Modular battery pack design is a critical aspect of modern electric vehicle (EV) development, requiring careful optimization of multiple competing objectives. Mixed-integer linear programming (MILP) has emerged as a powerful tool for solving such complex design challenges, enabling engineers to balance factors like cell count, thermal uniformity, and serviceability while adhering to manufacturing constraints. This mathematical approach combines discrete and continuous variables within a linear framework, making it well-suited for battery pack optimization where decisions involve both integer choices (e.g., number of cells) and continuous parameters (e.g., temperature distribution).

The MILP formulation for modular battery packs typically begins with defining decision variables. Integer variables represent discrete choices such as the number of parallel and series cell connections, module count, and cooling plate configuration. Continuous variables handle thermal gradients, state of charge distribution, and electrical performance metrics. The objective function often minimizes total system cost while maximizing performance metrics, subject to constraints that ensure safe operation and manufacturability.

Key constraints in the MILP model include thermal limits, where the maximum temperature difference between cells must stay below a threshold (typically 5-10°C for automotive applications) to prevent accelerated degradation. Electrical constraints ensure uniform current distribution, with cell-to-cell current imbalance ideally maintained below 5%. Mechanical constraints address pack volume and weight limitations, while serviceability constraints dictate minimum access requirements for module replacement. The modularity aspect introduces additional constraints on interface standardization and fault isolation capabilities.

Solver techniques for battery pack MILP problems leverage branch-and-bound algorithms enhanced with cutting-plane methods to handle the combinatorial complexity. Modern solvers use preprocessing to reduce problem size by eliminating redundant variables and constraints. Heuristics like feasibility pumps help find good initial solutions, while parallel computing techniques accelerate the search process. For large-scale problems, decomposition methods break the system into smaller subproblems - separating thermal analysis from electrical layout optimization, for example. Automotive applications often employ commercial solvers like Gurobi or CPLEX, which can handle problems with thousands of variables and constraints.

Thermal uniformity optimization presents particular challenges in MILP formulations. The model must account for heat generation rates that vary with cell chemistry (ranging from 1-5 W per cell during standard operation), cooling system efficiency, and pack geometry. Thermal constraints are typically linearized around operating points, with validation through computational fluid dynamics (CFD) simulations. The MILP solution determines optimal cooling plate placement, airflow distribution, and module spacing to maintain temperature differentials within safe limits while minimizing parasitic cooling energy consumption.

Serviceability considerations in MILP models address repair time reduction and failure isolation. The formulation incorporates constraints on module size (typically 8-24 cells per module in automotive designs) to balance replacement cost and diagnostic granularity. Electrical isolation requirements between modules add discrete constraints on contactor placement and busbar design. The MILP solution optimizes these factors against weight and volume penalties, often resulting in trade-off curves that guide final design choices.

Automotive applications demonstrate MILP's effectiveness in battery pack optimization. A typical passenger EV pack contains 4,000-9,000 cells arranged in modules; MILP helps determine the optimal module configuration between extremes of many small modules (better serviceability) versus few large modules (lower cost). The MILP approach has proven particularly valuable for platforms supporting multiple vehicle variants, where modularity requirements are stringent. Production data shows MILP-optimized packs achieve 10-15% better thermal uniformity compared to heuristic designs, translating to longer cell life and reduced warranty costs.

Validation of MILP results occurs through both simulation and physical testing. Electrical models verify current distribution predictions, while infrared thermography confirms thermal performance. Serviceability metrics are quantified through timed repair exercises using production tools and procedures. Discrepancies between predicted and actual performance feed back into constraint tightening or relaxation in subsequent MILP iterations.

The computational intensity of MILP for battery packs scales with design complexity. A full-pack optimization with detailed thermal and electrical constraints may require 8-24 hours on high-performance workstations. Automotive engineers often employ a hierarchical approach, using MILP for high-level architecture decisions followed by specialized tools for detailed component design. Reduced-order modeling techniques help maintain computational tractability while preserving accuracy in key performance areas.

Recent advances in MILP methodologies address previously challenging aspects of battery pack design. Multi-objective formulations generate Pareto fronts showing trade-offs between cost, performance, and serviceability. Robust optimization techniques incorporate parameter uncertainties, such as manufacturing variations in cell resistance (typically ±3-5%). Stochastic programming methods handle probabilistic load profiles, important for designing packs that perform well across diverse driving conditions.

Implementation challenges persist in MILP-based battery pack design. The quality of solutions depends heavily on accurate linearization of nonlinear phenomena like heat transfer and electrochemical behavior. Model fidelity must balance computational feasibility with engineering accuracy - oversimplification leads to non-optimal designs, while excessive detail makes problems computationally intractable. Data requirements are substantial, needing precise characterization of cell behavior under diverse operating conditions.

Future directions for MILP in battery pack optimization include tighter integration with manufacturing constraints and recycling considerations. Emerging techniques incorporate end-of-life disassembly requirements directly into the design optimization, influencing module geometry and material choices. The growing adoption of wireless BMS systems introduces new integer variables for antenna placement and communication node optimization. As computing power increases and algorithms improve, MILP will likely expand into real-time configuration optimization for adaptive battery systems.

The automotive industry's shift toward modular, scalable battery architectures underscores the importance of rigorous optimization techniques. MILP provides a structured mathematical framework for making design decisions that balance competing priorities in cell count, thermal management, and serviceability. While computational demands remain significant, the methodology delivers measurable improvements in pack performance, longevity, and maintenance costs. Continued refinement of solver techniques and model formulations will further enhance MILP's value in developing next-generation battery systems for electric vehicles.