System for the global solution of an event-dependent multicriteria non-convex optimization problem

Abstract

A system for solving an event-dependent multicriteria optimization problem of at least one cyber-physical system, comprising a control device for controlling the at least one cyber-physical system, the control device controlling the cyber-physical system in dependence on a list of prioritized objectives by solving at least one event-dependent suboptimization problem is characterized in that each objective from the list of prioritized objectives is captured as an objective function, each objective function consisting of at least two parts, a first part of which relates to directly capturing the objective and a second part of which describes a condition under which each result of one of the preceding objectives of each of the preceding suboptimization problems is substantially not negatively affected.

Claims

1. A system for solving an event-dependent multicriteria optimization problem of at least one cyber-physical system, comprising: a storage medium; and a control device for controlling the at least one cyber-physical system, the control device controlling the cyber-physical system in dependence on a list of prioritized objectives by solving at least one event-dependent suboptimization problem, wherein each objective from the list of prioritized objectives is captured as an objective function, each objective function comprising of at least two parts, including a first part of which relates to directly capturing the objective and a second part of which describes a condition under which each result of one of the preceding objectives of each of the preceding suboptimization problems is substantially not negatively affected.

2. The system according to claim 1, wherein the first part which relates to directly capturing the objective also relates to capturing an objective that can be described by an inequality condition.

3. The system according to claim 2, wherein at least one of the inequality conditions is captured using a minimum or maximum function.

4. The system according to claim 2, wherein at least one of the inequality conditions is captured using a smoothed minimum or maximum function.

5. The system according to claim 1, wherein the first part which relates to directly capturing the objective also relates to capturing an objective that can be described by minimizing or maximizing a function.

6. The system according to claim 1, wherein in the second part, the condition that each result of one of the preceding objectives of each of the preceding suboptimization problems is substantially not negatively affected is captured using a minimum or maximum function.

7. The system according to claim 1, wherein in the second part, the condition that each result of one of the preceding objectives of each of the preceding suboptimization problems is substantially not negatively affected is captured using a smoothed minimum or maximum function.

8. The system according to claim 1, wherein at least one of the objective functions is dependent on at least one continuation parameter.

9. The system according to claim 8, wherein a computational program which solves the suboptimization problems associated with the priorities using a continuation method.

10. The system according to claim 9, wherein each suboptimization problem is split into a plurality of micro-problems, the micro-problems having fixed continuation values.

11. The system according to claim 10, wherein at least some of the micro-problems are processed in parallel.

12. The system according to claim 1, wherein at least one constraint for the optimization is also dependent on at least one continuation parameter.

13. An electronic data processing device, on which a computer-readable computational program is installed, in which the system according to claim 1 is implemented.

14. A computer program product, comprising a non-transitory computer-readable storage medium on which a computer-readable computational program is stored in which the system according to claim 1 is implemented, wherein the computer-readable computational program, when executed on an electronic data processing device, causes the electronic data processing device to apply the system according to claim 1 in a computational process.

Description

DETAILED DESCRIPTION

(1) A preferred embodiment of the present invention is described in more detail below. The description of the preferred embodiment usually serves only to explain the invention by means of an example. The present invention is not limited to this example. Rather, the present invention comprises all embodiments covered by the claims.

(2) Within the scope of the present disclosure, a multicriteria optimization problem is meant to be a prioritized list of optimization objectives. Objective or optimization objective means either the maximization or minimization of a function or the best possible compliance with one or more inequalities, the inequalities being also based on a function. In the present invention, the term “continuation parameters” means the continuous change between a simplification of an original problem and the original problem. For example, the barrier parameters of the interior-points method as well as homotopy parameters that interpolate between simplified and complex physical models are continuation parameters.

(3) A preferred embodiment is used in water systems and is therefore described in more detail below with respect thereto. However, it can also be used in other cyber-physical systems and is explicitly not limited to water systems and water management systems. In general, water management systems should be optimized with respect to several objectives: the operators want to keep the water level in a reservoir, e.g., between the desired minimum and maximum water levels, while at the same time maximizing energy generation from hydropower. These objectives may conflict with each other, as it may be advantageous from an energy generation perspective to first allow the water level to rise above the maximum level and then lower it below the minimum level.

