Unlike simple single-objective optimization (e.g., "make it fastest"), embedded systems typically have multiple, often conflicting, objectives (e.g., "fastest AND lowest power AND lowest cost"). Improving one metric often degrades another. Furthermore, the design parameters can be continuous (e.g., clock frequency) or discrete (e.g., choosing between an ARM Cortex-M0 or Cortex-M4), leading to a highly complex, non-linear search space. The number of possible design points can be astronomically large, making exhaustive search impractical.

Performance: Quantified by specific metrics like maximum throughput (e.g., megabits per second for a network interface), minimum latency (e.g., reaction time of a control loop in microseconds), worst-case execution time (WCET) for real-time tasks, or frames per second for video processing.

Power/Energy Consumption: Crucial for battery life and thermal management. Measured as average power (Watts) and total energy (Joules) consumed over a typical operational cycle. Includes static (leakage) and dynamic power.

Area/Cost:
- Chip Area: For custom silicon, this directly translates to manufacturing cost and yield.
- Board Area: For PCB-based systems, smaller component footprints and fewer components reduce board size and manufacturing cost.
- Monetary Cost: The sum of component costs (BOM), NRE, manufacturing, and recurring software licensing.

Reliability: The probability of operating without failure for a specified period, often quantified by Mean Time Between Failures (MTBF). Design choices (e.g., component quality, redundancy, error correction codes) directly impact reliability.

Flexibility: The ease and cost of adapting the design to new requirements or fixing bugs after deployment. Hardware designs are less flexible than software.

Manual Exploration: Trying a limited number of design points based on designer experience and intuition. Suitable for small design spaces or minor refinements.

Analytical Modeling: Developing mathematical models (e.g., queuing theory for performance analysis, power models based on circuit characteristics) to quickly estimate design metrics for different parameter values. This allows for rapid evaluation of many design points without full simulation.

Simulation-based DSE: Running detailed simulations (e.g., system-level, RTL, instruction-set simulator) for a selected set of design points to obtain accurate metric values. This is more computationally intensive but offers higher fidelity.

Heuristic Search Algorithms: Algorithms that use "rules of thumb" or greedy approaches to efficiently explore the design space. Examples include:
- Hill Climbing: Iteratively moving towards a better solution by making small changes, but can get stuck in local optima.
- Simulated Annealing: Inspired by the annealing process in metallurgy, this allows occasional "bad" moves to escape local optima, improving chances of finding global optimum.
- Genetic Algorithms: Inspired by biological evolution, these maintain a population of design solutions, apply genetic operators (mutation, crossover), and select the "fittest" designs for the next generation, effectively exploring the space.

Meta-heuristics and Optimization Frameworks: Leveraging sophisticated optimization algorithms (like those mentioned above) integrated into DSE tools. These tools automate the process of generating design configurations, running simulations or analytical models, collecting results, and guiding the search.

In multi-objective optimization, a single "perfect" solution that optimizes all metrics simultaneously rarely exists. Instead, we look for Pareto optimal solutions.

Pareto Optimal Solution: A design solution is Pareto optimal if it's impossible to improve one design objective (e.g., make it faster) without making at least one other objective worse (e.g., increasing power consumption or cost).

Pareto Front (Trade-off Curve): When plotted on a graph (e.g., Power vs. Performance), the set of all Pareto optimal solutions forms a "Pareto front" or "trade-off curve." This curve visually represents the inherent compromises in the design space. Designers use the Pareto front to make informed decisions, choosing a point on the curve that best balances the specific needs of their application. For example, a battery-powered device might select a point on the curve that emphasizes low power, even if it means slightly lower performance.