group assignment optimization

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Assigning students to rank-ordered group projects with linear optimization.

It is fairly common in a classroom setting to have students who must be assiged to projects, either to work alone or in groups. If the students have each ranked the projects from most to least desirable, one typically wants to assign all of the students to their most desired projects.

This is a perfect scenario for optimization, in that we can come up with a "satisfaction" metric based on the rankings and let the solver try to find the best configuration. In this post, we will set up the problem using the proprietary Gurobi solver via their Python bindings , but it can be just as easily set up using PuLP or OR-Tools .

Here, we will consider the problem of assigning students to groups of at most 4 for projects that they have ranked from 1 (most desirable) up to the number projects, and we will try to make everyone as happy as possible in the resulting solution. The data is anonymized but is real data from a recent class (though slightly modified to make the problem harder).

Input the data ¶

Here's some data that was collected using a web form asking each student to rate each of the nine projects from 1 (most desired) to 9 (least desired). In our case, the form required a complete ordering from each student, but if that was not available we could easily create a constraint that prevents students from being assigned to a project they wanted so little that they refused to rate it.

And here are the students who have indicated that they would specifically like to be together with or apart from another students.

Setting up the optimization ¶

This setup naturally leads to a classic assignment ILP (integer linear program), where each decision variable is a one (assign a certain student to a certain project) or a zero (not assigned). Here's how the ILP breaks down:

Data ¶

• List of students indexed by $i \in I$
• List of projects indexed by $j \in J$
• Student preferences $\mathrm{rank}(i,j) \in {1, \ldots, J}$ available $\forall i \in I,\, j \in J$ or else assumed to be infeasible (set equal to 100)

Decision variables ¶

• Assignment matrix (binary):

Constraints ¶

• Each student is assigned to one and only one project
• Each project has less than or equal to four students

If two students mutually request on another, they are put in the same group.

If any student requests not to work with another, they are not put together.

The number of projects is less than or equal to some value $P$ (see below for discussion).

Objective function ¶

Place students in their most desired project, if possible. Higher (worse) preference rank results in a squared loss (making lower places much worse).

• student $i$ gets 1st choice $\implies Z_i = 0^2 = 0$
• student $i$ gets 2nd choice $\implies Z_i = 1^2 = 1$
• student $i$ gets 3rd choice $\implies Z_i = 2^2 = 4$

Implementation ¶

Given the problem definition above, we can start to set this up with code. Gurobi has a multidict object which allows for convenient summing and other relevant operations by indices:

The first object returned is a list of all of indices of decision variables, basically the $i$ and $j$ for each $X_{ij}$ but with the Python-native string keys instead of the actual indexes:

The ratings part is the same dictionary comprehension defined above that has all of these permutations as dict keys and then the currently assigned values as the dict values, except as a multidict it now has some extra functions that come in handy for defining the ILP:

Now we'll use the Gurobi built-ins to set this up. Here's the twist — above we set a maximum number of projects $P$, except we're going to put the problem solving inside a function and let that be the one variable we specifcy dynamically.

The motivation for this is that you can imagine having a soft constraint on the number of projects while still having a preference for fewer, so it could be helpful to see a few scenarios of number of projects and how that affects the objective function.

This could be set as a variable in the optimization, but in many assignment problems there is value to putting a "human in the loop" so we can make informed decisions about whether it's worth having some groups of three and one extra project with only two if that means everyone is much happier about their assignments.

A first pass ¶

Let's solve this for a maximum of 4 projects:

This solved almost immediately, and in fairness this problem is small enough that a person could get pretty close to optimal just going by hand. But you can probably imagine how hard this would be for a person to do once the class size got to be in the dozens of students. Meanwhile, the solver will still be very fast for almost any reasonably sized classroom.

The solve function gives us back a model object and an assignment dictionary, but we'll set up a function to turn this into some helpful dataframes:

So most students got their first choice, a few got their second, and then a couple students were lower than that.

Meanwhile, as specified this time around we only allowed four of the projects to be used, so with 16 students each project ended up with the maximum number of students.

Could we get better assignments if we allow another project instead of dense packing students into the maximum group size of 4 for each of 4 projects?

Solving again with a bit more slack ¶

This way we have demonstrated that going from 4 to 5 projects spreads the students out without causing much improvement in satisfaction. At this point, a human instructor could decide whether it is worthwhile or not to take on supervising another project.

