PEML3001 – Decision Making and Optimization Laboratory
Integrated Lab Experiment Manual and Viva-Voce Revision Guide
M.Tech Project Engineering and Management (PEM) · JUT Ranchi · Prepared by Vimal Noble, BIT Sindri
1. Course Map and How to Use This Manual
PEML3001 has ten experiments in two blocks. Block A (Experiments 1–7) covers Multi-Criteria Decision-Making (MCDM): you are given a finite set of alternatives and criteria and must rank them. Block B (Experiments 8–10) covers metaheuristic global optimisation: you search a continuous or discrete space for the best design or parameter set.
Every experiment below follows one fixed pattern so that lab records and viva answers stay consistent: Aim → Principle → Inputs → Procedure → Formulae → Decision rule → Worked illustration (where useful) → Strengths and limits → Applications → Viva questions.
1.1 Master Categorisation Matrix
Exp | Method | Core strategy | Computational nature | Best-fit application |
|---|---|---|---|---|
1a | SAW | Linear normalisation + weighted sum | Analytical, deterministic | Quick screening of design variants |
1b | WPM | Criteria raised to weight powers, multiplied | Analytical, deterministic | Cases where one bad attribute should veto a choice |
2 | AHP | Hierarchy + pairwise comparison matrices | Matrix algebra, eigenvector | Complex decisions with strong expert judgement |
3a | TOPSIS | Closest to ideal, farthest from anti-ideal | Geometric, Euclidean distance | Vendor and supplier selection |
3b | Modified TOPSIS | Linear top-bottom scaling anchor | Geometric, Euclidean distance | Clustered or skewed data sets |
4 | VIKOR | Group utility vs individual regret | Compromise ranking | Public projects, conflicting criteria |
5 | GTMA | Digraph → permanent matrix → index | Graph theory, combinatorial | Engineering systems with interacting criteria |
6 | ELECTRE | Outranking via concordance and discordance | Binary set relations | Eliminating unacceptable alternatives |
7 | PROMETHEE | Outranking via preference functions and flows | Vector flow operations | Ranking with smooth trade-offs |
8 | Genetic Algorithm (GA) | Selection, crossover, mutation | Stochastic, population-based | Discrete, non-linear structural design |
9 | Simulated Annealing (SA) | Cooling analogy, Metropolis acceptance | Stochastic, single trajectory | Scheduling, routing, escaping local optima |
10 | Particle Swarm Optimisation (PSO) | Pbest and Gbest velocity updates | Stochastic, agent-based | Continuous parameter tuning, e.g. CNC machining |
1.2 Common Notation (Block A)
- m = number of alternatives A1…Am; n = number of criteria C1…Cn.
- x(ij) = performance of alternative i on criterion j (decision matrix).
- w(j) = weight of criterion j, with the weights summing to 1.
- Beneficial (B) criterion: larger is better (strength, quality). Non-beneficial (NB) criterion: smaller is better (cost, time, defects).
1.3 Universal Workflow for Block A
- Define the goal, alternatives and criteria.
- Build the decision matrix and tag each criterion as B or NB.
- Assign weights (direct, entropy, or AHP-derived).
- Normalise the matrix with the method-specific scheme.
- Aggregate, compute the index, and rank.
- Run a sensitivity check: change the weights by ±10% and see whether the rank order holds.
- Interpret the result and state the decision.
Integration tip: AHP (Exp 2) is the standard engine for generating weights, which then feed SAW, WPM, TOPSIS, VIKOR, PROMETHEE and GTMA. Comparing the rank orders of all methods on one data set is the strongest way to present your lab record.
2. Block A – Multi-Criteria Decision-Making
Experiment 1 – SAW and WPM
Aim: To rank alternatives using Simple Additive Weighting (SAW) and the Weighted Product Method (WPM), and to compare how each treats weak performance.
Principle: SAW sums weighted normalised scores, so it is compensatory: a very high score on one criterion can hide a very poor one on another. WPM multiplies normalised scores raised to their weights, so a single poor attribute drags the whole product down.