(4) At the same time, it is not always physically possible for such a water management system to maintain the water level between the desired minimum and maximum value. For example, in a phase of drought, it is not always possible to maintain the minimum level. The water level then drops below the minimum level. In a phase in which there is a lot of precipitation or a strong snowmelt, floods occur, and the maximum level cannot always be maintained. The min/max problem itself is therefore also an optimization problem.

(5) In such scenarios, we are dealing with a prioritized cascade of optimization problems: 1. meeting environmental requirements (e.g., min/max values). 2. maximizing economic objectives (maximizing hydropower output, minimizing pump energy costs).

(6) This list could be refined into a list of any number of prioritized objectives, the prioritization being changeable. For transportation systems, conflicts of objectives could be minimizing travel time for motorists and minimizing CO2 emissions.

(7) The system for solving an event-dependent multicriteria optimization problem of at least one cyber-physical system comprises a control device for controlling the at least one cyber-physical system. Such a control device may be a computer, a mobile terminal, or any device that comprises an electronic computing unit and either comprises or can access a common storage medium. The control device can operate in a wired and/or wireless manner. The control device controls the cyber-physical system in dependence on a list of prioritized objectives stored in the storage medium and solves at least one event-dependent suboptimization problem.

(8) Each objective from the list of prioritized objectives is captured by the control device as an objective function, wherein in one embodiment at least one bipartite objective function may be dependent on at least one continuation parameter and/or at least one constraint for the optimization is dependent on at least one continuation parameter. These are constraints that are independent of the list of prioritized objectives.

(9) Each objective from the list of prioritized objectives is to be captured as an objective function, each objective function consisting of at least two parts, a first part of which relates to directly capturing the objective and a second part of which describes a condition under which each result of one of the preceding objective functions of each of the preceding suboptimization problems is substantially not negatively affected.

(10) In the preferred embodiment, the first part of each of the objective functions which relates to directly capturing the objective also relates to capturing an objective that can be described by an inequality condition. In other embodiments, this does not have to be the case. In the preferred embodiment, it can be beneficial that at least one of the inequality conditions is captured using a minimum or maximum function. In other embodiments, this does not have to be the case.

(11) In an alternative to the preferred embodiment, the first part of each of the objective functions which relates to directly capturing the objective also relates to capturing an objective that can be described by minimizing or maximizing a function. In other embodiments, this does not have to be the case.

(12) In the preferred embodiment, in the second part of each of the objective functions, the condition that each result of one of the preceding objectives of each of the preceding suboptimization problems is substantially not negatively affected is captured using a minimum or maximum function or, alternatively, using a smoothed minimum or maximum function. In other embodiments, this does not have to be the case.

(13) The aforementioned use of a minimum or maximum function or of a smoothed minimum or maximum function is part of a preferred embodiment. However, alternatives thereto which may be used in other embodiments exist.

(14) Thus, instead of the minimum and/or maximum function, at least one of the following mathematical expressions may be used: Heaviside function Dirac delta function any sigmoid function (there are several variants) functions that depend on one or more “conditional statements”/conditional expressions or smoothed versions of these expressions or any expressions, smoothed or not, that in any way attempt to replicate “if/else” or “sigmoid” behavior or contain such behavior.

(15) In the preferred embodiment, the control device computes with a computational program that solves the suboptimization problems associated with the priorities using a continuation method. For the computational process, each suboptimization problem is split into a plurality of micro-problems, the micro-problems having fixed continuation values. By splitting at least some of the suboptimization problems into micro-problems, some of the micro-problems can be processed in parallel. In other embodiments, this does not have to be the case.

(16) For example, if a plurality of micro-problems in the preferred embodiment depends on a single suboptimization problem, these micro-problems can then be executed in parallel once the suboptimization problem has been processed.

(17) Suitable for the present invention are algorithms that operate according to the above-mentioned three points, and in particular algorithms that parallelize computations of (in)dependent combinations across multiple (hyper)threads, CPU cores, CPUs or computers.

(18) The present invention has been described as a system. In the same manner, it can also be used in a method. The system or method according to the invention can also be implemented in a computer, e.g., in a mobile terminal.