Conclusion ¶

This is the type of problem that fits neatly into an optimization approach. It is extremely difficult to do by hand once the problem size grows past a handful of decision variables — try looking at the rank dataframe above and thinking about how you would do this manually if necessary. Meanwhile it is trivial to represent and solve as an ILP.

The approach can easily be extended to a situation where only one student can work on a given "thing" they have ranked and there are at least as many of the assignable things as students. For example, instead of groups they might have ranked physical resources or project topics they want to work on.

In the real world, assignment problems like this often need a "fudge factor." After all, you can optimize a problem like nurse scheduling or project assignment to 4 decimal places in the objective function, but people do messy things like calling in sick or dropping classes, and in practice our objective function isn't really one-to-one with actual happiness. Tiny changes rarely matter.

A better strategy than coming up with one perfect solution is to jump past all the hard work of figuring this out on paper but then put a human in the loop by showing a nunber of feasible and nearly-optimal solutions and let a person decide based on the totality of the circumstances.

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Use MIQP to improve the group assignment of college computer science courses

xiaohk/CS524-Group-Assignment-Optimization

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Cs 524 (intro to optimization) final project.

In the notebook , I designed a flexible and robust Mixed Integer Quadratic Programming model in Julia to solve college course group assignment problems.

CS 506 Group Assignment Optimization

I specialized my goal to improve CS 506 project assignment experience. The objective is to maximize the student happiness and group fairness. Through visualization, I gained many insights into the optimal solution and the domain problem.

Fortunately, the project got the highest grades in terms of "originality, creativity, insightful commentary, educational value, and general awesomeness." I am also honored to have a free lunch with our professor.

• To run all cells in the notebook , you want to have Gurobi correctly installed.
• Recommend to use nbviewer for better online rendering of this project.
• Jupyter Notebook 98.4%

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group membership assignment by preferences - optimization problem?

I have 30 users and 7 groups. All users will be members of exactly 2 groups. Each group must have between 4 and 6 members. The users have ordered their preferences for group membership (i.e., users have listed in order the groups they would like to be apart of). I would like a solution that assigns all users to groups that minimizes the total distance of all users from their top group preference.

I am trying to find a solution to this problem that is not a brute force calculation (as the search space is quite large). Is there a way to pose this problem such that it would be solvable by some optimization technique? It appears to be non-linear and non-smooth, which reduces the types of solutions, but I still can't figure out how to write the constraints. Or is there an entirely better way to solve this?

• optimization

• $\begingroup$ This sounds like one of those problems where you may have to take some naive algorithm, accept that its result won't be optimal, but prove that its result is somehow decent. $\endgroup$ –  2'5 9'2 Commented Apr 17, 2012 at 7:01
• $\begingroup$ Yes, I'm willing to accept a 'good enough' solution. $\endgroup$ –  maddyblue Commented Apr 17, 2012 at 15:15
• $\begingroup$ The Hungarian method ( en.wikipedia.org/wiki/Hungarian_algorithm ) might to be applicable, which runs in polynomial time. Not 100% sure, it might need some adaptation. Don't have time to get my head around... $\endgroup$ –  B0rk4 Commented Apr 19, 2012 at 17:06

Don't know if you're still looking for a solution, but it is a straight forward 0/1/ assignment model. 210 dec variables, 30 constraints for each user, 14 constraints (2 for each group) for groups, objective function is simply the (7-order) and it is a maximization.

Problem with your objective function is that there will likely be alternative optimal solutions given that the measure of preference is ordinal - there are ways in which we might implement different objectives for 'fairness' - minimize the maximum difference from the most preferred for all users, etc.

If you have the preference data in a "matrix"-style on a spreadsheet, I can get you a solution within minutes.

Interesting problem. Fish Doc

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Group assignment problem with optimisation methods

There’s a company organising a seminar, where 60 trainees will attend. The company plans to divide the participants into 10 groups, each of 6 trainees. Each of the trainees was asked beforehand to choose 5 other trainees they would like to work with. And each of the five is weighted equally. The problem is how we can assign the participants into groups so that the total satisfaction could to optimised.

