Benchmarking Randomized Optimization Algorithms on Binary, Permutation, and Combinatorial Problem Landscapes

TL;DR

The paper benchmarks four randomized optimization algorithms—Randomized Hill Climbing, Simulated Annealing, Genetic Algorithms, and MIMIC—across binary, permutation, and combinatorial problem landscapes to understand their performance trade-offs. Using benchmark fitness functions and the mlrose library, it highlights that GA and MIMIC typically achieve higher-quality solutions, with MIMIC excelling in more complex landscapes at a higher computational cost. RHC and SA offer lower-cost alternatives but show limited robustness on rugged landscapes and across problem groups. The findings provide practical guidance on algorithm selection based on problem type, accuracy requirements, and available computational resources, with implications for design choices in planning, scheduling, and related optimization tasks.

Abstract

In this paper, we evaluate the performance of four randomized optimization algorithms: Randomized Hill Climbing (RHC), Simulated Annealing (SA), Genetic Algorithms (GA), and MIMIC (Mutual Information Maximizing Input Clustering), across three distinct types of problems: binary, permutation, and combinatorial. We systematically compare these algorithms using a set of benchmark fitness functions that highlight the specific challenges and requirements of each problem category. Our study analyzes each algorithm's effectiveness based on key performance metrics, including solution quality, convergence speed, computational cost, and robustness. Results show that while MIMIC and GA excel in producing high-quality solutions for binary and combinatorial problems, their computational demands vary significantly. RHC and SA, while computationally less expensive, demonstrate limited performance in complex problem landscapes. The findings offer valuable insights into the trade-offs between different optimization strategies and provide practical guidance for selecting the appropriate algorithm based on the type of problems, accuracy requirements, and computational constraints.

Figures (11)

• Figure 1: Fitness vs. iterations for the OneMax using different randomized optimization algorithms: (a) RHC, (b) SA, (c) GA, and (d) MIMIC. The plots show the impact of varying key parameters—restarts for RHC, exponential cooling for SA, population sizes for GA, and population sizes for MIMIC—on the fitness progression over iterations.
• Figure 2: Fitness vs. iterations for the FlipFlop using different randomized optimization algorithms: (a) RHC, (b) SA, (c) GA, and (d) MIMIC. The plots show the impact of varying key parameters—restarts for RHC, exponential cooling for SA, population sizes for GA, and population sizes for MIMIC—on the fitness progression over iterations.
• Figure 3: Fitness vs. iterations for the FourPeaks using different randomized optimization algorithms: (a) RHC, (b) SA, (c) GA, and (d) MIMIC. The plots show the impact of varying key parameters—restarts for RHC, exponential cooling for SA, population sizes for GA, and population sizes for MIMIC—on the fitness progression over iterations.
• Figure 4: Fitness vs. iterations for the SixPeaks using different randomized optimization algorithms: (a) RHC, (b) SA, (c) GA, and (d) MIMIC. The plots show the impact of varying key parameters—restarts for RHC, exponential cooling for SA, population sizes for GA, and population sizes for MIMIC—on the fitness progression over iterations.
• Figure 5: Fitness vs. iterations for the ContinuousPeaks using different randomized optimization algorithms: (a) RHC, (b) SA, (c) GA, and (d) MIMIC. The plots show the impact of varying key parameters—restarts for RHC, exponential cooling for SA, population sizes for GA, and population sizes for MIMIC—on the fitness progression over iterations.