Inputs: Decision matrix, B/NB tags, weights.
Normalisation (linear ratio):
- Beneficial: r(ij) = x(ij) / max(x(j))
- Non-beneficial: r(ij) = min(x(j)) / x(ij)
Formulae:
- SAW: S(i) = Σ over j of w(j) · r(ij)
- WPM: P(i) = Π over j of r(ij)^w(j)
- WPM relative form (no normalisation): P(Ai/Ak) = Π (x(ij)/x(kj))^w(j); Ai is better than Ak if the ratio exceeds 1.
Procedure:
- Enter the decision matrix and weights.
- Normalise each column using the B or NB formula.
- For SAW, multiply by weights and sum across each row.
- For WPM, raise each normalised value to its weight and multiply across each row.
- Rank in descending order of S(i) or P(i).
Decision rule: The highest S(i) or P(i) is the best alternative.
Worked illustration (all three criteria beneficial; weights 0.5, 0.3, 0.2):
Alt | C1 Strength | C2 Durability | C3 Finish |
|---|---|---|---|
A1 | 8 | 6 | 7 |
A2 | 6 | 9 | 8 |
A3 | 9 | 5 | 6 |
Column maxima are 9, 9 and 8. Normalised values: A1 = (0.889, 0.667, 0.875); A2 = (0.667, 1.000, 1.000); A3 = (1.000, 0.556, 0.750).
Alt | SAW score | SAW rank | WPM score | WPM rank |
|---|---|---|---|---|
A1 | 0.819 | 2 | 0.813 | 2 |
A2 | 0.833 | 1 | 0.817 | 1 |
A3 | 0.817 | 3 | 0.791 | 3 |
A2 wins in both methods. Note the SAW scores of A1 and A3 are almost equal, while WPM separates them more because A3's weak durability (0.556) is penalised multiplicatively.
Strengths and limits: SAW is simple and transparent but fully compensatory. WPM is dimensionless and penalises weak attributes, but is less intuitive and sensitive to very small values.
Applications: Preliminary screening of design variants, material shortlisting, quick supplier scoring.
Viva questions:
- Why is SAW called compensatory? A high score on one criterion offsets a low score on another.
- When would you prefer WPM? When a single poor attribute should heavily penalise the alternative.
- Why must criteria be normalised? To make different units dimensionless and comparable.
- How are non-beneficial criteria handled? By inverting the ratio (min divided by x).
Experiment 2 – Analytic Hierarchy Process (AHP)
Aim: To derive criteria weights (and alternative priorities) from expert pairwise judgements and to verify their logical consistency.
Principle: The problem is decomposed into a hierarchy (Goal → Criteria → Sub-criteria → Alternatives). Elements at each level are compared in pairs using Saaty's 1–9 scale, and priority vectors are obtained from the principal eigenvector.
Saaty's scale:
Value | Meaning |
|---|---|
1 | Equal importance |
3 | Moderate importance of one over the other |
5 | Strong importance |
7 | Very strong importance |
9 | Extreme importance |
2, 4, 6, 8 | Intermediate values |
Reciprocals | If a(ij) = k then a(ji) = 1/k |
Procedure:
- Build the hierarchy of goal, criteria and alternatives.
- Form the n×n pairwise comparison matrix A (diagonal = 1, reciprocal below the diagonal).
- Normalise: divide each entry by its column sum.
- Priority vector w: average each row of the normalised matrix (the approximate eigenvector method).
- Principal eigenvalue: compute A·w, divide each component by the matching w(i), and take the mean to obtain λmax.
- Consistency Index: CI = (λmax − n) / (n − 1)
- Consistency Ratio: CR = CI / RI, using the Random Index below.
- Repeat for alternatives under each criterion, then synthesise: Global score(i) = Σ w(j) · priority(i, j).
Random Index (RI) table:
n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
RI | 0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |
Decision rule: If CR ≤ 0.10, the judgements are acceptable. If CR > 0.10, revise the pairwise comparisons. The alternative with the highest global score is selected.