• optimization

• define total satisfaction please –  juvian Commented Oct 29, 2018 at 18:49
• if a trainee were assigned to work with another one who he/she liked (prefer) to, then 1 point is added to the satisfaction. if not, then 0. –  Jørgen Andreasen Commented Oct 29, 2018 at 19:14
• What have you tried so far? –  G_B Commented Oct 29, 2018 at 23:18

let me give you a small example with CPO within CPLEX in OPL:

• Could you please explain a bit more about how come it is modulo operation here? int wishes[t in trainees][w in likes]=(t+w-1) mod nbTrainees+1; Thanks. –  Jørgen Andreasen Commented Oct 31, 2018 at 20:00
• This helped me enter values without too much effort: friends of 1 : 2,3,4,5,6 and firiends of 60 : 1,2,3,4,5 –  Alex Fleischer Commented Oct 31, 2018 at 20:53
• And how should I interpret x[t][g]*x[wishes[t][w]][g] in the optimisation function? I am quite confused about the latter part. –  Jørgen Andreasen Commented Nov 1, 2018 at 19:50
• x[t][g]*x[wishes[t][w]][g] is 1 iff both factors are 1 which mean trainee t is in group g and his friend wishes[t][w] is also in group g –  Alex Fleischer Commented Nov 2, 2018 at 8:05

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Solving an Assignment Problem

This section presents an example that shows how to solve an assignment problem using both the MIP solver and the CP-SAT solver.

In the example there are five workers (numbered 0-4) and four tasks (numbered 0-3). Note that there is one more worker than in the example in the Overview .

The costs of assigning workers to tasks are shown in the following table.

The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost. Since there are more workers than tasks, one worker will not be assigned a task.

MIP solution

The following sections describe how to solve the problem using the MPSolver wrapper .

Import the libraries

The following code imports the required libraries.

Create the data

The following code creates the data for the problem.

The costs array corresponds to the table of costs for assigning workers to tasks, shown above.

Declare the MIP solver

The following code declares the MIP solver.

Create the variables

The following code creates binary integer variables for the problem.

Create the constraints

Create the objective function.

The following code creates the objective function for the problem.

The value of the objective function is the total cost over all variables that are assigned the value 1 by the solver.

Invoke the solver

The following code invokes the solver.

Print the solution

The following code prints the solution to the problem.

Here is the output of the program.

Complete programs

Here are the complete programs for the MIP solution.

CP SAT solution

The following sections describe how to solve the problem using the CP-SAT solver.

Declare the model

The following code declares the CP-SAT model.

The following code sets up the data for the problem.

The following code creates the constraints for the problem.

Here are the complete programs for the CP-SAT solution.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-01-02 UTC.

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Assignment based on ranked preference

Assume that there are n students, who have to be evenly assigned to m groups. For every student, a preference ranking of of the m groups is given.

I partially order assignment by pointwise preference, i.e. one is better or equal to another if for every student, the assigned group is ranked higher or equal.

What algorithm can I use find “locally optimal” solutions, i.e. assignments where there are no strictly better solutions?

I assume there will be multiple locally optimal solutions. Is there a sensible way to order them without giving the students an incentive to be dishonest in their ranking, i.e. without encouraging strategic voting? If so, can that be solved?

And finally: What are the right terms to search for research that solves this and related problems?

• optimization
• combinatorics

• $\begingroup$ Check out the "stable marriage" problem. $\endgroup$ –  Tom van der Zanden Commented Nov 6, 2015 at 12:30
• $\begingroup$ Right, that’s related. I’ll see what I can find starting from there. $\endgroup$ –  Joachim Breitner Commented Nov 6, 2015 at 12:49
• 1 $\begingroup$ Did you end up solving this problem in a satisfiable manner? It appears to be a non-trivial step to go from the SMP to this particular problem. $\endgroup$ –  Joost Commented Mar 24, 2016 at 15:19
• $\begingroup$ I did not solve it at all, sorry. $\endgroup$ –  Joachim Breitner Commented Mar 24, 2016 at 17:30
• $\begingroup$ This post describes a similar problem and might be of use to you. $\endgroup$ –  Pim Commented Feb 23, 2021 at 21:08

The terms you can use to search the literature are stable marriage and the assignment problem .

As far as discouraging strategic voting, one relevant term might be strategy-proof . This might also be relevant to the general area of mechanism design . My vague recollection is that discouraging strategic voting in stable-marriage-like problems is a hard problem, but I don't know if I'm remembering that right.

