A criterion space search algorithm for mixed integer linear maximum multiplicative programs: a multiobjective optimization approach

2021 ◽  
Author(s):  
Payman Ghasemi Saghand ◽  
Hadi Charkhgard
Keyword(s):  
Multiobjective Optimization ◽  
Search Algorithm ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Criterion Space ◽  
Multiplicative Programs

A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs

2022 ◽  
Author(s):  
Vahid Mahmoodian ◽  
Iman Dayarian ◽  
Payman Ghasemi Saghand ◽  
Yu Zhang ◽  
Hadi Charkhgard
Keyword(s):  
Objective Function ◽  
Branch And Bound ◽  
Capacity Allocation ◽  
Branch And Cut ◽  
Nash Bargaining ◽  
Mixed Integer ◽  
Bargaining Solution ◽  
Reliability Optimization ◽  
Criterion Space ◽  
Multiplicative Programs

This study introduces a branch-and-bound algorithm to solve mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). This class of optimization problems arises in many applications, such as finding a Nash bargaining solution (Nash social welfare optimization), capacity allocation markets, reliability optimization, etc. The proposed algorithm applies multiobjective optimization principles to solve MIBL-MMPs exploiting a special characteristic in these problems. That is, taking each multiplicative term in the objective function as a dummy objective function, the projection of an optimal solution of MIBL-MMPs is a nondominated point in the space of dummy objectives. Moreover, several enhancements are applied and adjusted to tighten the bounds and improve the performance of the algorithm. The performance of the algorithm is investigated by 400 randomly generated sample instances of MIBL-MMPs. The obtained result is compared against the outputs of the mixed-integer second order cone programming (SOCP) solver in CPLEX and a state-of-the-art algorithm in the literature for this problem. Our analysis on this comparison shows that the proposed algorithm outperforms the fastest existing method, that is, the SOCP solver, by a factor of 6.54 on average. Summary of Contribution: The scope of this paper is defined over a class of mixed-integer programs, the so-called mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). The importance of MIBL-MMPs is highlighted by the fact that they are encountered in applications, such as Nash bargaining, capacity allocation markets, reliability optimization, etc. The mission of the paper is to introduce a novel and effective criterion space branch-and-cut algorithm to solve MIBL-MMPs by solving a finite number of single-objective mixed-integer linear programs. Starting with an initial set of primal and dual bounds, our proposed approach explores the efficient set of the multiobjective problem counterpart of the MIBL-MMP through a criterion space–based branch-and-cut paradigm and iteratively improves the bounds using a branch-and-bound scheme. The bounds are obtained using novel operations developed based on Chebyshev distance and piecewise McCormick envelopes. An extensive computational study demonstrates the efficacy of the proposed algorithm.

scholarly journals Efficient Operative Cost Reduction in Distribution Grids Considering the Optimal Placement and Sizing of D-STATCOMs Using a Discrete-Continuous VSA

2021 ◽  
Vol 11 (5) ◽  
pp. 2175
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Jesus C. Hernández
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Programming Model ◽  
Search Algorithm ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Solution Vector ◽  
The Impact

The problem of reactive power compensation in electric distribution networks is addressed in this research paper from the point of view of the combinatorial optimization using a new discrete-continuous version of the vortex search algorithm (DCVSA). To explore and exploit the solution space, a discrete-continuous codification of the solution vector is proposed, where the discrete part determines the nodes where the distribution static compensator (D-STATCOM) will be installed, and the continuous part of the codification determines the optimal sizes of the D-STATCOMs. The main advantage of such codification is that the mixed-integer nonlinear programming model (MINLP) that represents the problem of optimal placement and sizing of the D-STATCOMs in distribution networks only requires a classical power flow method to evaluate the objective function, which implies that it can be implemented in any programming language. The objective function is the total costs of the grid power losses and the annualized investment costs in D-STATCOMs. In addition, to include the impact of the daily load variations, the active and reactive power demand curves are included in the optimization model. Numerical results in two radial test feeders with 33 and 69 buses demonstrate that the proposed DCVSA can solve the MINLP model with best results when compared with the MINLP solvers available in the GAMS software. All the simulations are implemented in MATLAB software using its programming environment.

A mixed-integer optimization approach for homogeneous magnet design

TECHNOLOGY ◽  
2018 ◽  
Vol 06 (02) ◽  
pp. 49-58
Author(s):  
Iman Dayarian ◽  
Timothy C.Y. Chan ◽  
David Jaffray ◽  
Teo Stanescu
Keyword(s):  
Imaging Modality ◽  
Spatial Location ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Integer Optimization ◽  
Magnet Design ◽  
Field Homogeneity ◽  
Feasibility Constraints ◽  
Design Generation ◽  
Magnetic Resonance Imaging Mri

Magnetic resonance imaging (MRI) is a powerful diagnostic tool that has become the imaging modality of choice for soft-tissue visualization in radiation therapy. Emerging technologies aim to integrate MRI with a medical linear accelerator to form novel cancer therapy systems (MR-linac), but the design of these systems to date relies on heuristic procedures. This paper develops an exact, optimization-based approach for magnet design that 1) incorporates the most accurate physics calculations to date, 2) determines precisely the relative spatial location, size, and current magnitude of the magnetic coils, 3) guarantees field homogeneity inside the imaging volume, 4) produces configurations that satisfy, for the first time, small-footprint feasibility constraints required for MR-linacs. Our approach leverages modern mixed-integer programming (MIP), enabling significant flexibility in magnet design generation, e.g., controlling the number of coils and enforcing symmetry between magnet poles. Our numerical results demonstrate the superiority of our method versus current mainstream methods.

