# The Challenge of Generating Spatially Balanced Scientific Experiment Designs

@inproceedings{Gomes2004TheCO, title={The Challenge of Generating Spatially Balanced Scientific Experiment Designs}, author={Carla P. Gomes and Meinolf Sellmann and Cindy van Es and Harold van Es}, booktitle={CPAIOR}, year={2004} }

The development of the theory and construction of combinatorial designs originated with the work of Euler on Latin squares. A Latin square on n symbols is an n × n matrix (n is the order of the Latin square), in which each symbol occurs precisely once in each row and in each column. Several interesting research questions posed by Euler with respect to Latin squares, namely regarding orthogonality properties, were only solved in 1959 [3]. Many other questions concerning Latin squares…

## 25 Citations

### In Search of Balance: The Challenge of Generating Balanced Latin Rectangles

- MathematicsCPAIOR
- 2017

In this work, some of the properties of balanced Latin rectangles are studied, the nonexistence of perfect balance for an infinite family of sizes is proved, and several methods to generate the most balanced solutions are presented.

### An Efficient Local Search for Partial Latin Square Extension Problem

- Computer ScienceCPAIOR
- 2015

This paper proposes an efficient local search for the partial Latin square extension problem, and designs a prototype iterated local search algorithm that is effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.

### Iterated local search with Trellis-neighborhood for the partial Latin square extension problem

- Computer ScienceJ. Heuristics
- 2016

This work considers the local search such that the neighborhood is defined by (p, q)-swap, i.e., the operation of dropping exactly p symbols and then assigning symbols to at most q empty cells, and proposes a novel swap operation, Trellis-Swap, which is a generalization of (p), q-swap.

### From Streamlined Combinatorial Search to Efficient Constructive Procedures

- Mathematics, Computer ScienceAAAI
- 2012

This work proposes an approach that integrates specialized combinatorial search, using so-called streamlining, with a human computation component, and discovers two complementary efficient constructions for generatingSo-called Spatially Balanced Latin squares of any order N, such that 2N+1 is prime.

### Iterated Local Search with Trellis-Neighborhood for the Partial Latin Square Extension Proble1n*

- Computer Science
- 2018

This work considers the local search such that the neighborhood is defined by (p, q)-swap, i.e., the operation of dropping exactly p symbols and then assigning symbols to at most q empty cells, and proposes a novel swap operation, Trellisswap, which is a generalization of ( p, q-swap.

### Polynomial Time Construction for Spatially Balanced Latin Squares

- Computer Science
- 2012

This paper aims to demonstrate the efforts towards in-situ applicability of EMMARM, which aims to provide real-time information about the physical and social barriers to efficient and sustainable use of data storage and retrieval.

### Streamlining Local Search for Spatially Balanced Latin Squares

- MathematicsIJCAI
- 2005

This work uses so-called spatially balanced Latin squares to show how streamlining can also be very effective for local search, and believes that streamlined local search is a general technique suitable for solving a wide range of hard combinatorial design problems.

### Bound-Consistent Deviation Constraint

- Computer ScienceCP
- 2007

This work introduces bound-consistent propagators running in linear time with respect to the number of variables on the Balanced Academic Curriculum Problem and evaluates the improvement in terms of efficiency and pruning obtained with the new propagators.

### Global Constraints for the Mean Absolute Deviation and the Variance: Application to the Vertical Line Balancing

- Business
- 2008

Optimization with a balancing objective often appear in practical problems where humans are implied in the solution. For example, in tasks assignment problems it is a desirable property that the…

## References

SHOWING 1-10 OF 21 REFERENCES

### Spatial Nature of Randomization and Its Effect on the Outcome of Field Experiments

- Mathematics
- 1993

Many sites used for field trials exbibit a spatially-dependent variance structure in that nearby observations are autocorrelated. This may affect treatment comparisons made at unequal distances. This…

### ON THE FALSITY OF EULER'S CONJECTURE ABOUT THE NON-EXISTENCE OF TWO ORTHOGONAL LATIN SQUARES OF ORDER 4t + 2.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1959

Since R is a noetherian domain, it follows that a minimal prime ideal p is principal if the authors can show that hd Rip < 2, which completes the proof.

### Reducing Symmetry in a Combinatorial Design Problem

- Computer Science
- 2001

The most successful strategy for the problem of this paper employs a complex model with less inherent symmetry than the others, combined with symmetry breaking during search.

### Redundant Modeling for the QuasiGroup Completion Problem

- Computer ScienceCP
- 2003

It is shown that the pure constraint satisfaction approach can solve many problems of order 45 in the transition phase, which corresponds to the peak of difficulty.

### Specifying Latin square problems in propositional logic

- Mathematics
- 1997

This chapter discusses how to specify various Latin squares so that their existence can be eeciently decided by computer programs. The computer programs considered here are so-called general-purpose…

### Symmetry Breaking

- Computer ScienceCP
- 2001

This work presents an approach that detects symmetric choice points during the search and enables the user to find solutions for complex problems with minimal effort spent on modeling.

### Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems

- Computer ScienceJournal of Automated Reasoning
- 2004

It is shown that these runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.).

### Global Cut Framework for Removing Symmetries

- Computer ScienceCP
- 2001

A general technique for removing symmetries in CSPs during search to record no-goods, during the exploration of the search tree, whose symmetric counterpart should be removed, and presents a general, correct and complete filtering algorithm for SRCs.

### A simulated annealing approach to the traveling tournament problem

- Computer ScienceIJCAI
- 2003

A simulated annealing algorithm (TTSA) is proposed for the traveling tournament problem (TTP) which abstracts the salient features of major league baseball in the United States and is shown to be robust.

### Tabu Search

- BusinessHandbook of Heuristics
- 2018

From the Publisher:
This book explores the meta-heuristics approach called tabu search, which is dramatically changing our ability to solve a hostof problems that stretch over the realms of resource…