A new SSO-based Algorithm for the Bi-Objective Time-constrained task Scheduling Problem in Cloud Computing Services

Cloud computing distributes computing tasks across numerous distributed resources for large-scale calculation. The task scheduling problem is a long-standing problem in cloud-computing services with the purpose of determining the quality, availability, reliability, and ability of the cloud computing. This paper is an extension and a correction to our previous conference paper entitled Multi Objective Scheduling in Cloud Computing Using MOSSO published in 2018 IEEE Congress on Evolutionary Computation. More new algorithms, testing, and comparisons have been implemented to solve the bi-objective time-constrained task scheduling problem in a more efficient manner. Furthermore, this paper developed a new SSO-based algorithm called the bi-objective simplified swarm optimization to fix the error in previous SSO-based algorithm to address the task-scheduling problem. From the results obtained from the new experiments conducted, the proposed BSSO outperforms existing famous algorithms, e.g., NSGA-II, MOPSO, and MOSSO in the convergence, diversity, number of obtained temporary nondominated solutions, and the number of obtained real nondominated solutions. The results propound that the proposed BSSO can successfully achieve the aim of this work.

💡 Research Summary

The paper addresses the bi‑objective, time‑constrained task scheduling problem in cloud computing, where the two conflicting objectives are minimizing total energy consumption and minimizing makespan, subject to a deadline constraint. Recognizing errors in their earlier MOSSO (Multi‑Objective Simplified Swarm Optimization) implementation, the authors propose a corrected and enhanced algorithm called BSSO (Bi‑objective Simplified Swarm Optimization).

BSSO builds on the Simplified Swarm Optimization (SSO) framework but adapts it for multi‑objective optimization by removing the traditional global best (gBest) concept. Instead, each particle’s personal best (pBest) is selected from the current generation’s set of temporary nondominated solutions. This change allows the algorithm to handle multiple Pareto‑optimal candidates simultaneously. To maintain diversity, the crowding distance metric is employed to rank temporary nondominated solutions, and a hybrid elite selection mechanism is introduced to choose parents when the number of nondominated solutions differs from the required parent pool size.

Mathematically, each task i has a size (size_i) and each processor j has a speed (speed_j) and power consumption (power_j). Processing time t_{i,j}=size_i/speed_j and energy e_{i,j}=power_j·t_{i,j} are defined. The total energy objective is the sum of e_{i,j} over all task‑processor assignments, while makespan is the maximum completion time across all tasks. The optimization problem is: minimize F_e(X) and F_m(X) subject to F_m(X) ≤ T_ub (deadline).

The algorithm proceeds as follows: an initial population of task‑processor assignment vectors is randomly generated. For each generation, every variable (task assignment) is updated according to SSO’s stepwise probability distribution (c_g, c_p, c_w, c_r). After updating, if the new solution improves its pBest, the pBest is replaced. The set of temporary nondominated solutions is refreshed, crowding distances are computed, and the top N_sol solutions are selected as parents for the next generation. This loop repeats for a predefined number of generations.

Experimental evaluation uses three benchmark sizes (small, medium, large) and nine different parameter settings. BSSO is compared against three well‑known multi‑objective algorithms: NSGA‑II, MOPSO, and the earlier MOSSO. Performance metrics include convergence (IGD, Hypervolume), diversity (Spread), the number of temporary nondominated solutions, and the number of final (real) nondominated solutions. Across all scenarios, BSSO consistently outperforms the competitors, showing faster convergence, higher diversity, and a larger set of high‑quality Pareto solutions. The authors highlight that BSSO’s ability to retain many temporary nondominated solutions that later become true Pareto‑optimal points is a key strength.

However, the paper has several limitations. The benchmark specifications (task sizes, processor speeds, power profiles) are not fully disclosed, hindering reproducibility. Sensitivity analysis of the SSO parameters (c_g, c_p, c_w, c_r) is absent, leaving practitioners uncertain about how to tune the algorithm for different cloud environments. Statistical significance testing (e.g., Wilcoxon signed‑rank) is not reported, so the robustness of the observed improvements is unclear. Computational cost (runtime, memory usage) is not compared, which is critical for real‑time scheduling in large data centers. Finally, the algorithm’s behavior under dynamic workloads (tasks arriving online) is not examined.

In summary, BSSO represents a meaningful advancement by adapting the simple yet powerful SSO update mechanism to a multi‑objective cloud scheduling context. It demonstrates superior empirical performance over established algorithms for the static, bi‑objective, deadline‑constrained scheduling problem. Future work should address parameter sensitivity, statistical validation, runtime efficiency, and dynamic workload scenarios to fully establish BSSO’s practicality in real cloud infrastructures.