Author(s: SupriyaGhosh Optimization Multi-Objective Optimization in which Goal Programming wins, and Linear Programming give up …. Linear Algebra and Statistics are the three pillars in data science. They are all used almost everywhere in data science algorithms. Source : https://www.reddit.com/r/MathJokes/comments/f05kuv/lets_mathematically_optimize_our_life/ Optimization is said to be the heart of almost all machine learning and statistical techniques used in data science. Most machine learning algorithms work by creating an optimization model, then learning the parameters of the objective function using the data. This article will provide an in-depth explanation of Goal programming for multi-objective optimization problems. Source : https://users.ece.cmu.edu/~yuejiec/MachineLearning.html Multi-objective optimization also known as multi-objective programming or Pareto optimization deals with optimization problems involving more than one objective function to be optimized simultaneously. It has been used in many areas of science including engineering, logistics marketing transportation and economics. When optimal decisions must be made with trade-offs among two or more competing objectives. Some of these are the following: Maximizing comfort and cost-effectiveness when buying a car; and Maximizing performance and fuel consumption while minimising harmful pollutant emissions. These problems have two or three goals. In practice, however, it is possible to have more than one objective. To understand multi-objective optimization, it is necessary to fully understand Goal Programming. We will start by defining Goal Programming, as it is described in Wikipedia. Source : https://www.pinterest.com/pin/17099673557155171/ Goal programming is a branch of multi-objective optimization, which in turn is a branch of multi-criteria decision analysis. You can think of it as an extension of or generalization to linear programming that allows you to manage multiple objective measures, which are often conflicting. The question is: Why and how do we find multiple objectives? And why are there goals programming needed? Most organizations today have many competing objectives in order to succeed in the dynamic business world. Companies are not only focused on profit maximization and cost reduction, but also have non-profit objectives such as social responsibility, employee relations and public relations. Source : https://www.pinterest.com/pin/129337820520206879/ Under such situations, goal programming assumes utmost importance and serves as a powerful quantitative technique capable of handling multiple decision criteria. Why is Linear programming not used? Source : https://www.pinterest.ph/pin/314618723953095984/ To understand this let us see the differences between Linear Programming and Goal Programming with the help of the below table. Linear Programming and Goal Programming Source: Author. Now that we have a better understanding of the differences, let us see why Linear programming can’t be used for multi-objective issues. We will now discuss the Goal programming model using an actual example. Formulating the right model that is based on your problem is actually the hardest part of multi-objective optimization. It is easy to solve the problem and get results if you have a good model. Source : https://www.performanceinpeople.co.uk/blog/Introducing-Goal-Mapping/ Let me reiterate three main characteristics of Goal programming problems that we need to keep in mind while forming the model. 1. It is not possible to achieve a single goal. There are many goals. 2. As deviational variables, such as overachievement or underachievement, need to be reduced in goal programming models, they are all problems of minimization. 3. Before the next high-priority goal can be considered, it is important to minimize deviations from the highest priority goals. We will use an example to show how model formation works. A popular lighting company produces two product lines, LED lights and colorful lampshades. Each product is produced in two steps, which includes wiring and assembly. Each lamp shade is wired in approximately 2 hours and each light bulb takes 3 hours. The final assembly of each lampshade or LED light takes 6 hours and 5 respectively. Production is so fast that 12 hours are required for wiring and 30 hour of assembly. It is very strict about utilizing the wiring department’s hours as efficiently and without any waste. They also look forward to having no overtime in their assembly department. The company makes $7 per lamphade, and $6 for each LED light. The company is contractually required to deliver at least 7 LED lights. The company has also moved to a new location, and believes that initially maximising profit is unrealistic. The management sets an $30 profit level that will be acceptable during the period. Given the limited production times, the company seeks to determine the best product mix for achieving this goal. In this case, there are several objectives. First, let me give you a list of the goals. 1. 1. To make a profit of $30 in the production period. 2. 2. To make the most of all hours in our wiring department. 3. Goal #3: Avoid overtime at the assembly line 4. Fourth goal: Meet a contract obligation to produce at minimum 7 LED lights. The next step is to set up the variable deviations. Setting the choices variables: X1 = The number of lamp shades produced; X2 = The number of led lights produced. Setting the goal priority according to relevance to business and management. Therefore, P1 is less important than P2, and P2 is more important that P3, and so forth. It doesn’t impact management and business if the Profit Target is exceeded and LED production exceeds expectations. Now our model has been created and tailored to the specific problem. Here are the Goal Programming Model Formulation Steps. 1. Define choice variables, constants and goals The initial step to model formation is to define right-hand side constants and choice variables. Specific goal values/levels can be identified as right-hand side constants. It requires a careful analysis of the problem in order to identify all relevant variables that have some effect on the set of goals laid down by the business stakeholders/decision-makers. 2. Deviational variables can be added. Identify the variables and create them. These variables represent the possible deviations below(underachievement) or above the target value (overachievement). 3. It is important to clearly define the priorities associated with each goal. For example, Priority level P1 should be the most important. Priority Level P1 should be set first if it is the most important. Priority Level P2 should then follow. 4. Forming Constraints. A set of constraints should based on relationships between the variables selected and the relationship with the goals. You can either have a system constraint which may impact but not directly relate to goals, or you can have a goal constraint directly related. By adding deviational variables to each constraint equation, you can create a new one. If you don’t have any deviational variables, then create a new constraint that includes one. 5. The objective function should be developed. First, you must assign the relevant deviational variables to the priority factors that will prevent them from being lost. The second step is to assign weights at equal priority levels to the deviational variables. Important: Goals at the same priority levels must be comparable. Source : https://www.rosettatg.com/blogtoon/2018/3/12/what-are-you-optimizing-for With
