Hybrid Optimization


SAT Strategic Advisors for Transformation GmbH works with the following optimization technologies:

  • Mathematical Programming
  • Constraint Programming
  • Local Search and Evolutionary Algorithms
  • Dynamic Stochastic Optimization

Mathematical Programming

Mathematical Programming - as exemplified by the Linear Programming and Mixed Integer Programming techniques - is the "classic" optimization approach, and today highly developed implementations of these techniques are available as tools for the optimization algorithm developer. For Mathematical Programming, SAT GmbH commonly builds solutions using the Gurobi platform which - in our own experience as well as many published benchmarks and studies - has repeatedly proved the most powerful and flexible platform of its kind available. Gurobi is developed by a team intent on pushing the boundaries of the possible for the Mathematical Programming approach, and has a standard of service and support which is second to none.

The strengths of mathematical programming techniques apply to certain classes of problems and constraints - it is a common experience to find that a subset of a real-world problem can be modelled and solved using such techniques, or that an approximation is required to apply the techniques, while the whole problem in all its complexity remains out of reach. Through hybridisation, the powerful algorithms of Mathematical Programming can be applied where appropriate in the context of a higher-level solution strategy.

Constraint Programming

Constraint Programming offers the possibility to model and solve optimisation problems containing features and constraints that are not well suited to Mathematical Programming formulations. It is in general a more flexible paradigm than Mathematical programming, and offers more scope to design the problem representation and solving strategy for the specific problem at hand.

Local Search and Evolutionary Algorithms

Local Search and Evolutionary Algorithms represent a further alternative approach to optimization problems. They typically include stochastic elements, and seek high-quality solutions by making small, incremental changes to a single solution or population of solutions. Such algorithms can often be effective on very large-scale problems including non-standard constraints and requirements, where there is considerable potential for optimization.

Recent years have seen extensive progress and innovation in the development of implementation frameworks for local search algorithms, pioneered in particular by the work of Pascal van Hentenryck and Laurent Michel. As a consequence, many aspects of the programming of local search algorithms using different "meta-heuristics" - for example, tabu-search, simulated annealing, guided local search, variable depth neighborhood search - can now be unified from an implementation point-of-view. This frees the developer to concentrate on the important aspects of the implementation, and allows effective and robust solutions to be delivered within relatively short development times.

Dynamic Stochastic Optimization

Techniques of Dynamic Stochastic Optimization allow stochastic or historical data to inform decision-making and optimization, and are also valuable in environments where planning needs to be continuously revised as events unfold in time. In real-time systems, they enhance the ability to make good decision under tight time constraints.

Classic questions of Executive Management

Typical questions of Executive Management that are addressed with the methodology of optimization in real world entrepreneurial context are, for example:

  • Scenario analysis
  • Sustainability considerations
  • Strategic business planning
  • Strategic Asset Management
  • Decision support in strategic and operational management
  • Risk assessment and Robustness analysis
  • Innovation, production and project management

Typical fields of application of Optimization

Today, typical application areas for Hybrid Optimization are, for example:

  • Supply Chain Management
  • Production Planning
  • Capacity Planning
  • Resource Scheduling and Manpower Scheduling
  • Inventory reduction and net working capital optimization
  • Relevant industries include Manufacturing, Transportation, Networking, and Logistics
  • Planning horizon can be Strategic, Tactical or Operation, to address different business needs

Advantages of Management Flight Simulators

Simulation models that are based on the methodology of Algorithm-based Optimization have the following advantages for Executive Management in increasingly dynamic markets of the future:

  • Holistic capturing and transparent presentation of highly complex decision situations for industry or market development
  • Avoidance of tacit misunderstandings by disclosing the different perceptions of different decision-makers
  • Development and simulation of scenarios to make uncertainty about the future tangible
  • Identification of the levers for value-enhancing corporate governance in the face of high uncertainty and risks
  • Modeling of alternative strategies and testing by simulation and optimization before they are implemented in the business
  • Evaluation of sustainable business strategies in the context of innovation and technology change in competitive situations
  • Implementation of early-warning systems to indicate market changes, market position, to monitor strategic decisions and operational actions in real time