For instance, consider stable marriage. The traditional algorithm gives a matching that is male-optimal and female-pessimal (every male gets the best possible mate he possibly could have received in any stable matching; and every female gets the worst possible mate she could have received in any stable matching). Now suppose the females all get together and collude. In a world of perfect information, they can compute what the female-optimal matching would be, and then change their reported preferences to ensure that the female-optimal matching will be selected.

In fact, collusion is not necessary -- the same result happens if each female individually acts in their own self-interest, without any cooperation or conspiracy. Assume again a world of perfect information, where everyone's true preferences are known (to the females, at least). Then each female can compute the best possible mate she could hope for, i.e., the best mate out of all possible matches in all possible stable matchings; she can then change her reported preferences to list that male as her first preference. If the men use their true preferences and each woman uses this procedure to select her preferences strategically, and then we run the traditional algorithm, we end up with the female-optimal (and male-pessimal) matching. Each woman has an incentive to behave in this way, and no collusion is necessary (assuming perfect information).

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Computer Science > Machine Learning

Title: go4align: group optimization for multi-task alignment.

Abstract: This paper proposes \textit{GO4Align}, a multi-task optimization approach that tackles task imbalance by explicitly aligning the optimization across tasks. To achieve this, we design an adaptive group risk minimization strategy, compromising two crucial techniques in implementation: (i) dynamical group assignment, which clusters similar tasks based on task interactions; (ii) risk-guided group indicators, which exploit consistent task correlations with risk information from previous iterations. Comprehensive experimental results on diverse typical benchmarks demonstrate our method's performance superiority with even lower computational costs.

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The most touching moment was the happy eyes of the groom’s grandmother, the most estimable person on the wedding. And the fireworks were a bright end to that beautiful day.

Photography: LENA ELISEEVA PHOTO | Floral Design: Katerina Kazakova | Hair And Makeup: Svetlana Fischeva | Photography - Assistance: Katya Butenko

These photos from Lena Kozhina are so stunningly beautiful – as in you can’t help but stop and stare – it’s hard to believe it’s real life. But these pics are proof of this gorgeous Bride and her handsome Groom’s celebration at Moscow’s Fox Lodge , surrounded by vibrant colors and breathtaking blooms . Oh, and the idea of prepping for your Big Day outside in the sun ? Brilliant. See more bright ideas right here !

From Lena Kozhina … When we met with the couple for the first time, we immediately paid attention to Dima’s behavior towards Julia. There was a feeling of tenderness and awe, and we immediately wanted to recreate this atmosphere of love, care and warmth on their Big Day.

Later, when we had chosen a green meadow and an uncovered pavilion overlooking a lake as the project site, it only highlighted a light summer mood with colorful florals and a great number of natural woods. The name of the site is Fox Lodge and peach-orange color, as one of the Bride’s favorites, set the tone for the whole design – from the invitations, in which we used images of fox cubs to elements of serving guest tables and other decorative elements with the corresponding bright accents.

Photography: Lena Kozhina | Event Planning: Ajur Wedding | Wedding Dress: Rosa Clara | Shoes: Marc Jacobs | Catering: Fox Lodge | Makeup Artist: Elena Otrembskaya | Wedding Venue: Fox Lodge | Cake and Desserts: Yumbaker | Decor: Latte Decor

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• Title 43 —Public Lands: Interior
• Subtitle B —Regulations Relating to Public Lands
• Chapter II —Bureau of Land Management, Department of the Interior
• Subchapter C —Minerals Management (3000)
• Part 3100 —Oil and Gas Leasing
• Subpart 3107 —Continuation and Extension

