Using Functional Programming to recognize Named Structure in an Optimization Problem: Application to Pooling

Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting named special structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network structures; we show that we can additionally detect nonlinear pooling patterns. Finding named structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the named structure. To demonstrate the recognition algorithm, we use the recognized structure to apply primal heuristics to a test set of standard pooling problems

Ten years of feasibility pump, and counting

The Feasibility Pump (fp) is probably the best-known primal heuristic for mixed-integer programming. The original work by Fischetti et al. (Math Program 104(1):91\u2013104, 2005), which introduced the heuristic for 0\u20131 mixed-integer linear programs, has been succeeded by more than twenty follow-up publications which improve the performance of the fp and extend it to other problem classes. Year 2015 was the tenth anniversary of the first fp publication. The present paper provides an overview of the diverse Feasibility Pump literature that has been presented over the last decade

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

The SCIP Optimization Suite 9.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver.Comment: The release report of the SCIP Optimization Suite version 9.

Scylla: a matrix-free fix-propagate-and-project heuristic for mixed-integer optimization

We introduce Scylla, a primal heuristic for mixed-integer optimization problems. It exploits approximate solves of the Linear Programming relaxations through the matrix-free Primal-Dual Hybrid Gradient algorithm with specialized termination criteria, and derives integer-feasible solutions via fix-and-propagate procedures and feasibility-pump-like updates to the objective function. Computational experiments show that the method is particularly suited to instances with hard linear relaxations

Recent Advancements in Commercial Integer Optimization Solvers for Business Intelligence Applications

The chapter focuses on the recent advancements in commercial integer optimization solvers as exemplified by the CPLEX software package particularly but not limited to mixed-integer linear programming (MILP) models applied to business intelligence applications. We provide background on the main underlying algorithmic method of branch-and-cut, which is based on the established optimization solution methods of branch-and-bound and cutting planes. The chapter also covers heuristic-based algorithms, which include preprocessing and probing strategies as well as the more advanced methods of local or neighborhood search for polishing solutions toward enhanced use in practical settings. Emphasis is given to both theory and implementation of the methods available. Other considerations are offered on parallelization, solution pools, and tuning tools, culminating with some concluding remarks on computational performance vis-à-vis business intelligence applications with a view toward perspective for future work in this area

Learning Models for Discrete Optimization

We consider a class of optimization approaches that incorporate machine learning models into the algorithm structure. Our focus is on the algorithms that can learn the patterns in the search space in order to boost computational performance. The idea is to design optimization techniques that allow for computationally efficient tuning a priori. The final objective of this work is to provide efficient solvers that can be tuned for optimal performance in serial and parallel environments.This dissertation provides a novel machine learning model based on logistic regression and describes an implementation for scheduling problems. We incorporate the proposed learning model into a well-known optimization algorithm, tabu search, and demonstrate the potential of the underlying ideas. The dissertation also establishes a new framework for comparing optimization algorithms. This framework provides a comparison of algorithms that is statistically meaningful and intuitive. Using this framework, we demonstrate that the inclusion of the logistic regression model into the tabu search method provides significant boost of its performance. Finally, we study the parallel implementation of the algorithm and evaluate the algorithm performance when more connections between threads exist

Development of a hybrid metaheuristic for the efficient solution of strategic supply chain management problems: application to the energy sector

Supply chain management (SCM) addresses the strategic, tactical, and operational decision making that optimizes the supply chain performance. The strategic level defines the supply chain configuration: the selection of suppliers, transportation routes, manufacturing facilities, production levels, technologies. The tactical level plans and schedules the supply chain to meet actual demand. The operational level executes plans. Tactical and operational level decision-making functions are distributed across the supply chain. To increase or optimize performance, supply-chain functions must be perfectly coordinated. But the cycles of the enterprise and the market make this difficult: raw material does not arrive on time, production facilities fail, workers are ill, customers change or cancel orders, therefore, causing deviations from the plan. In some cases, these situations may be dealt with locally. In other cases, the problem cannot be ”locally contained” and modifications across many functions are required. Consequently, the supply chain management system must coordinate the revision of plans or schedules. The ability to better understand an algorithm is important to focus on the following variables: tactical and operational levels of the supply chain so that the timely dissemination of information, accurate coordination of decisions, and management of actions among people and systems is achieved ultimately determines the efficient, coordinated achievement of enterprise goal

Operational Research IO2017, Valença, Portugal, June 28-30

This proceedings book presents selected contributions from the XVIII Congress of APDIO (the Portuguese Association of Operational Research) held in Valença on June 28–30, 2017. Prepared by leading Portuguese and international researchers in the field of operations research, it covers a wide range of complex real-world applications of operations research methods using recent theoretical techniques, in order to narrow the gap between academic research and practical applications. Of particular interest are the applications of, nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management, and lot sizing and job scheduling problems. In most chapters, the problems, methods and methodologies described are complemented by supporting figures, tables and algorithms. The XVIII Congress of APDIO marked the 18th installment of the regular biannual meetings of APDIO – the Portuguese Association of Operational Research. The meetings bring together researchers, scholars and practitioners, as well as MSc and PhD students, working in the field of operations research to present and discuss their latest works. The main theme of the latest meeting was Operational Research Pro Bono. Given the breadth of topics covered, the book offers a valuable resource for all researchers, students and practitioners interested in the latest trends in this field.info:eu-repo/semantics/publishedVersio

Unlocking Solver Potential: A Framework for Analysis and Inter-Comparison of Optimisation Solvers

Linear and mixed integer optimisation problems have demonstrated their strength in the field of logistics and supply chain management for years. However, real-world optimisation problems are complex in nature, and various mathematical programming solvers are leveraged to solve these problems today. With several advances in solver technologies in recent years, there has been growing interest in carrying out comparative evaluations of solvers for a range of applications. However, there appears a lack of guidance for decision makers to conduct solver performance assessment and inter-comparison. To address this gap, we aim to derive a framework of parameters deemed most relevant for evaluating and comparing different solvers for a given application. To this end, we perform a systematic literature review. The resulting parameters are classified into three core categories: performance metrics, stopping conditions, and performance enhancing elements of a solver