Dolphin-Inspired Optimizer Charts Shorter Paths for Robot Teams in Dynamic Simulations

A new algorithm called the Dolphin Cooperative Foraging Optimizer, or DCFO, has shown that a dolphin-inspired strategy for dividing up search effort can help teams of simulated robots find shorter routes through cluttered, changing environments. In MATLAB simulations with six and twelve robots navigating among static and moving obstacles, the method produced the shortest aggregate path lengths of six planners tested, cutting path length by 2.74% against the next-best planner in the six-robot scenario and by 8.30% in the twelve-robot scenario. The study, published in Frontiers in Neurorobotics, also reports the lowest average simulation execution time in the larger scenario, although another planner was faster in the smaller one.

Online multi-robot path planning is a demanding coordination problem. Each robot must repeatedly convert information about its surroundings into motion, and every motion changes the conditions for the next decision. In a team, each robot must additionally account for the movements of its neighbors while responding to shifting collision risks from static obstacles, moving obstacles, and other robots. One way to handle this is to formulate a joint command covering all robots at once, which makes interactions explicit but causes the decision dimension to grow with team size. Threshold-based collision penalties can also make the resulting objective discontinuous, which is awkward for gradient-based optimizers.

Population-based methods sidestep that difficulty because they evaluate objectives without derivatives, but they pay a price in repeated candidate evaluations within a limited replanning budget. The DCFO addresses how to spend that budget wisely. It combines an elite-guided update derived from the Snow Ablation Optimizer with three differential evolution operators related to the CoBiDE, IDE, and jSO algorithms. Rather than running all operators every generation, the method uses historical operator-feedback counts to set roulette-selection probabilities: counters rise with the number of accepted trials for three of the operators, but only with strictly improving trials for the jSO-derived one. A stage-dependent rule then remaps which sampled operator actually executes, redirecting selections at defined fractions of the evaluation budget.

The dolphin analogy operates at the level of coordinated search behavior rather than biology. Cooperative herding maps to the elite-guided update, which concentrates candidates around high-quality command regions while retaining stochastic variation. Heterogeneous individual foraging maps to the mutation portfolio, which supplies complementary exploration and refinement behaviors. Feedback-driven redirection maps to a stagnation response: when every candidate in the population has an identical fitness value, the algorithm perturbs all of them using a masked, regularized inverse covariance matrix built from retained solution history, with a periodic amplitude factor modulating the update. The authors stress the method is not intended to reproduce dolphin cognition or neural processing.

Before the robot tests, the team benchmarked search performance on the CEC2020 and CEC2022 single-objective suites, using a population of 30, a nominal budget of 5,000 function evaluations, and 30 independent runs per function at both 10 and 20 dimensions. At the reported precision, DCFO attained or tied the lowest mean error on 7 of 10 CEC2020 functions at 10 dimensions and on 9 of 12 CEC2022 functions at each dimension, with ties included. Against its closest competitor, EA4eig, the outcome depended on the function: EA4eig achieved a slightly lower mean error on CEC2020 F3, while DCFO was lower on F6 and F9, and the two tied at zero mean error on CEC2022 F3 at the reported precision. A descriptive average of four Friedman summary ranks placed DCFO first at 1.72, ahead of EA4eig at 1.89.

The multi-robot simulations ran in MATLAB R2020a on a Windows 10 machine with an Intel Core i5-9300H processor and 16 GB of RAM, in a 100 cm by 100 cm workspace. Scenario 1 contained six robots, seven static obstacles, and three uniformly moving dynamic obstacles; Scenario 2 doubled the crowd with 12 robots, 14 static obstacles, and 6 moving obstacles. Each optimizer-based planner used an initial population of 30 and a nominal counter limit of 2,000 evaluations per replanning call, with command dimensions of 12 and 24 respectively. DCFO was compared against the Superb Fairy-wren Optimization Algorithm, the multi-strategy self-adaptive differential sine-cosine algorithm, SAO, EA4eig, and the classical Dynamic Window Approach, with each method evaluated over 30 runs per scenario.

The headline numbers come from aggregate path length, which sums distances traveled by individual robots. In the six-robot scenario, DCFO produced 448.94 cm against 461.57 cm for the next-shortest planner, sdSCA, a 2.74% reduction. In the twelve-robot scenario, DCFO reached 548.86 cm against 598.54 cm for EA4eig, an 8.30% reduction. DCFO also recorded the lowest finite total fitness in both scenarios and the lowest average execution time in the larger one, at 74.75 seconds. In the smaller scenario, however, sdSCA was faster at 40.21 seconds versus DCFO’s 54.19 seconds, illustrating a trade-off between path quality and recorded runtime.

The authors are careful about what these measures do and do not mean. Average execution time includes visualization and pauses, so it reflects simulation runtime rather than isolated optimizer speed or control-cycle latency. The Dynamic Window Approach logged the fewest total movement steps in both scenarios, but that does not imply shorter paths because displacement per step varies; it also produced the longest aggregate paths and a non-finite fitness output excluded from cost comparisons. At the robot level, DCFO achieved the shortest average path for five of six robots in Scenario 1 and eight of twelve in Scenario 2, yet other planners won for individual robots, showing that a team-level advantage does not guarantee the best route for every team member.

A separate stagnation analysis compared escape behavior among DCFO, standard differential evolution, CoBiDE, and jSO over 30 runs each. DCFO recorded 28 successful escapes and the highest event-based escape rate at 15.56%, compared with 6.67% for standard DE, 5.39% for CoBiDE, and 6.02% for jSO. The authors note this is an event-based rate, not the percentage of runs that succeed, and that these results describe the complete algorithms rather than isolated components. Component-level studies, they write, will be needed to separate the contributions of the perturbation scheme, population refresh, population reduction, and operator selection.

The evaluation remains bounded by its scope: two dynamic simulation scenarios with ideal state information and a one-step penalty-based objective, with no physical robots involved. The penalty structure strongly discourages threshold violations but does not impose a hard safety constraint, and the nominal evaluation counter excludes refresh and recovery evaluations, so total objective-call counts are not assumed equal across methods. The authors flag physical deployment as requiring evaluation under sensing and localization uncertainty, actuator dynamics, and communication delays, alongside hardware-in-the-loop tests of control-cycle timing. Future work will also extend the framework to three-dimensional motion and multi-objective planning, where path length, energy use, and inter-robot coordination could be weighed together. For now, the results position adaptive operator portfolios as a promising approach to generating joint motion commands for robot teams in dynamic simulated worlds.

Subject of Research: A dolphin-inspired adaptive optimizer for online multi-robot path planning in dynamic simulated environments

Article Title: Dolphin-inspired adaptive coordination for online multi-robot path planning in dynamic environments

Article References: Liu, M., Wu, H., Qin, L., Lu, Z., Cheng, R., & Chen, L. (2026). Dolphin-inspired adaptive coordination for online multi-robot path planning in dynamic environments. Frontiers in Neurorobotics, 20, Article 1993109. https://doi.org/10.3389/fnbot.2026.1993109

Image Credits: AI Generated

DOI: 10.3389/fnbot.2026.1993109

Keywords: multi-robot path planning, differential evolution, adaptive operator selection, bio-inspired optimization, dynamic obstacle avoidance, dolphin-inspired algorithm, robotics simulation, swarm coordination, CEC benchmarks, neurorobotics, Dolphin-inspired, adaptive