Extension of Leases Segregated by Assignment

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§ 3107.51 § 3107.52 § 3107.53 § 3107.60 Enhanced Content - Details 25 U.S.C. 396d and 2107 ; 30 U.S.C. 189 , 306 , 359 , and 1751 ; 43 U.S.C. 1701 et seq.; and 42 U.S.C. 15801 . 89 FR 30966 , Apr. 23, 2024, unless otherwise noted. Enhanced Content - Print Generate PDF This content is from the eCFR and may include recent changes applied to the CFR. The official, published CFR, is updated annually and available below under "Published Edition". You can learn more about the process here . Enhanced Content - Display Options The eCFR is displayed with paragraphs split and indented to follow the hierarchy of the document. This is an automated process for user convenience only and is not intended to alter agency intent or existing codification. A separate drafting site is available with paragraph structure matching the official CFR formatting. If you work for a Federal agency, use this drafting site when drafting amendatory language for Federal regulations: switch to eCFR drafting site . Enhanced Content - Subscribe Subscribe to: 43 CFR Part 3100 Subpart 3107 - Extension of Leases Segregated by Assignment Enhanced Content - Timeline 6/22/2024 view on this date view change introduced   Enhanced Content - Go to Date Enhanced content - compare dates, enhanced content - published edition. View the most recent official publication: View Title 43 on govinfo.gov View the PDF for 43 CFR Part 3100 Subpart 3107 - Extension of Leases Segregated by Assignment These links go to the official, published CFR, which is updated annually. As a result, it may not include the most recent changes applied to the CFR. Learn more . Enhanced Content - Developer Tools This document is available in the following developer friendly formats: Hierarchy JSON - Title 43 Content HTML - this subject group Content XML - this subject group Information and documentation can be found in our developer resources . eCFR Content The Code of Federal Regulations (CFR) is the official legal print publication containing the codification of the general and permanent rules published in the Federal Register by the departments and agencies of the Federal Government. The Electronic Code of Federal Regulations (eCFR) is a continuously updated online version of the CFR. It is not an official legal edition of the CFR. Enhanced Content § 3107.51 extension after discovery on other segregated portions.. Any lease segregated by assignment, including the retained portion, will continue in effect for the primary term of the original lease, or for 2 years after the date a well capable of production in paying quantities is established upon any other portion of the original lease, whichever is the longer period. § 3107.52 Undeveloped parts of leases in their extended term. Undeveloped parts of leases retained or assigned out of leases which are in their extended term will continue in effect for 2 years after the effective date of assignment, provided the parent lease was issued prior to September 2, 1960. § 3107.53 Undeveloped parts of producing leases. Undeveloped parts of leases retained or assigned out of leases which are extended by production, actual or suspended, or the payment of compensatory royalty will continue in effect for 2 years after the effective date of assignment and for so long thereafter as oil or gas is produced in paying quantities. § 3107.60 Extension of reinstated leases. Where a reinstatement of a terminated lease is granted under 43 CFR 3108.20 and the authorized officer finds that the reinstatement will not afford the lessee a reasonable opportunity to continue operations under the lease, the authorized officer may extend the term of such lease for a period sufficient to give the lessee such an opportunity. Any extension will be subject to the following conditions: ( a ) No extension will exceed a period equal to the unexpired portion of the lease or any extension thereof remaining at the date of termination. ( b ) When the reinstatement occurs after the expiration of the term or extension thereof, the lease may be extended from the date the authorized officer grants the petition, but in no event for more than 2 years from the date the reinstatement is authorized and so long thereafter as oil or gas is produced in paying quantities. Reader Aids Information. About This Site Legal Status Accessibility No Fear Act Continuity Information Current time by city For example, New York Current time by country For example, Japan Time difference For example, London For example, Dubai Coordinates For example, Hong Kong For example, Delhi For example, Sydney Geographic coordinates of Elektrostal, Moscow Oblast, Russia City coordinates Coordinates of Elektrostal in decimal degrees Coordinates of elektrostal in degrees and decimal minutes, utm coordinates of elektrostal, geographic coordinate systems. WGS 84 coordinate reference system is the latest revision of the World Geodetic System, which is used in mapping and navigation, including GPS satellite navigation system (the Global Positioning System). Geographic coordinates (latitude and longitude) define a position on the Earth’s surface. Coordinates are angular units. The canonical form of latitude and longitude representation uses degrees (°), minutes (′), and seconds (″). GPS systems widely use coordinates