# US 10,311,358 B2 · Systems and methods for multi-objective evolutionary algorithms with category discovery

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- Number: US 10,311,358 B2
- Document ID: US10311358B2
- Status: Granted
- Kind: B2
- Application number: 14/796,299
- Filed: 2015-07-10
- Published: 2017-01-12
- Granted: 2019-06-04
- Earliest claimed: 2015-07-10
- Assignees: The Aerospace Corporation
- Applicants: The Aerospace Corporation
- Inventors: Timothy Guy Thompson
- Web page: https://patentgrep.com/patent/US10311358B2

## CPC

- G06N 3/126: Evolutionary algorithms, e.g. genetic algorithms or genetic programming
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS

## Abstract

Systems and methods are provided to engage in multi-tiered optimization where there may be a first multi-objective optimization and a second constraint optimization. The multi-objective optimization may be used to drive to one or more goals of the optimization problem. The constraint optimization or minimization may be used to drive towards a reduced and/or no constraint situation where the solution to the overall problem is feasible or near-feasible.

## Claims

### Claim 1

A method, comprising:
identifying, by one or more processors, a plurality of items, including a first item and a second item;
identifying, by the one or more processors, a plurality of categories, including a first category and a second category;
providing, by the one or more processors, a first allocation of items by allocating the first item to the first category and the second item to the second category;
identifying, by the one or more processors, one or more constraint models;
determining, by the one or more processors and based at least in part on the one or more constraint models, that the first allocation of items is infeasible;
providing, by the one or more processors and based at least in part on determining that the first allocation of items is infeasible, a second allocation of items by allocating the first item to a third category;
determining, by the one or more processors and based at least in part on the one or more constraint models, that the second allocation is feasible;
providing, by the one or more processors, the second allocation as a feasible solution to a multi-objective optimization problem; and
performing, by the one or more processors, the multi-objective optimization problem using the second allocation.

### Claim 2 (depends on 1)

The method of claim 1, further comprising:
determining a first chromosome based at least in part on the second allocation;
identifying at least one objective model;
determining a set of objective values based at least in part on the at least one objective model and the first chromosome; and
comparing the set of respective objective values to one or more other sets of respective objective values to determine that the first chromosome is an optimized solution to the multi-objective optimization problem.

### Claim 3 (depends on 2)

The method of claim 2, wherein determining that the first chromosome is an optimized solution to the multi-objective optimization problem comprises:
identifying that the respective objective values are not dominated by the one or more other sets of respective objective values.

### Claim 4 (depends on 1)

The method of claim 1, wherein determining that the second allocation is feasible comprises:
determining a first constraint value corresponding to the first item, based at least in part on the third category and the one or more constraint models;
determining a second constraint value corresponding to the second item, based at least in part on the second category and the one or more constraint models;
identifying that the first constraint value satisfies a first threshold condition; and
identifying that the second constraint value satisfies a second threshold constraint.

### Claim 5 (depends on 4)

The method of claim 4, wherein determining that the second allocation is feasible further comprises identifying that a plurality of items, including the first item and the second item, are allocated to respective categories, such that respective constraints corresponding to each of the plurality of items meets a respective threshold condition.

### Claim 6 (depends on 1)

The method of claim 1, wherein the multi-objective optimization problem is a pricing problem and the first item is a first product type to be priced at a first price and the second item is a second product type that is to be priced at a second price, wherein the first price corresponds to the first category and the second price corresponds to the second category.

### Claim 7 (depends on 1)

The method of claim 1, wherein the first allocation is generated based at least in part on a third allocation and a fourth allocation.

### Claim 8 (depends on 7)

The method of claim 7, wherein the third allocation and fourth allocation are received from an objective optimization engine.

### Claim 9 (depends on 7)

The method of claim 7, wherein the first allocation is generated by blending the third allocation and the fourth allocation, wherein blending comprises selecting one or more first item allocations selected from the third allocation and combining the one or more first item allocations with one or more second item allocations selected from the fourth allocation.

