Highlights

Abstract

Keywords

Nomenclature

۱٫ Introduction

۲٫ The proposed SA-MODDE algorithm

۳٫ Numerical experiments

۴٫ Chemical engineering processes optimization

۵٫ Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Appendix A. Supplementary data

References

Abstract

This paper proposes a new multi-objective dynamic differential evolution algorithm with parameter self-adaptive strategies, named SA-MODDE. All components of the algorithm are synergically designed to reach its full potential, containing parental selection, mutation strategy, parameter setting, survival selection, constraint handling, and termination criteria. The improvement measures emphasize exploiting Pareto dominance information more efficiently. Particularly, parameter adaptation schemes are introduced based on both prior knowledges of current individual and feedback information on previous promising solutions, and their effectiveness is validated by comparison with three fixed-parameter combinations. Extensive numerical tests are conducted on multiple test suites with five state-of-the-art peer competitors. The statistical results demonstrated that the SA-MODDE exhibits good proximity and diversity in dealing with benchmark functions with various characteristics. Three industrial (bio)chemical processes, including two optimal control and one reformulated constrained tri-objective, are investigated to show the feasibility and robustness of the SA-MODDE.

۱٫ Introduction

Engineering problems always require the simultaneous optimization of several competing objectives of interests. So far, multi-objective optimization (MOO) has been an active research field in process systems engineering [1,2]. Particularly, various multi-objective evolutionary algorithms (MOEAs), such as NSGAII, GDE3, and MOPSO, have been widely used to solve both academic and industrial MOO problems [3–۵]. Usually, MOEAs have two main advantages: (1) As many diverse non-dominated solutions as possible can be found in a single run; (2) Various types of MOO problems can be handled without assumptions on objective functions and their mathematical characteristics [6].

The algorithm structure and search operator jointly affect the performance of MOEAs. The algorithm structure can be classified into two main categories: Pareto-based [3,7] and decompositionbased [8,9]. The former provides detailed Pareto dominance information of the population to facilitate individual comparison. The latter decomposes MOO problems into a set of scalar aggregation subproblems, each of which is optimized using the current information from neighboring subproblems. The two methods have their own advantages on different types of problems and are considered to be evenly matched [10]. In terms of search operator, differential evolution (DE) is simple to implement with only a few control parameters, i.e., scale factor (F ) and crossover rate (CR). Except for multi-objective DE (MODE) algorithms, many classic MOEAs also replaced the original evolutionary operators with DE and their performance was significantly enhanced, such as NSGAII-DE, SPEA2-DE, IBEA-DE, and MOEA/D-DE [11,12]. Through updates by dynamic population rather than generation to generation, Qing [13] presented the dynamic DE (DDE) operator, superior in efficiency, robustness, and storage requirements to the conventional DE. That is, each new individual that performs better than or similar to the corresponding old counterpart will immediately participate in the current population to provide information for subsequent evolution. This makes DDE more responsive to changes in population status. Despite of researches on multi-objective DDE (MODDE) algorithms [14,15], it is still very inadequate compared to MODE. Herein, we propose several improvement measures on the MODDE under Pareto-based structure. For convenience, the background of MOO problems and DDE operators are given in Supplementary Materials.