Strengths and limits: Handles qualitative and quantitative criteria and checks consistency, but the number of comparisons grows as n(n−1)/2 and the 1–9 scale is subjective. Rank reversal can occur when alternatives are added.
Applications: Weight generation for any other MCDM method, site selection, technology and vendor selection.
Viva questions:
- What does CR ≤ 0.10 mean? Inconsistency is within the acceptable 10% limit.
- Why is RI needed? It is the average CI of random reciprocal matrices of the same size, used as a benchmark.
- What is the CR of a 2×2 matrix? Always zero; it is perfectly consistent.
- What is the relationship between λmax and n? λmax ≥ n, with equality only for a perfectly consistent matrix.
Experiment 3 – TOPSIS and Modified TOPSIS
Aim: To rank alternatives by their geometric closeness to the ideal solution, and to study the effect of replacing vector normalisation with linear top-bottom scaling.
Principle: The best alternative should be nearest to the Positive Ideal Solution (PIS) and farthest from the Negative Ideal Solution (NIS).
3a Standard TOPSIS
- Vector normalisation: r(ij) = x(ij) / √(Σ over i of x(ij)²)
- Weighted matrix: v(ij) = w(j) · r(ij)
- PIS and NIS: For B criteria, v⁺(j) = max v(ij) and v⁻(j) = min v(ij); for NB criteria swap them.
- Separation measures: S⁺(i) = √(Σ (v(ij) − v⁺(j))²) and S⁻(i) = √(Σ (v(ij) − v⁻(j))²)
- Closeness coefficient: C(i) = S⁻(i) / (S⁺(i) + S⁻(i)), with 0 ≤ C(i) ≤ 1.
- Rank in descending order of C(i).
3b Modified TOPSIS
Replace step 1 with linear top-bottom scaling, anchored on the best and worst value in each column:
- Beneficial: r(ij) = (x(ij) − x(j,min)) / (x(j,max) − x(j,min))
- Non-beneficial: r(ij) = (x(j,max) − x(ij)) / (x(j,max) − x(j,min))
The remaining steps are the same. Because the best alternative is always scaled to 1 and the worst to 0 on every criterion, tightly clustered data cannot be squashed into near-identical values, as can happen with vector normalisation.
Decision rule: The alternative with the highest closeness coefficient is best.
Strengths and limits: Easy, logical and compensatory in geometry; the classic method for supplier selection. Standard TOPSIS is sensitive to the normalisation chosen and can show rank reversal. Modified TOPSIS reduces distortion but may exaggerate small differences when the data range is tiny.
Applications: Supply chain tracking, vendor selection, machine and material selection.
Viva questions:
- What are PIS and NIS? Hypothetical solutions made of the best and worst values on every criterion.
- Why does TOPSIS use Euclidean distance? It measures simultaneous closeness to the ideal and distance from the anti-ideal.
- What is the range of C(i)? 0 to 1; 1 means the alternative equals the PIS.
- Why use Modified TOPSIS? To avoid skew from clustered data.
Experiment 4 – VIKOR
Aim: To obtain a compromise ranking that balances majority utility against individual regret, and to test whether the winner is robust.
Principle: VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) measures closeness to the ideal using an aggregating function that balances group utility (S) and maximum individual regret (R).
Procedure:
- Find the best value f*(j) and worst value f⁻(j) for each criterion (for NB criteria swap them).
- Group utility: S(i) = Σ over j of w(j) · (f*(j) − x(ij)) / (f*(j) − f⁻(j))
- Individual regret: R(i) = max over j of [ w(j) · (f*(j) − x(ij)) / (f*(j) − f⁻(j)) ]
- Compromise index: Q(i) = v · (S(i) − S*) / (S⁻ − S*) + (1 − v) · (R(i) − R*) / (R⁻ − R*) where S* = min S, S⁻ = max S, R* = min R, R⁻ = max R, and v is the weight of the "majority strategy" (usually 0.5).
- Rank alternatives by S, R and Q. Smaller values are better.
Acceptance conditions for the compromise solution A(1) (best Q):
- C1 – Acceptable advantage: Q(A2) − Q(A1) ≥ 1/(m − 1), where A2 is the second-ranked alternative.
