The Optimal Intertemporal Management of the Soil and Phosphorus and the Equilibrium in Economic and Biophysical Models

The paper proposes the use of meta models to determine the optimal intertemporal management of soil and phosphorus losses from agricultural land. This approach allows finding a equilibrium of the economic and biophysical system simultaneously. In contrast to the existing literature the model takes account of nonlinear relationships and of a large number of agricultural activities. The mathematical problems arising from this complex setup are addressed and the model is solved numerically. The results show that the second best policy in form of soil protection scores is highly inefficient, while another second best policy in form of land-use taxes is nearly as efficient as the first best policy.Soil erosion, Phosphorus runoffs, Land-use tax, Soil protection scores, Dynamic optimization, Resource /Energy Economics and Policy,

GALINI: an extensible solver for mixed-integer quadratically-constrained problems

Many industrial relevant optimization problems can be formulated as Mixed-Integer Quadratically Constrained Problems. This class of problems are difficult to solve because of 1) the non-convex bilinear terms 2) integer variables. This thesis develops the Python library \suspect{} for detecting special structure (monotonicity and convexity) of Pyomo models. This library can be extended to provide specialized detection for complex expressions. As a motivating example, we show how the library can be used to detect the convexity of the reciprocal of the log mean temperature difference. This thesis introduces GALINI: a novel solver that is easy to extend at runtime with new 1) cutting planes, 2) primal heuristics, 3) branching strategies, 4) node selection strategies, and 5) relaxations.GALINI uses Pyomo to represent optimization problems, this decision makes it possible to integrate with the existing Pyomo ecosystem to provide, for example, building blocks for relaxations. We test the solver on two large datasets and show that the performance is comparable to existing open source solvers. Finally, we present a library to formulate pooling problems, a class of network flow problems, using Pyomo. The library provides a mechanism to automatically generate the PQ-formulation for pooling problems. Since the library keeps the knowledge of the original network, it can 1) use a mixed-integer programming primal heuristic specialized for the pooling problem to find a feasible solution, and 2) generate valid cuts for the pooling problem. We use this library to develop an extension for GALINI that uses the mixed-integer programming primal heuristic to find a feasible solution and that generates cuts at every node of the branch & cut algorithm. We test GALINI with the pooling extensions on large scale instances of the pooling problem and show that we obtain results that are comparable to or better than the best available commercial solver on dense instances.Open Acces

Analyzing Mathematical Programs Using MProbe

Just as modern general-purpose programming languages (e.g., C++, Java) are supported by a suite of tools (debuggers, profilers, etc.), mathematical programming languages need supporting tools. MProbe is an example of a suite of tools supporting a mathematical programming language, in this case AMPL. MProbe includes tools for empirically estimating the shape of nonlinear functions of many variables, nonlinearly-constrained region shape, the effect of the objective shape on the ability to find a global optimum, tools for estimating the effectiveness of constraints and for navigating through the model, among others