in degrees and decimal minutes, or in decimal degrees. Latitude varies from −90° to 90°. The latitude of the Equator is 0°; the latitude of the South Pole is −90°; the latitude of the North Pole is 90°. Positive latitude values correspond to the geographic locations north of the Equator (abbrev. N). Negative latitude values correspond to the geographic locations south of the Equator (abbrev. S). Longitude is counted from the prime meridian ( IERS Reference Meridian for WGS 84) and varies from −180° to 180°. Positive longitude values correspond to the geographic locations east of the prime meridian (abbrev. E). Negative longitude values correspond to the geographic locations west of the prime meridian (abbrev. W). UTM or Universal Transverse Mercator coordinate system divides the Earth’s surface into 60 longitudinal zones. The coordinates of a location within each zone are defined as a planar coordinate pair related to the intersection of the equator and the zone’s central meridian, and measured in meters. Elevation above sea level is a measure of a geographic location’s height. We are using the global digital elevation model GTOPO30 . Elektrostal , Moscow Oblast, Russia Games & Quizzes History & Society Science & Tech Biographies Animals & Nature Geography & Travel Arts & Culture On This Day One Good Fact New Articles Lifestyles & Social Issues Philosophy & Religion Politics, Law & Government World History Health & Medicine Browse Biographies Birds, Reptiles & Other Vertebrates Bugs, Mollusks & Other Invertebrates Environment Fossils & Geologic Time Entertainment & Pop Culture Sports & Recreation Visual Arts Demystified Image Galleries Infographics Top Questions Britannica Kids Saving Earth Space Next 50 Student Center Elektrostal Our editors will review what you’ve submitted and determine whether to revise the article. Elektrostal , city, Moscow oblast (province), western Russia . It lies 36 miles (58 km) east of Moscow city. The name, meaning “electric steel,” derives from the high-quality-steel industry established there soon after the October Revolution in 1917. During World War II , parts of the heavy-machine-building industry were relocated there from Ukraine, and Elektrostal is now a centre for the production of metallurgical equipment. Pop. (2006 est.) 146,189. Eel and grouper optimizer: a nature-inspired optimization algorithm Published: 17 June 2024 Cite this article Ali Mohammadzadeh 1 , 2 & Seyedali Mirjalili 3 , 4   214 Accesses Explore all metrics This paper proposes a meta-heuristic called Eel and Grouper Optimizer (EGO). The EGO algorithm is inspired by the symbiotic interaction and foraging strategy of eels and groupers in marine ecosystems. The algorithm’s efficacy is demonstrated through rigorous evaluation using nineteen benchmark functions, showcasing its superior performance compared to established meta-heuristic algorithms. The findings and results on the benchmark functions demonstrate that the EGO algorithm outperforms well-known meta-heuristics. This work also considers solving a wide range of real-world practical engineering case studies including tension/compression spring, pressure vessel, piston lever, and car side impact, and the CEC 2020 Real-World Benchmark using EGO to illustrate the practicality of the proposed algorithm when dealing with the challenges of real search spaces with unknown global optima. The results show that the proposed EGO algorithm is a reliable soft computing technique for real-world optimization problems and can efficiently outperform the existing algorithms in the literature. This is a preview of subscription content, log in via an institution to check access. Access this article Price includes VAT (Russian Federation) Instant access to the full article PDF. Rent this article via DeepDyve Institutional subscriptions Similar content being viewed by others Pied kingfisher optimizer: a new bio-inspired algorithm for solving numerical optimization and industrial engineering problems GOOSE algorithm: a powerful optimization tool for real-world engineering challenges and beyond Enhanced gorilla troops optimizer powered by marine predator algorithm: global optimization and engineering design Data availability. The data produced during the current study can be obtained from the corresponding author upon reasonable request. Khanduja, N., Bhushan, B.: Recent Advances and Application of Metaheuristic Algorithms: A Survey (2014–2020), pp. 207–228. Algorithms and Applications, Metaheuristic and Evolutionary Computation (2021) Google Scholar   Mohammadzadeh, A., Masdari, M., Gharehchopogh, F.S.: Energy and cost-aware workflow scheduling in cloud computing data centers using a multi-objective optimization algorithm. J. Netw. Syst. 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Mathematics 8 (11), 2016 (2020) Chhabra, A., Sahana, S.K., Sani, N.S., Mohammadzadeh, A., Omar, H.A.: Energy-aware bag-of-tasks scheduling in the cloud computing system using hybrid oppositional differential evolution-enabled whale optimization algorithm. Energies 15 (13), 4571 (2022) Mohammadzadeh, A., Masdari, M.: Scientific workflow scheduling in multi-cloud computing using a hybrid multi-objective optimization algorithm. J. Ambient Intell. Humaniz. Compu. 