پیکربندی محصول و برنامه ریزی عملیات همزمان : برخی از نتایج تجربی بهینه سازی

In nowadays industrial competition, optimizing concurrently the configured product and the planning of its production process becomes a key issue in order to achieve mass customization development. However, if many studies have addressed these two problems separately, very few have considered them concurrently. We therefore consider in this article a multi-criteria optimization problem that follows an interactive configuration and planning process. The configuration and planning problems are considered as constraint satisfaction problems (CSPs). After some recalls about this two-step approach, we propose to evaluate a recent evolutionary optimization algorithm called CFB-EA (for constraint filtering based evolutionary algorithm). CFB-EA, specially designed to handle constrained problems, is compared with an exact branch and bound approach on small problem instances and with another evolutionary approach carefully selected for larger instances. Various experiments, with solutions spaces up to 1017, permit us to conclude that CFB-EA sounds very promising for the concurrent optimization of a configured product and its production process.

This paper concerns aiding mass customization, or, more accurately, how the two activities of product configuration and production planning can be achieved, optimized and computer supported in a concurrent way. An example relevant to the configuration and planning of a small aircraft illustrates our propositions all along the paper. 1.1. Concurrent configuration and planning Product configuration can be defined as deriving the definition of a specific or customized product (through a set of properties, sub-assemblies or bill of materials, etc.) from a generic product or a product family [1] or [2]. Similarly, deriving a specific production plan (operations, resources to be used, etc.) from some kind of generic process plan, while respecting the product characteristics and the customer requirements, can define production planning with respect to product configuration [3] or [4]. As the decisions relevant to each of these two activities are closely dependent: • decisions associated with the configuration of a product can have strong consequences on the planning of its production process (for example, a luxury finish requires additional manufacturing time), • planning decisions can imply tough constraints to product configuration (for example, a given assembly duration prevents from using a particular kind of engine). It is necessary to associate them in order to avoid inconsistencies and the traditional sequence “product configuration, then production planning”. If many scientific works have been independently achieved on configuration or planning, as far as we know, scientific production is far less important when they are considered concurrently. Some initial ideas where proposed by Steward and Tate [5] and Schierholt [3]. More recent works can be found in [12] or [6]. 1.2. Different requirements, two configuration/planning steps Most of the times, configuration techniques support interactively the processing of customer requirements. This means that the consequences of each “elementary requirement” are computed and shown to the customer. By elementary requirement, we mean a restriction of the domain of a variable involved in configuration (for example “plane capacity belongs to [6, 12]”), or in planning (for example “final assembly operation should be located in Italy”). As the goal of a company that uses concurrent configuration and planning techniques is to put on the market a product diversity that covers a large demand segment, the elementary requirements can become very diverse and numerous. The process in turn can be tricky and longer. Each customer can be interested in different kinds of requirements, for example customer “A” can be mainly interested in the product “performance” (speed, altitude, etc.) while the product “comfort” (finish level, seat-space, etc.) may mostly attract customer “B”. The idea is to limit the collection of requirements to those that mainly interest each customer. These requirements are named “non-negotiable requirements”, while the remaining ones are named “negotiable requirements”. Therefore, a first step interactively processes the non-negotiable requirements and then asks the software to complete autonomously the processing of the negotiable requirements in a second step. This autonomous computation can be achieved either with default values or with some multi-criteria optimization (cost, due-date, performances, etc.). This paper focuses on this last optimization issue. For paper clarity, we will only consider the two conflicting criteria cost and cycle time. We therefore consider the concurrent configuration and planning process presented in Fig. 1 in two successive steps. Step1: interactive configuration and planning which processes non-negotiable requirements and provides a first solution space reduction. Step 2: response optimization which processes negotiable requirements and provides a Pareto front shown to the customer for a solution selection. This paper is mainly concerned by this second step. Full-size image (50 K) Fig. 1. A two-step approach for concurrent configuration and planning. Figure options 1.3. Goal and organization of the paper In a previous paper [7] we have proposed an original adapted evolutionary algorithm for this problem “CFB-EA” (for constrained filtering based evolutionary algorithm). However, the presentation was mainly descriptive and only some initial experimental results could be presented. Our objective in this paper is to prove that CFB-EA is a good candidate for optimizing concurrent configuration/planning problems. Thus, we propose to: • evaluate the CFB-EA algorithm in detail. For that purpose, a survey of the scientific literature will help us identify a competitive evolutionary algorithm “FRB-EA” (for feasibility rules based evolutionary algorithm), in order to set up experimental comparisons, • for a given problem, identify a size limit where exact optimization, a branch and bound (B&B) in our case, cannot be used due to computation duration and must be replaced by evolutionary computations (CFB-EA or FRB-EA) in our case. The paper is consequently organized as follows. In the next section, we describe how the previous two steps approach can be supported with constraint processing and discusses industrial and practical issues. In the third section, we formalize the optimization problem, review optimization techniques and finally detail the three optimization algorithms that will be used for experimentations. In the last section, we present experimental results that highlight the performance of CFB-EA and the limit where the exact approach should