An Evolutionary Multi-Objective Optimization Approach to the Topology Optimization of Auxetic Structures

2002 ◽  
Author(s):  
Ashraf O. Nassef
Keyword(s):  
Topology Optimization ◽  
Elastic Modulus ◽  
Finite Elements ◽  
Multiobjective Optimization ◽  
Poisson Ratio ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Finite Elements Analysis ◽  
Multi Objective ◽  
Auxetic Structures

Auxetic structures are ones, which exhibit an in-plane negative Poisson ratio behavior. Such structures can be obtained by specially designed honeycombs or by specially designed composites. The design of such honeycombs and composites has been tackled using a combination of optimization and finite elements analysis. Since, there is a tradeoff between the Poisson ratio of such structures and their elastic modulus, it might not be possible to attain a desired value for both properties simultaneously. The presented work approaches the problem using evolutionary multiobjective optimization to produce several designs rather than one. The algorithm provides the designs that lie on the tradeoff frontier between both properties.

Design of hydrogen supply chains under demand uncertainty – a case study of passenger transport in Germany

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anton Ochoa Bique ◽  
Leonardo K. K. Maia ◽  
Ignacio E. Grossmann ◽  
Edwin Zondervan
Keyword(s):  
Stochastic Optimization ◽  
Demand Uncertainty ◽  
Programming Model ◽  
Cost Minimization ◽  
Water Electrolysis ◽  
Scenario Tree ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Strong Impact ◽  
Hydrogen Supply

Abstract A strategy for the design of a hydrogen supply chain (HSC) network in Germany incorporating the uncertainty in the hydrogen demand is proposed. Based on univariate sensitivity analysis, uncertainty in hydrogen demand has a very strong impact on the overall system costs. Therefore we consider a scenario tree for a stochastic mixed integer linear programming model that incorporates the uncertainty in the hydrogen demand. The model consists of two configurations, which are analyzed and compared to each other according to production types: water electrolysis versus steam methane reforming. Each configuration has a cost minimization target. The concept of value of stochastic solution (VSS) is used to evaluate the stochastic optimization results and compare them to their deterministic counterpart. The VSS of each configuration shows significant benefits of a stochastic optimization approach for the model presented in this study, corresponding up to 26% of infrastructure investments savings.

A Novel Approach for Two-Stage UAV Path Planning in Pipeline Network Inspection

2020 ◽  
Author(s):  
Rui Qiu ◽  
Yongtu Liang
Keyword(s):  
Path Planning ◽  
Large Scale ◽  
Flight Path ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Two Stage ◽  
Calculation Time ◽  
Pipeline Network ◽  
Second Stage ◽  
Computational Performance

Abstract Currently, unmanned aerial vehicle (UAV) provides the possibility of comprehensive coverage and multi-dimensional visualization of pipeline monitoring. Encouraged by industry policy, research on UAV path planning in pipeline network inspection has emerged. The difficulties of this issue lie in strict operational requirements, variable flight missions, as well as unified optimization for UAV deployment and real-time path planning. Meanwhile, the intricate structure and large scale of the pipeline network further complicate this issue. At present, there is still room to improve the practicality and applicability of the mathematical model and solution strategy. Aiming at this problem, this paper proposes a novel two-stage optimization approach for UAV path planning in pipeline network inspection. The first stage is conventional pre-flight planning, where the requirement for optimality is higher than calculation time. Therefore, a mixed integer linear programming (MILP) model is established and solved by the commercial solver to obtain the optimal UAV number, take-off location and detailed flight path. The second stage is re-planning during the flight, taking into account frequent pipeline accidents (e.g. leaks and cracks). In this stage, the flight path must be timely rescheduled to identify specific hazardous locations. Thus, the requirement for calculation time is higher than optimality and the genetic algorithm is used for solution to satisfy the timeliness of decision-making. Finally, the proposed method is applied to the UAV inspection of a branched oil and gas transmission pipeline network with 36 nodes and the results are analyzed in detail in terms of computational performance. In the first stage, compared to manpower inspection, the total cost and time of UAV inspection is decreased by 54% and 56% respectively. In the second stage, it takes less than 1 minute to obtain a suboptimal solution, verifying the applicability and superiority of the method.

scholarly journals Comparative Assessment of Priority Listing and Mixed Integer Linear Programming Unit Commitment Methods for Non-Interconnected Island Systems

Energies ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 657 ◽  
Author(s):  
Georgios Psarros ◽  
Stavros Papathanassiou
Keyword(s):  
Linear Programming ◽  
Power Systems ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Unit Commitment ◽  
Renewable Energy Sources ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Droop Characteristic

The generation management concept for non-interconnected island (NII) systems is traditionally based on simple, semi-empirical operating rules dating back to the era before the massive deployment of renewable energy sources (RES), which do not achieve maximum RES penetration, optimal dispatch of thermal units and satisfaction of system security criteria. Nowadays, more advanced unit commitment (UC) and economic-dispatch (ED) approaches based on optimization techniques are gradually introduced to safeguard system operation against severe disturbances, to prioritize RES participation and to optimize dispatch of the thermal generation fleet. The main objective of this paper is to comparatively assess the traditionally applied priority listing (PL) UC method and a more sophisticated mixed integer linear programming (MILP) UC optimization approach, dedicated to NII power systems. Additionally, to facilitate the comparison of the UC approaches and quantify their impact on systems security, a first attempt is made to relate the primary reserves capability of each unit to the maximum acceptable frequency deviation at steady state conditions after a severe disturbance and the droop characteristic of the unit’s speed governor. The fundamental differences between the two approaches are presented and discussed, while daily and annual simulations are performed and the results obtained are further analyzed.

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