- C2 – Acceptable stability: A1 must also rank best by S or R (or both).
Decision rule:
- If both conditions hold, A1 is the single compromise solution.
- If C2 fails, A1 and A2 are both proposed as compromise solutions.
- If C1 fails, propose A1, A2, … A(M), where A(M) is the last alternative satisfying Q(A(M)) − Q(A1) < 1/(m − 1).
Strengths and limits: Handles conflicting criteria and reports a compromise rather than a forced winner. It requires the acceptance check, and the result depends on the choice of v.
Applications: Public infrastructure projects, environmental trade-offs, conflict-laden multi-stakeholder choices.
Viva questions:
- What do S and R represent? S is group utility (majority); R is individual regret (the worst single criterion).
- What does v = 0.5 mean? Equal emphasis on majority utility and individual regret.
- Why is the acceptable advantage condition needed? To confirm the winner leads by a meaningful margin, not by chance.
- Is a high Q good or bad? Bad; VIKOR ranks the minimum Q first.
Experiment 5 – Graph Theory and Matrix Approach (GTMA)
Aim: To evaluate alternatives by modelling the criteria and their interdependencies as a digraph and converting it into a permanent matrix function.
Principle: Each criterion is a node of a directed graph; each directed edge carries the relative importance of one criterion over another. The graph is converted into a variable permanent matrix, and its permanent function is the single evaluation index for the alternative.
Procedure:
- Identify the attributes (nodes) that affect the decision.
- Draw the attribute digraph with directed edges for the interdependence among attributes.
- Normalise each attribute value for every alternative (beneficial: x / x(max); non-beneficial: x(min) / x).
- Rate the relative importance a(ij) of attribute i over attribute j (Rao's scale; a(ij) + a(ji) = 1).
- Build the variable permanent matrix A for each alternative: the diagonal holds the attribute values Ci and the off-diagonal entries hold a(ij) (zero where no edge exists).
- Compute the permanent per(A). It follows the determinant expansion, but all terms take a positive sign.
- Rank alternatives by their permanent value; the highest value is best.
Why the permanent, not the determinant? The determinant has alternating signs, so interacting terms can cancel each other. The permanent keeps every term positive, so no interaction is lost.
Strengths and limits: Captures criteria interactions and gives a single index per alternative. The calculation grows factorially with the number of attributes, so software is used beyond about 5 criteria, and the relative-importance inputs are subjective.
Applications: Machine tool and FMS selection, heavy engineering systems, product design choice.
Viva questions:
- What does the permanent function do differently? It uses all positive signs so interactions never cancel.
- What does a node represent? A criterion or attribute.
- What does an edge represent? The relative importance or interdependence between two attributes.
- What is the diagonal of the matrix? The normalised attribute values of the alternative.
Experiment 6 – ELECTRE (Outranking)
Aim: To determine, through pairwise outranking, which alternatives are dominated and can be eliminated, leaving a kernel of preferred choices.
Principle: Alternative Ai outranks Ak if, on enough criteria (concordance) and without a severely opposing criterion (discordance), Ai is at least as good as Ak.
Procedure (ELECTRE I):
- Normalise the decision matrix (vector normalisation) and weight it: v(ij) = w(j) · r(ij).
- For each ordered pair (i, k), split criteria into the concordance set C(ik) (Ai at least as good as Ak) and the discordance set D(ik) (Ai worse than Ak).
- Concordance index: c(ik) = Σ of w(j) over j in C(ik)
- Discordance index: d(ik) = max over j in D(ik) of |v(ij) − v(kj)| / max over all j of |v(ij) − v(kj)|
- Set thresholds: c̄ = average of all c(ik), and d̄ = average of all d(ik).
- Build the Boolean concordance dominance matrix (1 if c(ik) ≥ c̄) and discordance dominance matrix (1 if d(ik) ≤ d̄).
- Aggregate dominance matrix = element-wise product of the two Boolean matrices.
- Ai outranks Ak where the aggregate entry is 1. Alternatives that are not outranked by any other form the kernel.
