18650 series-parallel battery-pack sizing (cost minimization)

A fixed-topology optimization variant that chooses the rectangular series and parallel counts of an 18650 pack to minimize cost under the packaged battery requirements.

See Optimization Problem Catalog for the optimization family index.

Quick Facts

Field	Value
Problem ID	battery_pack_18650_series_parallel_cost_min
Problem Family	optimization
Implementation	design_research_problems.problems.optimization._battery_grid:BatteryGridSizingProblem
Capabilities	baseline-solver, bounded-variables, statement-markdown
Study Suitability	none
Tags	optimization, battery, series-parallel, grid, sizing, cost

Taxonomy

Formulation

mixed_discrete_optimization

Convexity

nonconvex

Design Variable Type

discrete

Is Dynamic

no

Orientation

engineering_practical

Feasibility Ratio Hint

0.1

Objective Mode

single

Constraint Nature

hard

Bounds Summary

integer series and parallel counts within the packaged rectangular battery envelope

Tags

optimization, battery, series-parallel, grid, sizing, cost

Statement

Choose the rectangular electrical size of an 18650 battery pack by selecting the number of series stages S and parallel branches P. The physical layout is fixed to the library’s canonical one-layer rectangular grid with one cell per logical slot and deterministic wiring between stages and branches.

The objective is to minimize pack cost while meeting the packaged voltage, capacity, current, and envelope requirements. This optimization-family variant reuses the same battery backend as the grammar-family pack problems, but it restricts the search to canonical rectangular layouts parameterized only by S and P.

Problem Shape

Field	Value
Design Variable Count	2
Bound Summary	integer series and parallel counts within the packaged rectangular battery envelope
Total Constraint Count	7
Equality Constraint Count	0
Inequality Constraint Count	7

Variable Bounds

Variable	Lower Bound	Upper Bound
x[0]	1	24
x[1]	1	27

Manifest Parameters

Key	Value
max_depth_mm	500
max_height_mm	250
max_width_mm	500
minimum_capacity_ah	10
minimum_current_a	60
target_voltage_v	14.8
voltage_tolerance_v	0.1

Library Interface

• generate_initial_solution(seed=None)

• objective(x)

• evaluate(x)

• solve(initial_solution=None, seed=None, maxiter=200)