Adrián Sosa Hernández ◽

Adriana Lara ◽

Heike Trautmann ◽

Günter Rudolph ◽

Oliver Schütze

Keyword(s):

Optimization Problems ◽

Search Method ◽

Directed Search ◽

Multi Objective Optimization ◽

Multi Objective ◽

Parameter Dependent

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An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation

Mathematical and Computational Applications ◽

10.3390/mca25040073 ◽

2020 ◽

Vol 25 (4) ◽

pp. 73

Author(s):

Xiatong Cai ◽

Abdolmajid Mohammadian ◽

Hamidreza Shirkhani

Keyword(s):

Optimization Problems ◽

Drainage System ◽

Mixed Integer ◽

Engineering Optimization ◽

Continuous Variables ◽

Objective Functions ◽

Multi Objective Optimization ◽

Integer Optimization ◽

Framework Structure ◽

Multi Objective

Combining multiple modules into one framework is a key step in modelling a complex system. In this study, rather than focusing on modifying a specific model, we studied the performance of different calculation structures in a multi-objective optimization framework. The Hydraulic and Risk Combined Model (HRCM) combines hydraulic performance and pipe breaking risk in a drainage system to provide optimal rehabilitation strategies. We evaluated different framework structures for the HRCM model. The results showed that the conventional framework structure used in engineering optimization research, which includes (1) constraint functions; (2) objective functions; and (3) multi-objective optimization, is inefficient for drainage rehabilitation problem. It was shown that the conventional framework can be significantly improved in terms of calculation speed and cost-effectiveness by removing the constraint function and adding more objective functions. The results indicated that the model performance improved remarkably, while the calculation speed was not changed substantially. In addition, we found that the mixed-integer optimization can decrease the optimization performance compared to using continuous variables and adding a post-processing module at the last stage to remove the unsatisfying results. This study (i) highlights the importance of the framework structure inefficiently solving engineering problems, and (ii) provides a simplified efficient framework for engineering optimization problems.

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Spiral water cycle algorithm for solving multi-objective optimization and truss optimization problems

Engineering With Computers ◽

10.1007/s00366-020-01237-y ◽

2021 ◽

Author(s):

Heba F. Eid ◽

Laura Garcia-Hernandez ◽

Ajith Abraham

Keyword(s):

Optimization Problems ◽

Water Cycle ◽

Truss Optimization ◽

Multi Objective Optimization ◽

Water Cycle Algorithm ◽

Multi Objective

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A Multi-Objective Approach toward Optimal Design of Sustainable Integrated Biodiesel/Diesel Supply Chain Based on First- and Second-Generation Feedstock with Solid Waste Use

Energies ◽

10.3390/en14082261 ◽

2021 ◽

Vol 14 (8) ◽

pp. 2261

Author(s):

Evgeniy Ganev ◽

Boyan Ivanov ◽

Natasha Vaklieva-Bancheva ◽

Elisaveta Kirilova ◽

Yunzile Dzhelil

Keyword(s):

Supply Chain ◽

Optimal Design ◽

Solid Waste ◽

Second Generation ◽

Agricultural Land ◽

Optimization Problems ◽

Biodiesel Production ◽

Mixed Integer ◽

Economic Criterion ◽

Multi Objective

This study proposes a multi-objective approach for the optimal design of a sustainable Integrated Biodiesel/Diesel Supply Chain (IBDSC) based on first- (sunflower and rapeseed) and second-generation (waste cooking oil and animal fat) feedstocks with solid waste use. It includes mixed-integer linear programming (MILP) models of the economic, environmental and social impact of IBDSC, and respective criteria defined in terms of costs. The purpose is to obtain the optimal number, sizes and locations of bio-refineries and solid waste plants; the areas and amounts of feedstocks needed for biodiesel production; and the transportation mode. The approach is applied on a real case study in which the territory of Bulgaria with its 27 districts is considered. Optimization problems are formulated for a 5-year period using either environmental or economic criteria and the remainder are defined as constraints. The obtained results show that in the case of the economic criterion, 14% of the agricultural land should be used for sunflower and 2% for rapeseed cultivation, while for the environmental case, 12% should be used for rapeseed and 3% for sunflower. In this case, the price of biodiesel is 14% higher, and the generated pollutants are 6.6% lower. The optimal transport for both cases is rail.

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