Decision rule: Eliminate alternatives outranked by others; the most frequently outranking alternative (largest row count, smallest column count) is preferred.
Strengths and limits: Handles incomparability and reduces a large set quickly. The binary yes/no relation ignores the size of the preference, and the result can leave several alternatives in the kernel.
Applications: Screening out unacceptable design ideas, project shortlisting, site elimination.
Viva questions:
- What is concordance? The weight of criteria supporting the claim "Ai is at least as good as Ak".
- What is discordance? The strength of the strongest criterion opposing that claim.
- What is the kernel? The set of alternatives not outranked by any other.
- Why is ELECTRE a screening tool? Its output is binary dominance, mainly used to filter.
Experiment 7 – PROMETHEE (Outranking with Flows)
Aim: To rank alternatives using preference functions and net outranking flows.
Principle: For every pair of alternatives, the degree of preference on each criterion is a function of the difference d(j) = x(ij) − x(kj), shaped by a preference function P(j)(d).
Common preference functions:
Type | Shape | Parameters |
|---|---|---|
I – Usual | Strict: P = 0 if d ≤ 0, else 1 | None |
II – U-shape | P = 0 if d ≤ q, else 1 | Indifference threshold q |
III – V-shape | P rises linearly from 0 to 1 up to d = p | Preference threshold p |
IV – Level | P = 0 up to q, 0.5 between q and p, 1 beyond p | q and p |
V – Linear | P rises linearly between q and p | q and p |
VI – Gaussian | Smooth S-curve | σ |
Procedure:
- For each criterion pick a preference function and thresholds.
- Compute pairwise differences and the preference degree P(j)(Ai, Ak).
- Aggregated preference index: π(Ai, Ak) = Σ over j of w(j) · P(j)(Ai, Ak)
- Leaving flow: Φ⁺(i) = (1 / (m − 1)) · Σ over k of π(Ai, Ak) (how strongly Ai outranks the others)
- Entering flow: Φ⁻(i) = (1 / (m − 1)) · Σ over k of π(Ak, Ai) (how strongly Ai is outranked)
- Net flow: Φ(i) = Φ⁺(i) − Φ⁻(i)
Decision rule:
- PROMETHEE I: partial ranking from Φ⁺ and Φ⁻ (incomparability is allowed).
- PROMETHEE II: complete ranking in descending order of Φ(i). The highest net flow is best.
Strengths and limits: Flexible, handles gradual preferences, and is easy to explain. The choice of preference function and thresholds is subjective.
Applications: Ranking process alternatives, environmental and energy choices, supplier ranking with smooth trade-offs.
Viva questions:
- Why is PROMETHEE smoother than ELECTRE? It uses continuous preference functions rather than binary thresholds.
- What do Φ⁺ and Φ⁻ mean? Strength and weakness of an alternative relative to all the others.
- What is the sum of all net flows? Zero.
- Difference between PROMETHEE I and II? I gives a partial ranking; II gives a complete ranking.
3. Block B – Metaheuristic Global Optimisation
In Block B the decision variables are not a short list of alternatives but a search space. You define an objective function f(x), decision variables with bounds, and constraints, then let a stochastic algorithm search. Because the algorithms are random, run each experiment at least 10–30 times and report the best, mean and standard deviation of the objective value.
Experiment 8 – Genetic Algorithm (GA)
Aim: To minimise or maximise a function using a population-based algorithm inspired by natural selection.
Terminology: Chromosome (one candidate solution), gene (one variable), population, fitness, generation.
Procedure:
- Encode the variables (binary, integer or real-coded chromosomes).
- Initialise a random population of size N.
- Evaluate fitness of every chromosome (for minimisation use fitness = 1 / (1 + f) or rank-based scaling).
- Selection: choose parents by roulette wheel, tournament or rank selection.
- Crossover: combine two parents with probability pc (typically 0.6–0.9), e.g. single-point, two-point or uniform.
- Mutation: flip or perturb genes with a small probability pm (typically 0.001–0.05).
