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The extractive dividing-wall column (EDWC) is one of the most efficient technologies for separation of azeotropic or close boiling-point mixtures, but its design is fairly challenging. In this paper we extend the hybrid feasible path optimisation algorithm (Ma Y, McLaughlan M, Zhang N, Li J. Computers & Chemical Engineering, 2020, 143: 107058) for such optimal design. The tolerances-relaxation integration method is refined to allow for long enough integration time that can ensure the solution of the pseudo-transient continuation simulation close to the steady state before the required tolerance is used. To ensure the gradient and Jacobian information available for optimisation, we allow a relaxed tolerance for the simulation in the sensitivity analysis mode when the simulation diverges under small tolerance. In addition, valid lower bounds on purity of the recycled entrainer and the vapour flow rate in column sections are imposed to improve computational efficiency. The computational results demonstrate that the extended hybrid algorithm can achieve better design of the EDWC compared to those in literature. The energy consumption can be reduced by more than 20% compared with existing literature report. In addition, the optimal design of the heat pump assisted EDWC is achieved using the improved hybrid algorithm for the first time.

This paper studies the constrained optimization problem for nonlinear diesel blending. A new hybrid algorithm called cultural harmony search algorithm is presented to solve the proposed optimization problem, which uses cultural knowledge in the belief space of the cultural algorithm to guide the evolving and searching process of the harmony search algorithm. Then, an improved harmony improvisation in the population space of cultural algorithm is developed for new harmony generation to enrich the population diversity. Moreover, in order to accelerate convergence, the domain of decision variables is scaled down by a simplex method at the beginning of the algorithm, and a simplex improved cultural harmony search algorithm is provided. Finally, benchmark functions and the results of application in nonlinear diesel blending of a real-world refinery show the feasibility and effectiveness of the proposed algorithms. The contrasted experiments show that our proposed hybrid algorithm is better than other hybrid algorithms, especially in diesel blending optimization problem.

The hybrid flowshop scheduling problem with unrelated parallel machines exists in many industrial manufacturers, which is an NP-hard combinatorial optimisation problem. To solve this problem more effectively, an improved gravitational search (IGS) algorithm is proposed which combines three strategies: generate new individuals using the mutation strategy of the standard differential evolution (DE) algorithm and preserve the optimal solution via a greedy strategy; substitute the exponential gravitational constant of the standard gravitational search (GS) algorithm with a linear function; improve the velocity update formula of the standard GS algorithm by mixing an adaptive weight and the global search strategy of the standard particle swarm optimisation (PSO) algorithm. Benchmark examples are solved to demonstrate the proposed IGS algorithm is superior to the standard genetic algorithm, DE, GS, DE with local search, estimation of distribution algorithm and artificial bee colony algorithms. Two more examples from a real-world water-meter manufacturing enterprise are effectively solved.

Scheduling gasoline blending and order delivery operations is an important routine task in an oil refinery since gasoline can account for as much as 60-70% of total revenue. In this work we improve the mixed-integer nonlinear programming (MINLP) model of Li et al. (2016) to ensure optimality and incorporate nonlinear property correlations. To solve such nonconvex MINLP model to 8- global optimality, a global optimization method is proposed. It is shown that our improved model and proposed method can solve industrial examples to 1%- global optimality and generate the same or better solutions with less CPU time than those from Cerda et al. (2016). Using nonlinear property correlations could lead to more accurate prediction than linear correlations.

Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP (Error Back Propagation) neural networks. To solve this model, a new 3-layer cultural evolving algorithm framework which has a population space, a medium space and a belief space is firstly conceived. Standard differential evolution algorithm (DE), genetic algorithm (GA), and particle swarm optimization algorithm (PSO) are embedded in this framework to build 3-layer mixed cultural DE/GA/PSO (3LM-CDE, 3LM-CGA, and 3LM-CPSO) algorithms. The accuracy and efficiency of the proposed hybrid algorithms are firstly tested in 20 benchmark nonlinear constrained functions. Then, the operational optimization model for syngas production in a Texaco coal-water slurry gasifier of a real-world chemical plant is solved effectively. The simulation results are encouraging that the 3-layer cultural algorithm evolving framework suggests ways in which the performance of DE, GA, PSO and other population-based evolutionary algorithms (EAs) can be improved, and the optimal operational parameters based on 3LM-CDE algorithm of the syngas production in the Texaco coal-water slurry gasifier shows outstanding computing results than actual industry use and other algorithms.

