Algebraic languages for mathematical programming

Kuip, C. A. C.

doi:10.1016/0377-2217(93)90320-m

Cited by 34 publications

(8 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Examples of popular ones are AMPL [29,30], GAMS [58], AIMMS [59], and Xpress-Mosel [60], and more can be found in general surveys [61,62,63]. These modeling languages are mixtures of declarative and imperative programming styles using sets of objects to index multidimensional parameters and LP variables.…”

Section: Languages For Mathematical Programmingmentioning

confidence: 99%

Relational linear programming

Kersting

Mladenov

Tokmakov

2017

Artificial Intelligence

View full text Add to dashboard Cite

We propose relational linear programming, a simple framework for combining linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical concepts of objects, relations, and quantified variables. This allows one to express the LP objective and constraints relationally for a varying number of individuals and relations among them without enumerating them. Together with a logical knowledge base, effectively a logic program consisting of logical facts and rules, it induces a ground LP. This ground LP is solved using lifted linear programming. That is, symmetries within the ground LP are employed to reduce its dimensionality, if possible, and the reduced program is solved using any off-the-shelf LP solver. In contrast to mainstream LP template languages such as AMPL, which features a mixture of declarative and imperative programming styles, RLP's relational nature allows a more intuitive representation of optimization problems, in particular over relational domains. We illustrate this empirically by experiments on approximate inference in Markov logic networks using LP relaxations, on solving Markov decision processes, and on collective inference using LP

show abstract

Section: Languages For Mathematical Programmingmentioning

confidence: 99%

Relational linear programming

Kersting

Mladenov

Tokmakov

2017

Artificial Intelligence

View full text Add to dashboard Cite

show abstract

“…In order to solve the model, the authors used the modeling language GAMS 2.0.10.0 and the optimization software CPLEX 7.0.0 (Brooke et al 1998;Kiup 1993). A basic microcomputer (Intel Pentium-4, 2.20 GHz, 496 MB of usable RAM, and HD of 40 GB) was used for these experiments, and the original model resulted in 4,758 linear equations and 6,679 variables.…”

Section: Production and Transportation In Multistagesmentioning

confidence: 99%

Production and Logistics Planning in Seed Corn

Junqueira

Morábito

2015

International Series in Operations Research &Amp; Management Science

View full text Add to dashboard Cite

In wide countries like Brazil, the USA, and others, supply chains of seed corn can involve multiple disperse crop fields, processing plants, and demand spots, which require complex and elaborate aggregate production and distribution planning to attend predefined harvest plans and meet forecasted product demands. The limited processing capacities of the plants are also relevant for this tactical planning.Seed corn enterprises that have experienced rapid growth or operate in a complex and changing environment had a tendency to create simple practical rules, sometimes disconnected, to develop production and logistics plans. For instance, some of them have focused on only a few variables relevant to planning, like the distances between crop fields and processing plants, disregarding other relevant variables, such as the unit production and distribution costs and the goods and services circulation taxes involved.Optimization approaches have been applied to support production, inventory, and distribution aggregate planning decisions in different agribusiness settings, considering several technical and economical criteria and constraints. As these approaches are incorporated into decision support systems, they become powerful and flexible for the analysis and planning of these systems under different scenarios. Several examples of successful applications in production and logistics planning of agribusiness supply chains can be found

show abstract

“…The flexibility of integer programming has been further strengthened by the development of several modeling languages [Bisschop82, Fourer83,Kuip93] that permit general formulations to be written in a way that is concise and natural for modelers, yet is capable of efficient processing by computer. For example the collection of all constraints of the form (2), enforcing the relationship between the Add and the Do variables for all combinations of fluents and timesteps, can be written in the AMPL language [Fourer03] as…”

Section: Operations Research Approaches To Ai Planningmentioning

confidence: 99%