- Elitism: carry the best one or two chromosomes unchanged into the next generation.
- Form the new generation and repeat until the stopping criterion (maximum generations or no improvement).
Typical parameters: N = 20–100, pc = 0.8, pm = 0.01, generations = 50–200.
Role of operators: Crossover exploits good building blocks; mutation maintains diversity and prevents premature convergence.
Strengths and limits: Handles discrete, non-linear and non-differentiable problems and is not trapped easily; however it needs many function evaluations and parameter tuning, and offers no guarantee of the global optimum.
Applications: Structural design, scheduling, layout and facility planning.
Viva questions:
- Why is mutation necessary? It restores lost genetic diversity.
- What is premature convergence? The population becomes uniform around a local optimum too early.
- What is elitism? Copying the best solutions directly into the next generation.
- How does GA differ from classical search? It works with a population and probabilistic rules, not gradients.
Experiment 9 – Simulated Annealing (SA)
Aim: To find a global optimum by simulating the slow cooling of a hot metal, accepting occasional worse moves to escape local optima.
Principle: A single solution moves through the search space. At high temperature T the algorithm often accepts worse moves; as T falls it becomes greedy.
Procedure:
- Choose the initial solution x, initial temperature T0, final temperature Tf, cooling rate α (0 < α < 1) and the number of iterations per temperature level.
- Generate a neighbour x′ by a small random change.
- Compute ΔE = f(x′) − f(x) (for minimisation).
- Metropolis criterion:
- If ΔE ≤ 0, accept x′ (it is better).
- If ΔE > 0, accept x′ with probability P = exp(−ΔE / T); draw a random number r in [0,1] and accept if r < P.
- Cool: T(new) = α · T (geometric cooling, α typically 0.90–0.99).
- Repeat until T ≤ Tf, and report the best solution found.
Behaviour: High T gives exploration; low T gives exploitation. If cooling is too fast the search is trapped; if too slow the run time is excessive.
Strengths and limits: Very simple, needs little memory, and can escape local optima; but it follows one trajectory only and is sensitive to the cooling schedule.
Applications: Job-shop scheduling, travelling salesman and routing problems, layout design.
Viva questions:
- Why accept a worse move? To escape local optima.
- What happens to P as T decreases? It falls, so worse moves become rarer.
- What is the Metropolis criterion? The probabilistic acceptance rule exp(−ΔE / T).
- What is a cooling schedule? The rule for lowering T over time.
Experiment 10 – Particle Swarm Optimisation (PSO)
Aim: To optimise continuous functions using a swarm of particles that learn from their own and the group's best experience.
Principle: Each particle has a position x and velocity v. It remembers its personal best (Pbest) and knows the swarm's global best (Gbest).
Update equations:
- Velocity: v(new) = w · v + c1 · r1 · (Pbest − x) + c2 · r2 · (Gbest − x)
- Position: x(new) = x + v(new)
where w is the inertia weight, c1 and c2 are the cognitive and social acceleration coefficients, and r1, r2 are uniform random numbers in [0,1].
Procedure:
- Initialise positions and velocities of the swarm randomly within the bounds.
- Evaluate the objective for each particle.
- Update each Pbest and the swarm Gbest.
- Update velocity and position; clamp to the variable bounds and maximum velocity.
- Repeat until the maximum iterations or convergence.
Typical parameters: swarm size 20–50, w = 0.9 decreasing to 0.4, c1 = c2 ≈ 2.
Strengths and limits: Few parameters, fast convergence and easy coding for real-valued problems; it can converge prematurely on multimodal functions.
Applications: Tuning of CNC machining parameters (speed, feed, depth of cut), controller tuning, process parameter optimisation.
Viva questions:
- What are Pbest and Gbest? The best position found by a particle and by the whole swarm.
- Role of inertia weight? It balances exploration (high w) against exploitation (low w).
- What do c1 and c2 control? Pull toward personal and social experience respectively.
- How does PSO differ from GA? PSO has no crossover or mutation; it uses velocity updates and memory.