14 (4), 3509–3529 (2023) Mirjalili, S., Mirjalili, S.M., Saremi, S., Mirjalili, S.: Whale optimization algorithm: theory, literature review, and application in designing photonic crystal filters. In: Mirjalili, S., Song Dong, J., Lewis, A. (eds.) Nature-inspired optimizers theories, literature reviews and applications, pp. 219–238. Springer International Publishing, Cham (2020) Download references Acknowledgements The author would like to thank Mickey Charteris for providing his outstanding eel and grouper photos. No specific grant from any funding agency in the public, commercial, or not-for-profit sectors was received for this research. Author information Authors and affiliations. Department of Computer Engineering, Shahindezh Branch, Islamic Azad University, Shahindezh, Iran Ali Mohammadzadeh MEU Research Unit, Middle East University, Amman, 11831, Jordan Center for Artificial Intelligence Research and Optimization, Torrens University Australia, Fortitude Valley, Brisbane, QLD, 4006, Australia Seyedali Mirjalili University Research and Innovation Center, Obuda University, Budapest, Hungary You can also search for this author in PubMed   Google Scholar Contributions The design and implementation of the research, the analysis of the results, and the writing of the manuscript were done by Ali Mohammadzadeh and Seyedali Mirjalili. All authors have read and approved the published version of the manuscript. Corresponding author Correspondence to Ali Mohammadzadeh . Ethics declarations Competing interests. The authors have no competing interests to declare that are relevant to the content of this article. Additional information Publisher's note. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Rights and permissions Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Reprints and permissions About this article Mohammadzadeh, A., Mirjalili, S. Eel and grouper optimizer: a nature-inspired optimization algorithm. Cluster Comput (2024). https://doi.org/10.1007/s10586-024-04545-w Download citation Received : 18 February 2024 Revised : 23 April 2024 Accepted : 01 May 2024 Published : 17 June 2024 DOI : https://doi.org/10.1007/s10586-024-04545-w Share this article Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative Eel and Grouper Optimizer Engineering design problems Meta-heuristic Optimization Real-World Benchmark Functions Find a journal Publish with us Track your research 477 IMAGES Group Assignment Optimization Group Project Instructions.docx GitHub Group Assignments Optimization Group Project Instructions.doc Group 5 VIDEO Reading Assignment 3 OPTIMIZATION OF WATER QUALITY MONITORING PROGRAMS BY DATA MINING Classroom Assignment Optimization For FKMP's Student Group Assignment Macroeconomics (Group 15): Mexico DRL-based Pin Assignment Optimization of BGAs considering Signal Integrity with Graph Representation IMC151 Optimization Group Iteration Release May 2nd COMMENTS Group assignment optimization with very large number of elements Performance of these assignments can then be evaluated for each element or group individually ti. a performance score can be computed for each element or group of elements. The question: What optimization algorithm would you recommend for efficiently solving (maximizing the sum of scores of individual elements) this problem with very large ... Assigning students to rank-ordered group projects with linear optimization 7 Mar 2021. It is fairly common in a classroom setting to have students who must be assiged to projects, either to work alone or in groups. If the students have each ranked the projects from most to least desirable, one typically wants to assign all of the students to their most desired projects. This is a perfect scenario for optimization, in ... Assignment problem The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. Assignment One of the most well-known combinatorial optimization problems is the assignment problem. Here's an example: suppose a group of workers needs to perform a set of tasks, and for each worker and task, there is a cost for assigning the worker to the task. The problem is to assign each worker to at most one task, with no two workers performing the ... xiaohk/CS524-Group-Assignment-Optimization CS 506 Group Assignment Optimization. I specialized my goal to improve CS 506 project assignment experience. The objective is to maximize the student happiness and group fairness. Through visualization, I gained many insights into the optimal solution and the domain problem. group membership assignment by preferences All users will be members of exactly 2 groups. Each group must have between 4 and 6 members. The users have ordered their preferences for group membership (i.e., users have listed in order the groups they would like to be apart of). I would like a solution that assigns all users to groups that minimizes the total distance of all users from ... Schedule-Based Group Assignment Using Constraint Programming In §§3 and 4, we describe our constraint pro-gramming model for assigning students to groups. Section 5 presents computational results from apply-ing our model (with various objective functions) to seven test problems. Section 6 concludes the paper and gives directions for future work. 2. Effective approaches to group role assignment with a flexible formation Group role assignment with a flexible formation (GRAFF) is essential for group performance optimization in collaborative systems. In this paper, problems of GRAFF are formalized based