(60f) Variable Neighborhood Search with Active Specification Switching Repair Strategy Applied to Crude Distillation Energy Integration Problem

Variable Neighborhood Search with Active Specification Switching Repair Strategy Applied to Crude Distillation Energy Integration Problem

G. Robertson, J.A.  Romagnoli

Louisiana State University, Baton Rouge, LA, U.S.A

  Supply chain management (SCM) is the oversight of materials, information, and finances as they move in a process from suppliers to manufacturers to wholesalers to retailers and then ultimately to consumers. Global solutions for supply chain problems can be computationally burdensome due to the size of the problem and the number of alternatives. Therefore, both within and among companies, objectives are naturally separated horizontally along the supply chain, with entities along the supply chain having their own local objective. The decision making can also be separated vertically into layers by the time horizons they consider.

The longer the time horizon a decision considers, the less frequent the decision is made and the greater its ramifications. Here, we have broken down decision making into four layers (strategic, tactical, production, and operational.) Strategic level problems are long term, around 5 years, and can include building or expanding a facility and contract negotiations. Within the time period of the strategic layer problem, many medium term tactical layer decisions are made such as resource allocation and transportation problems. Production layer problems include the scheduling of production units and blending problems. Operational layer problems are online problems including plant diagnosis, fault detection, and process unit optimization. Challenges to the integration of problems in different layers are reconciling their different implementation frequencies and the magnitudes of order of their cost. Decomposition of problems both vertically and horizontally leads to a feasible but not necessarily an optimal solution.

Process industry supply chains are striving to improve efficiency and profitability (Shah, 2005). Integrating different levels within a supply chain can improve profitability. Many planning problems have been addressed using managerial judgments where complex interactions between different decision-making levels were disregarded. Recent developments in mixed integer process optimization provide new tools to help solve more complex problems of a company’s hierarchy (Puigjaner and Heyen, 2006.) The decisions made by planning, scheduling, and control functions have a substantial economic impact on process industry operations - estimated to be as high as US $10 increased margin per ton of feed for many plants (Puigjaner and Heyen, 2006.) Hence decision support tools for scheduling and planning can have a profound effect on the profitability of an enterprise. 

Modern petroleum refining has become an extremely competitive business due to the deteriorating quality of crude oil coupled with tighter product specifications and more stringent environmental regulations. Furthermore, refineries today receive shipments of crude from a variety of sources. These crude oils are of different quality and composition and usually blending can improve the economics of the refinery. Therefore, refineries deal with a dynamic schedule of incoming crude which cause them to frequently change unit’s operating conditions to reduce operating expenses including environmental impact. Final products in a petroleum refinery are created by combining feed stocks emerging from distillation units, reformers, and catalytic cracker. The input streams which have varying chemical compositions and physical properties, are sent into common tanks or pools to be mixed into final products.

Lee et al. (1996) and Shah (1996) first addressed the CSP by developing an MILP model for short-term refinery scheduling using discrete time formulation. Jia et al. (2003) approached the same problem using unit and event based continuous time formulation.  Reddy et al. (2004) designed an approximation algorithm in order to address the extensive time requirement to solve the CSP in order to reach a feasible point.

Robertson et al. demonstrated the importance of integrating the problems on the different decision making layers by incorporating the CSP with the heat integration of the distillation units and demonstrated the method integrating the different decision making layers. Sylvia et al. proposed a global optimization approach for integrating the CSP and the final product blending pooling problems with a lagrange decomposition approach. This can be troublesome for larger scale problems. Here we illustrate an algorithm possessing a more robust operational model capable of operating underneath a scheduling algorithm.  

Metaheuristics are solution methods of optimization problems that orchestrate an interaction between local improvement procedures and higher level strategies to create a process of escaping local optima and performing robust searches of solution spaces. Hybrid metaheuristics take advantage of the strengths of their individual metaheuristic components to better explore solution spaces. On the front of applications, metaheuristics are used to find high-quality solutions to an ever-growing number of complex, ill-defined real world problems.

An optimization problem is typically modeled as an objective function along with variable relationships and constraints. In an optimization problem, a set of variables, decision variables (D.V.), are manipulated to optimize (minimize or maximize) an objective function while other variables, parameters, are held constant. Among the constraints are physically limiting constraints as well as relationship constraints violated by a certain combination of decision variables which can be more difficult to define in a mathematical model. In process system engineering groups, large models are constructed to mimic complex processes in software such as Aspen tech. A process simulation can be utilized as the model for an optimization problem.

When a simulation is used as a model, the optimizer is a separate entity which treats the model as a black box. The optimizer sends a set of D.V.’s to the model, and the model returns values necessary to solve the objective function. If the set of D.V.’s are outside the solutions s pace, the model will not converge. A converged solution is one where all equations in the model are satisfied.

The model can also not converge if the optimizer makes large jumps in the solution space. For a nonlinear set of equations to be solved simultaneously, modeling equations are typically solved through an iterative procedure. Despite the advances of algorithms such as the inside-out distillation algorithm, the convergence is a function of the initial estimate given to the algorithm. The modeling solver’s initial estimate contains the values of the previous point solved. Therefore, increasing the solution space can help find global optima; however, taking larger steps increases the probability of a non-converging solution by worsening the model solver’s initial condition.

In order to handle complex optimization models with solution spaces made of ill-defined constraints, we demonstrate a hybrid metaheuristic where Variable Neighborhood Search is aided by a Threshold Acceptance search. This hybrid operates separately from the model and includes a repair strategy for a non-converging result of a D.V. set. The method is applied to a heat integration problem of a distillation train to have robust optimization under a higher level scheduler and demonstrates competitive improvement and superior handling of non-convergent models when compared to SQP, Fletcher-Reeves, and Newton-Rhapson optimization techniques with no repair strategy.  

Keywords: Variable neighborhood Search, Refinery Optimization, Heat Integration Distillation, Crude Oil Scheduling