# 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={Integration of AI and OR Techniques in Constraint Programming}, 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…

## 26 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.

### 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.

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

- Materials ScienceJournal of Heuristics
- 2016

A partial Latin square (PLS) is a partial assignment of n symbols to an n×n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

### 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…

### Solving balancing and bin-packing problems with constraint programming

- Computer Science
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Two real problems are modelled and efficiently solved in CP using the new algorithms: - The assembly line balancing design problem, and - A nurse rostering problem.

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