4. Integrated Comparison and Selection Guide
4.1 Block A at a glance
Method | Compensatory? | Weights needed | Output | Key check |
|---|---|---|---|---|
SAW | Fully | Yes | Score | Normalise first |
WPM | Partly (penalises weak criteria) | Yes | Score or ratio | Avoid zeros |
AHP | Yes | Generated | Priorities | CR ≤ 0.10 |
TOPSIS | Yes | Yes | Closeness C(i) | PIS and NIS correct |
VIKOR | Controlled by v | Yes | S, R, Q | Conditions C1 and C2 |
GTMA | Yes, with interaction | Relative importance | Permanent index | Digraph correct |
ELECTRE | No (outranking) | Yes | Kernel, dominance | Thresholds |
PROMETHEE | Partly | Yes | Net flow Φ | Preference function |
4.2 Block B at a glance
Feature | GA | SA | PSO |
|---|---|---|---|
Search unit | Population | Single solution | Swarm |
Inspiration | Genetics | Metallurgical cooling | Bird flocking |
Key operators | Selection, crossover, mutation | Metropolis acceptance, cooling | Velocity and position update |
Best for | Discrete and combinatorial | Routing and scheduling | Continuous variables |
Main parameters | N, pc, pm | T0, α | w, c1, c2 |
Main risk | Premature convergence | Wrong cooling schedule | Stagnation in local optimum |
4.3 Which method should I choose?
- Need a quick, transparent screen? SAW.
- One weak attribute must disqualify? WPM.
- Weights come from experts? AHP.
- Closeness to an ideal is natural? TOPSIS (use Modified TOPSIS for clustered data).
- Stakeholders disagree and a compromise is needed? VIKOR.
- Criteria interact? GTMA.
- Many alternatives to filter first? ELECTRE.
- Smooth, gradual preferences? PROMETHEE.
- Discrete non-linear design? GA. Scheduling or routing? SA. Continuous parameter tuning? PSO.
5. Lab Record Format and Good Practice
Standard page layout for each experiment record:
- Aim
- Software and tools (Excel, MATLAB, Python)
- Theory and formulae
- Problem statement and data
- Step-by-step calculation or algorithm flowchart
- Results table and graph (e.g. convergence curve for GA, SA and PSO)
- Sensitivity or parameter study
- Conclusion
- Viva questions
Good practice and common errors:
- Tag every criterion as B or NB before normalising; the commonest error is treating cost as beneficial.
- Check that weights sum to 1.
- In AHP always report λmax, CI and CR; never use a matrix with CR > 0.10.
- In TOPSIS and VIKOR, swap best and worst for NB criteria.
- In VIKOR, smaller Q is better; test both acceptance conditions.
- In GTMA, use the permanent (all positive signs), not the determinant.
- In ELECTRE, state the thresholds you used; they decide the kernel.
- For GA, SA and PSO, fix a random seed for reproducibility, but also report results over multiple runs.
- Compare the ranks from all methods on the same data and comment on agreement (a rank correlation such as Spearman's is a good addition).
6. Rapid Revision Sheet (Exam Day)
- SAW: sum of w·r. WPM: product of r^w.
- AHP: CI = (λmax − n)/(n − 1); CR = CI/RI; accept if CR ≤ 0.10.
- TOPSIS: C = S⁻/(S⁺ + S⁻); higher is better. Modified TOPSIS: linear top-bottom scaling.
- VIKOR: minimise Q; advantage ≥ 1/(m − 1) and stability by S or R.
- GTMA: digraph → permanent matrix → permanent index.
- ELECTRE: concordance and discordance with thresholds; kernel survives.
- PROMETHEE: Φ = Φ⁺ − Φ⁻; PROMETHEE II gives a complete ranking.
- GA: selection, crossover, mutation, elitism.
- SA: accept worse with P = exp(−ΔE/T); cool by α.
- PSO: v = w·v + c1·r1·(Pbest − x) + c2·r2·(Gbest − x).
Note on the source summary: the original revision guide described SAW normalisation as "multiplicative". In standard practice SAW uses linear ratio normalisation (x/max for be