on the Environment-Class, Agent, Role, Group, and Object (E-CARGO) model. Then, based on group role assignment (GRA) and linear programming (LP), two algorithms are proposed. Experiments are developed to analyze ... GO4Align: Group Optimization for Multi-Task Alignment • We develop a heuristic optimization pipeline in GO4Align to tractably achieve the principle, involving dynamical group assignment and risk-guided group indicators. The pipeline incor-porates beneficial task interactions into the group assignments and exploits task correlations for multi-task alignment, improving the overall multi-task ... optimization The company plans to divide the participants into 10 groups, each of 6 trainees. Each of the trainees was asked beforehand to choose 5 other trainees they would like to work with. And each of the five is weighted equally. The problem is how we can assign the participants into groups so that the total satisfaction could to optimised. optimization. OptAssign—A web-based tool for assigning students to groups Table 3 summarizes the optimization results for 16 courses, including nine for which the group assignment was done manually and the preference sheets were still available, and two where primarily the computer tool was employed, but a manual assignment was created additionally by some lecturers (not knowing the results of the computer tool). All ... Solving an Assignment Problem This section presents an example that shows how to solve an assignment problem using both the MIP solver and the CP-SAT solver. Example. In the example there are five workers (numbered 0-4) and four tasks (numbered 0-3). Note that there is one more worker than in the example in the Overview. optimization 2. Assume that there are n students, who have to be evenly assigned to m groups. For every student, a preference ranking of of the m groups is given. I partially order assignment by pointwise preference, i.e. one is better or equal to another if for every student, the assigned group is ranked higher or equal. Optimization Group Project Instructions Optimization Group Project Instructions Instructions. This is a group assignment. In order to complete the assignment, first read the "Hawley Lighting Company" case study. Conduct necessary calculations and answer the questions listed below. Submit your Excel spreadsheet(s) with calculations to the assignment dropbox before the posted deadline. GO4Align: Group Optimization for Multi-Task Alignment This paper proposes \\textit{GO4Align}, a multi-task optimization approach that tackles task imbalance by explicitly aligning the optimization across tasks. To achieve this, we design an adaptive group risk minimization strategy, compromising two crucial techniques in implementation: (i) dynamical group assignment, which clusters similar tasks based on task interactions; (ii) risk-guided group ... Excel for Group Assignments: Progress & Budget Optimization 1: Conflict Resolution Strategies. Conflicts among team members can disrupt the harmony essential for successful group assignments. Excel can be a valuable tool for tracking and addressing these conflicts. By creating a log within Excel, you can document conflicts, their resolutions, and any ongoing issues. Optimized group formation for solving collaborative tasks Group formation for solving collaborative tasks The optimization goals for task assignment is putatively similar between collaborative task and traditional microtask—maximize the quality of the completed tasks while minimizing cost by assigning appropriate tasks to appropriate workers. Task assignment has been extensively studied for ... Logic Configuration Those in the Fleet Optimization logical group can be used by multiple processes. For the Optimize Driver Assignments action, use the parameters under the 'General' and 'Savings Merge Algorithm' groups to define values used by the savings merge algorithm when Savings Merge is selected for the Fleet Assignment Algorithm parameter. If 'Column ... PDF Optimized group formation for solving collaborative tasks Group formation for solving collaborative tasks The optimization goals for task assignment is putatively simi-lar between collaborative task and traditional microtask— maximize the quality of the completed tasks while mini-mizing cost by assigning appropriate tasks to appropriate workers. Service Provider Assignment and Resource Management Service provider assignment can use commitments to assign service providers to shipments on legs that share equipment with other legs. 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The name, meaning "electric steel," derives from the high-quality-steel industry established there soon after the October Revolution in 1917. During World War II, parts of the heavy-machine-building industry were relocated there from Ukraine, and Elektrostal is now a centre for the ... Eel and grouper optimizer: a nature-inspired optimization ... This paper proposes a meta-heuristic called Eel and Grouper Optimizer (EGO). The EGO algorithm is inspired by the symbiotic interaction and foraging strategy of eels and groupers in marine ecosystems. The algorithm's efficacy is demonstrated through rigorous evaluation using nineteen benchmark functions, showcasing its superior performance compared to established meta-heuristic algorithms ... 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