The goal of this article has been to propose a detailed evaluation of an evolutionary algorithm, called CFB-EA for Constraint filtering based evolutionary algorithm, that deals with concurrent product configuration and production planning. The problem has been presented and modeled as a constraint satisfaction problem, and then a two-steps approach, gathering an interactive configuration and planning process followed by a multi-criteria optimization, has been presented with a simple example. Once the optimization problem highlighted, a detail survey of evolutionary algorithms that handle constrained problem permits us to identify the most suitable competing optimizing approach (FRB-EA for feasibility rule based evolutionary algorithm). An exact branch and bound procedure (BB) is also recalled for small instances. For small instances, from 12 to 15 decision variables with 3 values for each (0.2–2.106 solutions), BB is globally better than EA approaches. Logically the proposed EA works better when the size of the problem gets larger compared to BB, however the tendency goes to the opposite when the problem tends to be more constrained. As the size of the optimization problem is directly dependent of the quantity of negotiable requirements (first step interactive configuration/planning), an interesting result is that it is possible to propose a kind of limit that can trigger the selection of BB or EA optimization. Of course this limit is specific to the addressed problem. For these small instances, it must also be pointed out that FRB-EA and CFB-EA have similar performances (much less than 2 h) with a very low sensitivity to problem sizes and constraint levels. When the problem gets larger, BB cannot be considered. On a problem of 21 decision variables (12 product variables with 6 values and 9 process variables with 9 values), when the constraint level is low (solution space between 1015 and 1017), CFB-EA and FRB-EA perform very closely, when the constraint level increases (solution space between 1013 and 1014) CFB-EA is a little better. In terms of convergence speed, CFB-EA reaches around 90% of the hypervolume in less than 3 h and 99% in less than 10 h. The low sensitivity of CFB-EA with respect to constraint level can be also noticed. That leads us to consider that the CFB-EA approach is competitive for this kind of configuration/planning problems even if some further improvements could be investigated for both EA approaches. Therefore the two steps process object of this paper can be considered with no doubt, as a significant assistance for optimal configuration and planning achievement. It allows the user to decide efficiently about his cost/cycle-time compromise when dealing simultaneously with configuration and planning. These promising results introduce some prospective studies: convergence speed, evolutionary parameter tuning and also problems with more than two objectives. For convergence speed or larger problems, we are currently developing an iterative optimization process that aims to reduce considerably the time required to obtain a near-optimal Pareto front using a kind of zoom on a specific area selected by the user during the optimization process. For parameters tuning, we are thinking of considering the possibility of an automated setting with a variable population and archive size. Finally, configuration and planning problems taking into account several objectives such as performance, risk, or sustainable aspects are in our short list.