UDE-III: An Enhanced Unified Differential Evolution Algorithm for Constrained Optimization Problems

In this paper, an enhanced unified differential evolution algorithm, named UDE-III, is presented for real parameter-constrained optimization problems (COPs). The proposed UDE-III is a significantly enhanced version of the Improved UDE (i.e., IUDE or UDE-II), which secured the 1st rank in the CEC 2018 competition on real parameter COPs. To design UDE-III, we extensively targeted the weaknesses of UDE-II. Specifically, UDE-III uses three trial vector generation strategies - DE/rand/1, DE/current-to-rand/1, and DE/current-to-pbest/1. It is based on a dual population approach, and for each generation, it divides the current population into two sub-populations. In the top sub-population, it employs all three trial vector generation strategies on each target vector. On the other hand, the bottom sub-population employs strategy adaptation and one trial vector generation strategy is implemented on each target vector. The mutation operation in UDE-III is based on ranking-based mutation. Further, it employs the parameter adaptation principle of SHADE. The constraint handling principle in UDE-III is based on a combination of the feasibility rule and epsilon-constraint handling technique. We observed that stagnation is a major weakness of UDE-II. To overcome this weakness, we took inspiration from the best-discarded vector selection (BDVS) strategy proposed in the literature and integrated a novel strategy in UDE-III to address stagnation. Additionally, unlike UDE-II, UDE-III considers the size of the two sub-populations to be a design element. Moreover, in comparison to UDE-II, UDE-III improves upon the strategy adaptation, ranking-based mutation, and the constraint handling technique. The proposed UDE-III algorithm is tested on the 28 benchmark 30D problems provided for the CEC 2024 competition on real parameter COPs. The experimental results demonstrate the superiority of UDE-III over UDE-II.

A Multi-operator Ensemble LSHADE with Restart and Local Search Mechanisms for Single-objective Optimization

In recent years, multi-operator and multi-method algorithms have succeeded, encouraging their combination within single frameworks. Despite promising results, there remains room for improvement as only some evolutionary algorithms (EAs) consistently excel across all optimization problems. This paper proposes mLSHADE-RL, an enhanced version of LSHADE-cnEpSin, which is one of the winners of the CEC 2017 competition in real-parameter single-objective optimization. mLSHADE-RL integrates multiple EAs and search operators to improve performance further. Three mutation strategies such as DE/current-to-pbest-weight/1 with archive, DE/current-to-pbest/1 without archive, and DE/current-to-ordpbest-weight/1 are integrated in the original LSHADE-cnEpSin. A restart mechanism is also proposed to overcome the local optima tendency. Additionally, a local search method is applied in the later phase of the evolutionary procedure to enhance the exploitation capability of mLSHADE-RL. mLSHADE-RL is tested on 30 dimensions in the CEC 2024 competition on single objective bound constrained optimization, demonstrating superior performance over other state-of-the-art algorithms in producing high-quality solutions across various optimization scenarios.

Modified CMA-ES Algorithm for Multi-Modal Optimization: Incorporating Niching Strategies and Dynamic Adaptation Mechanism

This study modifies the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm for multi-modal optimization problems. The enhancements focus on addressing the challenges of multiple global minima, improving the algorithm's ability to maintain diversity and explore complex fitness landscapes. We incorporate niching strategies and dynamic adaptation mechanisms to refine the algorithm's performance in identifying and optimizing multiple global optima. The algorithm generates a population of candidate solutions by sampling from a multivariate normal distribution centered around the current mean vector, with the spread determined by the step size and covariance matrix. Each solution's fitness is evaluated as a weighted sum of its contributions to all global minima, maintaining population diversity and preventing premature convergence. We implemented the algorithm on 8 tunable composite functions for the GECCO 2024 Competition on Benchmarking Niching Methods for Multi-Modal Optimization (MMO), adhering to the competition's benchmarking framework. The results are presenting in many ways such as Peak Ratio, F1 score on various dimensions. They demonstrate the algorithm's robustness and effectiveness in handling both global optimization and MMO- specific challenges, providing a comprehensive solution for complex multi-modal optimization problems.

Orthogonally Initiated Particle Swarm Optimization with Advanced Mutation for Real-Parameter Optimization

This article introduces an enhanced particle swarm optimizer (PSO), termed Orthogonal PSO with Mutation (OPSO-m). Initially, it proposes an orthogonal array-based learning approach to cultivate an improved initial swarm for PSO, significantly boosting the adaptability of swarm-based optimization algorithms. The article further presents archive-based self-adaptive learning strategies, dividing the population into regular and elite subgroups. Each subgroup employs distinct learning mechanisms. The regular group utilizes efficient learning schemes derived from three unique archives, which categorize individuals based on their quality levels. Additionally, a mutation strategy is implemented to update the positions of elite individuals. Comparative studies are conducted to assess the effectiveness of these learning strategies in OPSO-m, evaluating its optimization capacity through exploration-exploitation dynamics and population diversity analysis. The proposed OPSO-m model is tested on real-parameter challenges from the CEC 2017 suite in 10, 30, 50, and 100-dimensional search spaces, with its results compared to contemporary state-of-the-art algorithms using a sensitivity metric. OPSO-m exhibits distinguished performance in the precision of solutions, rapidity of convergence, efficiency in search, and robust stability, thus highlighting its superior aptitude for resolving intricate optimization issues.