### Claim 10 (depends on 1)

The method of claim 1, wherein determining that the first allocation of items is infeasible comprises determining that the first item allocated to the first category results in a constraint value that fails to meet a threshold condition and wherein providing the second allocation of items by allocating the first item to a third category is based at least in part on the determining that the first item allocated to the first category results in the constraint value that fails to meet the threshold condition.

### Claim 11

A system, comprising:
a memory that stores computer-executable instructions;
at least one processor configured to access the memory, wherein the at least one processor is further configured to execute the computer-executable instructions to:
identify a plurality of items, including a first item and a second item;
identify a plurality of categories, including a first category and a second category;
provide a first allocation of items by allocating the first item to the first category and the second item to the second category;
identify one or more constraint models;
determine, based at least in part on the one or more constraint models, that the first allocation of items is infeasible;
provide, based at least in part on determining that the first allocation of items is infeasible, a second allocation of items by allocating the first item to a third category;
determine, based at least in part on the one or more constraint models, that the second allocation is feasible;
provide the second allocation as a feasible solution to a multi-objective optimization problem; and
perform the multi-objective optimization problem using the second allocation.

### Claim 12 (depends on 11)

The system of claim 11, wherein the at least one processor is further configured to execute the computer-executable instructions to:
determine a first chromosome based at least in part on the second allocation;
identify at least one objective model;
determine a set of objective values based at least in part on the at least one objective model and the first chromosome; and
compare the set of respective objective values to one or more other sets of respective objective values to determine that the first chromosome is an optimized solution to the multi-objective optimization problem.

### Claim 13 (depends on 12)

The system of claim 12, wherein the at least one processor to determine that the first chromosome is an optimized solution to the multi-objective optimization problem comprises the at least one processor to identify that the respective objective values are not dominated by the one or more other sets of respective objective values.

### Claim 14 (depends on 11)

The system of claim 11, wherein the at least one processor to determine that the second allocation is feasible comprises the at least one processor to:
determine a first constraint value corresponding to the first item, based at least in part on the third category and the one or more constraint models;
determine a second constraint value corresponding to the second item, based at least in part on the second category and the one or more constraint models;
identify that the first constraint value satisfies a first threshold condition; and
identify that the second constraint value satisfies a second threshold constraint.

### Claim 15 (depends on 14)

The system of claim 14, wherein the at least one processor to determine that the second allocation is feasible further comprises the at least one processor to identify that a plurality of items, including the first item and the second item, are allocated to respective categories, such that respective constraints corresponding to each of the plurality of items meets a respective threshold condition.

### Claim 16 (depends on 11)

The system of claim 11, wherein the multi-objective optimization problem is a pricing problem and the first item is a first product type to be priced at a first price and the second item is a second product type that is to be priced at a second price, wherein the first price corresponds to the first category and the second price corresponds to the second category.

### Claim 17 (depends on 11)

The system of claim 11, wherein the first allocation is generated based at least in part on a third allocation and a fourth allocation.

### Claim 18 (depends on 17)

The system of claim 17, wherein the third allocation and fourth allocation are received from an objective optimization engine.

### Claim 19 (depends on 17)

The system of claim 17, wherein the first allocation is generated by blending the third allocation and the fourth allocation, wherein blending comprises selecting one or more first item allocations selected from the third allocation and combining the one or more first item allocations with one or more second item allocations selected from the fourth allocation.

### Claim 20 (depends on 11)

The system of claim 11, wherein the at least one processor to determine that the first allocation of items is infeasible comprises the at least one processor to determine that the first item allocated to the first category results in a constraint value that fails to meet a threshold condition and wherein the at least one processor to provide the second allocation of items by allocating the first item to a third category is based at least in part on the determining that the first item allocated to the first category results in the constraint value that fails to meet the threshold condition.