This paper presents robust optimization models for a multi-product integrated problem of planning and scheduling (based on the work of Terrazas-Moreno & Grossmann (2011) [1]) under products prices uncertainty. With the objective of maximizing the total profit in planning time horizon, the planning section determines the amount of each product, each product distributed to each market, and the inventory level in each manufacturing site during each scheduling time period; the scheduling section determines the products sequence, start and end time of each product running in each production site during each scheduling time period. The uncertainty sets used in robust optimization model are box set, ellipsoidal set, polyhedral set, combined box and ellipsoidal set, combined box and polyhedral set, combined box, ellipsoidal and polyhedral set. The genetic algorithm is utilized to solve the robust optimization models. Case studies show that the solutions obtained from robust optimization models are better than the solutions obtained from the original integrated planning and scheduling when the prices are changed.

Stochastic chance constrained mixed-integer nonlinear programming (SCC-MINLP) models are developed in this paper to solve the refinery short-term crude oil scheduling problem which concerns crude oil unloading, mixing, transferring and multilevel inventory control under demands uncertainty of distillation units. The objective of these models is the minimum expected value of total operation cost. It is the first time that the uncertain demands of Crude oil Distillation Units (CDUs) in these problems are set as random variables which have discrete and continuous joint probability distributions. This situation is close to the real world industry use. To reduce the computation complexity, these SCC-MINLP models are transformed into their equivalent stochastic chance constrained mixed-integer linear programming models (SCC-MILP). Stochastic simulation and stochastic sampling technologies are introduced in detail to solve these complex SCC-MILP models. Finally, case studies are effectively solved with the proposed approaches.

In this paper, a novel competitive co-evolutionary quantum genetic algorithm (CCQGA) is proposed for a stochastic job shop scheduling problem (SJSSP) with the objective to minimize the expected value of makespan. Three new strategies named as competitive hunter, cooperative surviving and the big fish eating small fish are developed in population growth process. Based on improved co-evolution idea of multi-population and concepts of quantum theory, this algorithm could not only adjust population size dynamically to increase the diversity of genes and avoid premature convergence, but also accelerate the convergence speed with Q-bit representation and quantum rotation gate. FT benchmark-based problems where the processing times are subjected to independent normal distributions are solved effectively by CCQGA. The experiment results achieved by CCQGA are compared with quantum-inspired genetic algorithm (QGA) and standard genetic algorithm (GA), which shows that CCQGA has better feasibility and effectiveness.

The main objective of this work is to put forward chance constrained mixed-integer nonlinear stochastic and fuzzy programming models for refinery short-term crude oil scheduling problem under demands uncertainty of distillation units. The scheduling problem studied has characteristics of discrete events and continuous events coexistence, multistage, multiproduct, nonlinear, uncertainty and large scale. At first, the two models are transformed into their equivalent stochastic and fuzzy mixed-integer linear programming (MILP) models by using the method of Quesada and Grossmann [I. Quesada, I E. Grossmann, Global optimization of bilinear process networks with multicomponent flows, Comput. Chem. Eng. 19 (12) (1995) 1219–1242], respectively. After that, the stochastic equivalent model is converted into its deterministic MILP model through probabilistic theory. The fuzzy equivalent model is transformed into its crisp MILP model relies on the fuzzy theory presented by Liu and Iwamura [B.D. Liu, K. Iwamura, Chance constrained programming with fuzzy parameters, Fuzzy Sets Syst. 94 (2) (1998) 227–237] for the first time in this area. Finally, the two crisp MILP models are solved in LINGO 8.0 based on scheduling time discretization. A case study which has 267 continuous variables, 68 binary variables and 320 constraints is effectively solved with the solution approaches proposed.

Optimizing operation parameters for Texaco coal-water slurry gasifier with the consideration of multiple objectives is a complicated nonlinear constrained problem concerning 3 BP neural networks. In this paper, multi-objective 3-layer mixed cultural differential evolution (MO-3LM-CDE) algorithms which comprise of 4 multi-objective strategies and a 3LM-CDE algorithm are firstly presented. Then they are tested in 6 benchmark functions. Finally, the MO-3LM-CDE algorithms are applied to optimize 3 control parameters of the Texaco coal-water slurry gasifier in methanol production of a real-world chemical plant. The simulation results show that multi-objective optimal results are better than the respective single-objective optimal operations.

This paper develops an improved particle swarm optimization algorithm based on cultural algorithm for constrained optimization problems. Firstly, chaos method is utilized in the initialization process of single swarm in population space to assure the searching breadth, and evolves with standard particle swarm optimization (PSO). Secondly, fixed proportion elites are selected from population space to construct the swarm of belief space through acceptance function. Then, the belief space updates its normative knowledge and situational knowledge according to the elite particles, and the elite-swarm in the belief space performs PSO operation according to the update knowledge and generates new particles. After that, the belief space renews the knowledge again, and passes down the new knowledge which has been updated twice to give better guidance to all the particles in the population space. The efficiency of the initialization strategy and the double evolving knowledge strategy are verified in six constrained optimization problems.

A novel modified goal programming genetic algorithm (MGPGA) is presented in this paper to solve constrained non-convex nonlinear programming (NLP) problems. This new method eliminates the complex equality constraints from original model and transforms them as parts of goal functions with higher priority weighting factors. At the same time, the original objective function has the lowest priority weighting factor. After all the absolute deviations of these equality constraints objectives are minimized, the final optimized solutions can be gained. Some applications in chemical engineering field are tested by this MGPGA. The proposed MGPGA demonstrates its advantages in better performances and abilities of solving non-convex NLP problems especially for those with equality constraints.

A stochastic flexible scheduling problem subject to random breakdowns is studied in this paper, which objective is to minimize the expected value of makespan. We consider a preemptive-resume model of breakdown. The processing times, breakdown intervals and repair times are random variables subjected to independent normal distributions. An expanding method inspired by paper [1] is devised through predicting expected breakdown time of machines. Based on some concepts of quantum evolution, an Improved Quantum Genetic Algorithm (IQGA) is proposed, which is tested on a sampling problem compared with Cooperative Co-evolutionary Genetic Algorithm (CCGA) and Genetic Algorithm (GA). Experiment results show IQGA has better feasibility and effectiveness.

Three kinds of credibility fuzzy chance constrained mixed-integer nonlinear programming models (CFCC-MINLP) and the solution methods for the integrated problem of refinery short-term crude oil scheduling and storage management under demands uncertainty of CDUs (Crude-oil Distillation Units) are developed in this paper. To reduce the calculation complexity of these models, they are transformed into their equivalent fuzzy chance constrained mixed-integer linear programming (CFCC-MILP) models. After that these CFCC-MILP models are solved through their crisp equivalent algorithms based on the theory presented by Liu & Liu [2002] for the first time in refinery scheduling area. Finally, a case study which has 265 continuous variables, 68 binary variables and 318 constraints is effectively solved in LINGO 8.0 with the proposed approaches.

A stochastic chance constrained mixed-integer nonlinear programming (SCC-MINLP) model is developed in this paper to solve the integrated problem of refinery short term crude oil scheduling, blending and storage management under demands uncertainty of crude oil distillation units (CDUs). It is the first time that the uncertain CDUs' demands in this problem are set as random variables which have discrete and continuous probability distributions. To reduce the computation complexity, the SCC-MINLP model is transformed into its equivalent stochastic chance constrained mixed-integer linear programming model (SCC-MILP) by using the method of reference. Stochastic simulation and stochastic sampling technologies are adopted to solve the complex SCC-MILP model. Finally, a case study which has 265 continuous variables, 68 binary variables and 318 constraints is effectively solved with the proposed approaches.

This paper develops three kinds of possibility fuzzy chance constrained (PFCC) mixed-integer nonlinear programming models (MINLP) and the solution methods for the integrated problem of refinery short-term crude oil scheduling and storage management under demands uncertainty of CDUs (Crude-oil Distillation Units). To reduce the calculation complexity of these models, they are transformed into its equivalent fuzzy chance constrained mixed-integer linear programming (PFCC-MILP) models by using the method of Quesada & Grossmann [1995]. After that these PFCC-MILP models are solved through their crisp equivalent algorithm and fuzzy simulation algorithms rely on the theory presented by Liu & Iwamura [1998] for the first time in this area. Finally, a case study which has 265 continuous variables, 68 binary variables and 318 constraints is effectively solved in LINGO 8.0 [Xie et al., 2005] with the proposed approaches.

In order to solve the logistic activities optimal control problem which related to oil barges arrival, berthing, transportation, and storage process under input rate uncertainty, a stochastic dynamic multilevel queuing network model was presented in this paper. Non-standard service stations, arrival rate, and special storage allocation policies prevented the use of ordinary analytical approaches to its solution. Through discrete-event stochastic simulation calculations of the entire queuing network, the synthetic optimal mechanism ratio was gained. The final optimal unload machine numbers at docks and warehouses and the numbers of transportation vehicles in a case study shows that this model and algorithm can provide the actual whole system a feasibly strategy.